forked from pola-rs/polars
-
Notifications
You must be signed in to change notification settings - Fork 0
/
binomial.rs.html
689 lines (650 loc) · 54 KB
/
binomial.rs.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Source of the Rust file `/home/runner/.cargo/registry/src/github.com-1ecc6299db9ec823/rand_distr-0.3.0/src/binomial.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>binomial.rs - source</title><link rel="stylesheet" type="text/css" href="../../normalize.css"><link rel="stylesheet" type="text/css" href="../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../light.css" id="themeStyle"><link rel="stylesheet" type="text/css" href="../../dark.css" disabled ><link rel="stylesheet" type="text/css" href="../../ayu.css" disabled ><script id="default-settings"></script><script src="../../storage.js"></script><script src="../../crates.js"></script><noscript><link rel="stylesheet" href="../../noscript.css"></noscript><link rel="shortcut icon" href="https://www.rust-lang.org/favicon.ico"><style type="text/css">#crate-search{background-image:url("../../down-arrow.svg");}</style></head><body class="rustdoc source"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu" role="button">☰</div><a href='../../rand_distr/index.html'><div class='logo-container'><img src='https://www.rust-lang.org/logos/rust-logo-128x128-blk.png' alt='logo'></div></a></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!" aria-haspopup="menu"><img src="../../brush.svg" width="18" height="18" alt="Pick another theme!"></button><div id="theme-choices" role="menu"></div></div><nav class="sub"><form class="search-form"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" disabled autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"></div><button type="button" class="help-button">?</button>
<a id="settings-menu" href="../../settings.html"><img src="../../wheel.svg" width="18" height="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><pre class="line-numbers"><span id="1"> 1</span>
<span id="2"> 2</span>
<span id="3"> 3</span>
<span id="4"> 4</span>
<span id="5"> 5</span>
<span id="6"> 6</span>
<span id="7"> 7</span>
<span id="8"> 8</span>
<span id="9"> 9</span>
<span id="10"> 10</span>
<span id="11"> 11</span>
<span id="12"> 12</span>
<span id="13"> 13</span>
<span id="14"> 14</span>
<span id="15"> 15</span>
<span id="16"> 16</span>
<span id="17"> 17</span>
<span id="18"> 18</span>
<span id="19"> 19</span>
<span id="20"> 20</span>
<span id="21"> 21</span>
<span id="22"> 22</span>
<span id="23"> 23</span>
<span id="24"> 24</span>
<span id="25"> 25</span>
<span id="26"> 26</span>
<span id="27"> 27</span>
<span id="28"> 28</span>
<span id="29"> 29</span>
<span id="30"> 30</span>
<span id="31"> 31</span>
<span id="32"> 32</span>
<span id="33"> 33</span>
<span id="34"> 34</span>
<span id="35"> 35</span>
<span id="36"> 36</span>
<span id="37"> 37</span>
<span id="38"> 38</span>
<span id="39"> 39</span>
<span id="40"> 40</span>
<span id="41"> 41</span>
<span id="42"> 42</span>
<span id="43"> 43</span>
<span id="44"> 44</span>
<span id="45"> 45</span>
<span id="46"> 46</span>
<span id="47"> 47</span>
<span id="48"> 48</span>
<span id="49"> 49</span>
<span id="50"> 50</span>
<span id="51"> 51</span>
<span id="52"> 52</span>
<span id="53"> 53</span>
<span id="54"> 54</span>
<span id="55"> 55</span>
<span id="56"> 56</span>
<span id="57"> 57</span>
<span id="58"> 58</span>
<span id="59"> 59</span>
<span id="60"> 60</span>
<span id="61"> 61</span>
<span id="62"> 62</span>
<span id="63"> 63</span>
<span id="64"> 64</span>
<span id="65"> 65</span>
<span id="66"> 66</span>
<span id="67"> 67</span>
<span id="68"> 68</span>
<span id="69"> 69</span>
<span id="70"> 70</span>
<span id="71"> 71</span>
<span id="72"> 72</span>
<span id="73"> 73</span>
<span id="74"> 74</span>
<span id="75"> 75</span>
<span id="76"> 76</span>
<span id="77"> 77</span>
<span id="78"> 78</span>
<span id="79"> 79</span>
<span id="80"> 80</span>
<span id="81"> 81</span>
<span id="82"> 82</span>
<span id="83"> 83</span>
<span id="84"> 84</span>
<span id="85"> 85</span>
<span id="86"> 86</span>
<span id="87"> 87</span>
<span id="88"> 88</span>
<span id="89"> 89</span>
<span id="90"> 90</span>
<span id="91"> 91</span>
<span id="92"> 92</span>
<span id="93"> 93</span>
<span id="94"> 94</span>
<span id="95"> 95</span>
<span id="96"> 96</span>
<span id="97"> 97</span>
<span id="98"> 98</span>
<span id="99"> 99</span>
<span id="100">100</span>
<span id="101">101</span>
<span id="102">102</span>
<span id="103">103</span>
<span id="104">104</span>
<span id="105">105</span>
<span id="106">106</span>
<span id="107">107</span>
<span id="108">108</span>
<span id="109">109</span>
<span id="110">110</span>
<span id="111">111</span>
<span id="112">112</span>
<span id="113">113</span>
<span id="114">114</span>
<span id="115">115</span>
<span id="116">116</span>
<span id="117">117</span>
<span id="118">118</span>
<span id="119">119</span>
<span id="120">120</span>
<span id="121">121</span>
<span id="122">122</span>
<span id="123">123</span>
<span id="124">124</span>
<span id="125">125</span>
<span id="126">126</span>
<span id="127">127</span>
<span id="128">128</span>
<span id="129">129</span>
<span id="130">130</span>
<span id="131">131</span>
<span id="132">132</span>
<span id="133">133</span>
<span id="134">134</span>
<span id="135">135</span>
<span id="136">136</span>
<span id="137">137</span>
<span id="138">138</span>
<span id="139">139</span>
<span id="140">140</span>
<span id="141">141</span>
<span id="142">142</span>
<span id="143">143</span>
<span id="144">144</span>
<span id="145">145</span>
<span id="146">146</span>
<span id="147">147</span>
<span id="148">148</span>
<span id="149">149</span>
<span id="150">150</span>
<span id="151">151</span>
<span id="152">152</span>
<span id="153">153</span>
<span id="154">154</span>
<span id="155">155</span>
<span id="156">156</span>
<span id="157">157</span>
<span id="158">158</span>
<span id="159">159</span>
<span id="160">160</span>
<span id="161">161</span>
<span id="162">162</span>
<span id="163">163</span>
<span id="164">164</span>
<span id="165">165</span>
<span id="166">166</span>
<span id="167">167</span>
<span id="168">168</span>
<span id="169">169</span>
<span id="170">170</span>
<span id="171">171</span>
<span id="172">172</span>
<span id="173">173</span>
<span id="174">174</span>
<span id="175">175</span>
<span id="176">176</span>
<span id="177">177</span>
<span id="178">178</span>
<span id="179">179</span>
<span id="180">180</span>
<span id="181">181</span>
<span id="182">182</span>
<span id="183">183</span>
<span id="184">184</span>
<span id="185">185</span>
<span id="186">186</span>
<span id="187">187</span>
<span id="188">188</span>
<span id="189">189</span>
<span id="190">190</span>
<span id="191">191</span>
<span id="192">192</span>
<span id="193">193</span>
<span id="194">194</span>
<span id="195">195</span>
<span id="196">196</span>
<span id="197">197</span>
<span id="198">198</span>
<span id="199">199</span>
<span id="200">200</span>
<span id="201">201</span>
<span id="202">202</span>
<span id="203">203</span>
<span id="204">204</span>
<span id="205">205</span>
<span id="206">206</span>
<span id="207">207</span>
<span id="208">208</span>
<span id="209">209</span>
<span id="210">210</span>
<span id="211">211</span>
<span id="212">212</span>
<span id="213">213</span>
<span id="214">214</span>
<span id="215">215</span>
<span id="216">216</span>
<span id="217">217</span>
<span id="218">218</span>
<span id="219">219</span>
<span id="220">220</span>
<span id="221">221</span>
<span id="222">222</span>
<span id="223">223</span>
<span id="224">224</span>
<span id="225">225</span>
<span id="226">226</span>
<span id="227">227</span>
<span id="228">228</span>
<span id="229">229</span>
<span id="230">230</span>
<span id="231">231</span>
<span id="232">232</span>
<span id="233">233</span>
<span id="234">234</span>
<span id="235">235</span>
<span id="236">236</span>
<span id="237">237</span>
<span id="238">238</span>
<span id="239">239</span>
<span id="240">240</span>
<span id="241">241</span>
<span id="242">242</span>
<span id="243">243</span>
<span id="244">244</span>
<span id="245">245</span>
<span id="246">246</span>
<span id="247">247</span>
<span id="248">248</span>
<span id="249">249</span>
<span id="250">250</span>
<span id="251">251</span>
<span id="252">252</span>
<span id="253">253</span>
<span id="254">254</span>
<span id="255">255</span>
<span id="256">256</span>
<span id="257">257</span>
<span id="258">258</span>
<span id="259">259</span>
<span id="260">260</span>
<span id="261">261</span>
<span id="262">262</span>
<span id="263">263</span>
<span id="264">264</span>
<span id="265">265</span>
<span id="266">266</span>
<span id="267">267</span>
<span id="268">268</span>
<span id="269">269</span>
<span id="270">270</span>
<span id="271">271</span>
<span id="272">272</span>
<span id="273">273</span>
<span id="274">274</span>
<span id="275">275</span>
<span id="276">276</span>
<span id="277">277</span>
<span id="278">278</span>
<span id="279">279</span>
<span id="280">280</span>
<span id="281">281</span>
<span id="282">282</span>
<span id="283">283</span>
<span id="284">284</span>
<span id="285">285</span>
<span id="286">286</span>
<span id="287">287</span>
<span id="288">288</span>
<span id="289">289</span>
<span id="290">290</span>
<span id="291">291</span>
<span id="292">292</span>
<span id="293">293</span>
<span id="294">294</span>
<span id="295">295</span>
<span id="296">296</span>
<span id="297">297</span>
<span id="298">298</span>
<span id="299">299</span>
<span id="300">300</span>
<span id="301">301</span>
<span id="302">302</span>
<span id="303">303</span>
<span id="304">304</span>
<span id="305">305</span>
<span id="306">306</span>
<span id="307">307</span>
<span id="308">308</span>
<span id="309">309</span>
<span id="310">310</span>
<span id="311">311</span>
<span id="312">312</span>
<span id="313">313</span>
<span id="314">314</span>
<span id="315">315</span>
<span id="316">316</span>
<span id="317">317</span>
<span id="318">318</span>
<span id="319">319</span>
<span id="320">320</span>
<span id="321">321</span>
<span id="322">322</span>
<span id="323">323</span>
<span id="324">324</span>
<span id="325">325</span>
<span id="326">326</span>
<span id="327">327</span>
<span id="328">328</span>
<span id="329">329</span>
<span id="330">330</span>
<span id="331">331</span>
<span id="332">332</span>
<span id="333">333</span>
<span id="334">334</span>
<span id="335">335</span>
<span id="336">336</span>
<span id="337">337</span>
<span id="338">338</span>
<span id="339">339</span>
<span id="340">340</span>
<span id="341">341</span>
<span id="342">342</span>
</pre><div class="example-wrap"><pre class="rust ">
<span class="comment">// Copyright 2018 Developers of the Rand project.</span>
<span class="comment">// Copyright 2016-2017 The Rust Project Developers.</span>
<span class="comment">//</span>
<span class="comment">// Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or</span>
<span class="comment">// https://www.apache.org/licenses/LICENSE-2.0> or the MIT license</span>
<span class="comment">// <LICENSE-MIT or https://opensource.org/licenses/MIT>, at your</span>
<span class="comment">// option. This file may not be copied, modified, or distributed</span>
<span class="comment">// except according to those terms.</span>
<span class="doccomment">//! The binomial distribution.</span>
<span class="kw">use</span> <span class="kw">crate</span>::{<span class="ident">Distribution</span>, <span class="ident">Uniform</span>};
<span class="kw">use</span> <span class="ident">rand</span>::<span class="ident">Rng</span>;
<span class="kw">use</span> <span class="ident">core</span>::<span class="ident">fmt</span>;
<span class="doccomment">/// The binomial distribution `Binomial(n, p)`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// This distribution has density function:</span>
<span class="doccomment">/// `f(k) = n!/(k! (n-k)!) p^k (1-p)^(n-k)` for `k >= 0`.</span>
<span class="doccomment">///</span>
<span class="doccomment">/// # Example</span>
<span class="doccomment">///</span>
<span class="doccomment">/// ```</span>
<span class="doccomment">/// use rand_distr::{Binomial, Distribution};</span>
<span class="doccomment">///</span>
<span class="doccomment">/// let bin = Binomial::new(20, 0.3).unwrap();</span>
<span class="doccomment">/// let v = bin.sample(&mut rand::thread_rng());</span>
<span class="doccomment">/// println!("{} is from a binomial distribution", v);</span>
<span class="doccomment">/// ```</span>
<span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>)]</span>
<span class="kw">pub</span> <span class="kw">struct</span> <span class="ident">Binomial</span> {
<span class="doccomment">/// Number of trials.</span>
<span class="ident">n</span>: <span class="ident">u64</span>,
<span class="doccomment">/// Probability of success.</span>
<span class="ident">p</span>: <span class="ident">f64</span>,
}
<span class="doccomment">/// Error type returned from `Binomial::new`.</span>
<span class="attribute">#[<span class="ident">derive</span>(<span class="ident">Clone</span>, <span class="ident">Copy</span>, <span class="ident">Debug</span>, <span class="ident">PartialEq</span>, <span class="ident">Eq</span>)]</span>
<span class="kw">pub</span> <span class="kw">enum</span> <span class="ident">Error</span> {
<span class="doccomment">/// `p < 0` or `nan`.</span>
<span class="ident">ProbabilityTooSmall</span>,
<span class="doccomment">/// `p > 1`.</span>
<span class="ident">ProbabilityTooLarge</span>,
}
<span class="kw">impl</span> <span class="ident">fmt</span>::<span class="ident">Display</span> <span class="kw">for</span> <span class="ident">Error</span> {
<span class="kw">fn</span> <span class="ident">fmt</span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">f</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">fmt</span>::<span class="ident">Formatter</span><span class="op"><</span><span class="lifetime">'_</span><span class="op">></span>) <span class="op">-</span><span class="op">></span> <span class="ident">fmt</span>::<span class="prelude-ty">Result</span> {
<span class="ident">f</span>.<span class="ident">write_str</span>(<span class="kw">match</span> <span class="self">self</span> {
<span class="ident">Error</span>::<span class="ident">ProbabilityTooSmall</span> <span class="op">=</span><span class="op">></span> <span class="string">"p < 0 or is NaN in binomial distribution"</span>,
<span class="ident">Error</span>::<span class="ident">ProbabilityTooLarge</span> <span class="op">=</span><span class="op">></span> <span class="string">"p > 1 in binomial distribution"</span>,
})
}
}
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">"std"</span>)]</span>
<span class="kw">impl</span> <span class="ident">std</span>::<span class="ident">error</span>::<span class="ident">Error</span> <span class="kw">for</span> <span class="ident">Error</span> {}
<span class="kw">impl</span> <span class="ident">Binomial</span> {
<span class="doccomment">/// Construct a new `Binomial` with the given shape parameters `n` (number</span>
<span class="doccomment">/// of trials) and `p` (probability of success).</span>
<span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">n</span>: <span class="ident">u64</span>, <span class="ident">p</span>: <span class="ident">f64</span>) <span class="op">-</span><span class="op">></span> <span class="prelude-ty">Result</span><span class="op"><</span><span class="ident">Binomial</span>, <span class="ident">Error</span><span class="op">></span> {
<span class="kw">if</span> <span class="op">!</span>(<span class="ident">p</span> <span class="op">></span><span class="op">=</span> <span class="number">0.0</span>) {
<span class="kw">return</span> <span class="prelude-val">Err</span>(<span class="ident">Error</span>::<span class="ident">ProbabilityTooSmall</span>);
}
<span class="kw">if</span> <span class="op">!</span>(<span class="ident">p</span> <span class="op"><</span><span class="op">=</span> <span class="number">1.0</span>) {
<span class="kw">return</span> <span class="prelude-val">Err</span>(<span class="ident">Error</span>::<span class="ident">ProbabilityTooLarge</span>);
}
<span class="prelude-val">Ok</span>(<span class="ident">Binomial</span> { <span class="ident">n</span>, <span class="ident">p</span> })
}
}
<span class="doccomment">/// Convert a `f64` to an `i64`, panicing on overflow.</span>
<span class="comment">// In the future (Rust 1.34), this might be replaced with `TryFrom`.</span>
<span class="kw">fn</span> <span class="ident">f64_to_i64</span>(<span class="ident">x</span>: <span class="ident">f64</span>) <span class="op">-</span><span class="op">></span> <span class="ident">i64</span> {
<span class="macro">assert</span><span class="macro">!</span>(<span class="ident">x</span> <span class="op"><</span> (<span class="ident">core</span>::<span class="ident">i64</span>::<span class="ident">MAX</span> <span class="kw">as</span> <span class="ident">f64</span>));
<span class="ident">x</span> <span class="kw">as</span> <span class="ident">i64</span>
}
<span class="kw">impl</span> <span class="ident">Distribution</span><span class="op"><</span><span class="ident">u64</span><span class="op">></span> <span class="kw">for</span> <span class="ident">Binomial</span> {
<span class="attribute">#[<span class="ident">allow</span>(<span class="ident">clippy</span>::<span class="ident">many_single_char_names</span>)]</span> <span class="comment">// Same names as in the reference.</span>
<span class="kw">fn</span> <span class="ident">sample</span><span class="op"><</span><span class="ident">R</span>: <span class="ident">Rng</span> <span class="op">+</span> <span class="question-mark">?</span><span class="ident">Sized</span><span class="op">></span>(<span class="kw-2">&</span><span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">R</span>) <span class="op">-</span><span class="op">></span> <span class="ident">u64</span> {
<span class="comment">// Handle these values directly.</span>
<span class="kw">if</span> <span class="self">self</span>.<span class="ident">p</span> <span class="op">=</span><span class="op">=</span> <span class="number">0.0</span> {
<span class="kw">return</span> <span class="number">0</span>;
} <span class="kw">else</span> <span class="kw">if</span> <span class="self">self</span>.<span class="ident">p</span> <span class="op">=</span><span class="op">=</span> <span class="number">1.0</span> {
<span class="kw">return</span> <span class="self">self</span>.<span class="ident">n</span>;
}
<span class="comment">// The binomial distribution is symmetrical with respect to p -> 1-p,</span>
<span class="comment">// k -> n-k switch p so that it is less than 0.5 - this allows for lower</span>
<span class="comment">// expected values we will just invert the result at the end</span>
<span class="kw">let</span> <span class="ident">p</span> <span class="op">=</span> <span class="kw">if</span> <span class="self">self</span>.<span class="ident">p</span> <span class="op"><</span><span class="op">=</span> <span class="number">0.5</span> { <span class="self">self</span>.<span class="ident">p</span> } <span class="kw">else</span> { <span class="number">1.0</span> <span class="op">-</span> <span class="self">self</span>.<span class="ident">p</span> };
<span class="kw">let</span> <span class="ident">result</span>;
<span class="kw">let</span> <span class="ident">q</span> <span class="op">=</span> <span class="number">1.</span> <span class="op">-</span> <span class="ident">p</span>;
<span class="comment">// For small n * min(p, 1 - p), the BINV algorithm based on the inverse</span>
<span class="comment">// transformation of the binomial distribution is efficient. Otherwise,</span>
<span class="comment">// the BTPE algorithm is used.</span>
<span class="comment">//</span>
<span class="comment">// Voratas Kachitvichyanukul and Bruce W. Schmeiser. 1988. Binomial</span>
<span class="comment">// random variate generation. Commun. ACM 31, 2 (February 1988),</span>
<span class="comment">// 216-222. http://dx.doi.org/10.1145/42372.42381</span>
<span class="comment">// Threshold for prefering the BINV algorithm. The paper suggests 10,</span>
<span class="comment">// Ranlib uses 30, and GSL uses 14.</span>
<span class="kw">const</span> <span class="ident">BINV_THRESHOLD</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="number">10.</span>;
<span class="kw">if</span> (<span class="self">self</span>.<span class="ident">n</span> <span class="kw">as</span> <span class="ident">f64</span>) <span class="op">*</span> <span class="ident">p</span> <span class="op"><</span> <span class="ident">BINV_THRESHOLD</span> <span class="op">&&</span> <span class="self">self</span>.<span class="ident">n</span> <span class="op"><</span><span class="op">=</span> (<span class="ident">core</span>::<span class="ident">i32</span>::<span class="ident">MAX</span> <span class="kw">as</span> <span class="ident">u64</span>) {
<span class="comment">// Use the BINV algorithm.</span>
<span class="kw">let</span> <span class="ident">s</span> <span class="op">=</span> <span class="ident">p</span> <span class="op">/</span> <span class="ident">q</span>;
<span class="kw">let</span> <span class="ident">a</span> <span class="op">=</span> ((<span class="self">self</span>.<span class="ident">n</span> <span class="op">+</span> <span class="number">1</span>) <span class="kw">as</span> <span class="ident">f64</span>) <span class="op">*</span> <span class="ident">s</span>;
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">r</span> <span class="op">=</span> <span class="ident">q</span>.<span class="ident">powi</span>(<span class="self">self</span>.<span class="ident">n</span> <span class="kw">as</span> <span class="ident">i32</span>);
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">u</span>: <span class="ident">f64</span> <span class="op">=</span> <span class="ident">rng</span>.<span class="ident">gen</span>();
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">x</span> <span class="op">=</span> <span class="number">0</span>;
<span class="kw">while</span> <span class="ident">u</span> <span class="op">></span> <span class="ident">r</span> <span class="kw">as</span> <span class="ident">f64</span> {
<span class="ident">u</span> <span class="op">-</span><span class="op">=</span> <span class="ident">r</span>;
<span class="ident">x</span> <span class="op">+</span><span class="op">=</span> <span class="number">1</span>;
<span class="ident">r</span> <span class="kw-2">*</span><span class="op">=</span> <span class="ident">a</span> <span class="op">/</span> (<span class="ident">x</span> <span class="kw">as</span> <span class="ident">f64</span>) <span class="op">-</span> <span class="ident">s</span>;
}
<span class="ident">result</span> <span class="op">=</span> <span class="ident">x</span>;
} <span class="kw">else</span> {
<span class="comment">// Use the BTPE algorithm.</span>
<span class="comment">// Threshold for using the squeeze algorithm. This can be freely</span>
<span class="comment">// chosen based on performance. Ranlib and GSL use 20.</span>
<span class="kw">const</span> <span class="ident">SQUEEZE_THRESHOLD</span>: <span class="ident">i64</span> <span class="op">=</span> <span class="number">20</span>;
<span class="comment">// Step 0: Calculate constants as functions of `n` and `p`.</span>
<span class="kw">let</span> <span class="ident">n</span> <span class="op">=</span> <span class="self">self</span>.<span class="ident">n</span> <span class="kw">as</span> <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">np</span> <span class="op">=</span> <span class="ident">n</span> <span class="op">*</span> <span class="ident">p</span>;
<span class="kw">let</span> <span class="ident">npq</span> <span class="op">=</span> <span class="ident">np</span> <span class="op">*</span> <span class="ident">q</span>;
<span class="kw">let</span> <span class="ident">f_m</span> <span class="op">=</span> <span class="ident">np</span> <span class="op">+</span> <span class="ident">p</span>;
<span class="kw">let</span> <span class="ident">m</span> <span class="op">=</span> <span class="ident">f64_to_i64</span>(<span class="ident">f_m</span>);
<span class="comment">// radius of triangle region, since height=1 also area of region</span>
<span class="kw">let</span> <span class="ident">p1</span> <span class="op">=</span> (<span class="number">2.195</span> <span class="op">*</span> <span class="ident">npq</span>.<span class="ident">sqrt</span>() <span class="op">-</span> <span class="number">4.6</span> <span class="op">*</span> <span class="ident">q</span>).<span class="ident">floor</span>() <span class="op">+</span> <span class="number">0.5</span>;
<span class="comment">// tip of triangle</span>
<span class="kw">let</span> <span class="ident">x_m</span> <span class="op">=</span> (<span class="ident">m</span> <span class="kw">as</span> <span class="ident">f64</span>) <span class="op">+</span> <span class="number">0.5</span>;
<span class="comment">// left edge of triangle</span>
<span class="kw">let</span> <span class="ident">x_l</span> <span class="op">=</span> <span class="ident">x_m</span> <span class="op">-</span> <span class="ident">p1</span>;
<span class="comment">// right edge of triangle</span>
<span class="kw">let</span> <span class="ident">x_r</span> <span class="op">=</span> <span class="ident">x_m</span> <span class="op">+</span> <span class="ident">p1</span>;
<span class="kw">let</span> <span class="ident">c</span> <span class="op">=</span> <span class="number">0.134</span> <span class="op">+</span> <span class="number">20.5</span> <span class="op">/</span> (<span class="number">15.3</span> <span class="op">+</span> (<span class="ident">m</span> <span class="kw">as</span> <span class="ident">f64</span>));
<span class="comment">// p1 + area of parallelogram region</span>
<span class="kw">let</span> <span class="ident">p2</span> <span class="op">=</span> <span class="ident">p1</span> <span class="op">*</span> (<span class="number">1.</span> <span class="op">+</span> <span class="number">2.</span> <span class="op">*</span> <span class="ident">c</span>);
<span class="kw">fn</span> <span class="ident">lambda</span>(<span class="ident">a</span>: <span class="ident">f64</span>) <span class="op">-</span><span class="op">></span> <span class="ident">f64</span> {
<span class="ident">a</span> <span class="op">*</span> (<span class="number">1.</span> <span class="op">+</span> <span class="number">0.5</span> <span class="op">*</span> <span class="ident">a</span>)
}
<span class="kw">let</span> <span class="ident">lambda_l</span> <span class="op">=</span> <span class="ident">lambda</span>((<span class="ident">f_m</span> <span class="op">-</span> <span class="ident">x_l</span>) <span class="op">/</span> (<span class="ident">f_m</span> <span class="op">-</span> <span class="ident">x_l</span> <span class="op">*</span> <span class="ident">p</span>));
<span class="kw">let</span> <span class="ident">lambda_r</span> <span class="op">=</span> <span class="ident">lambda</span>((<span class="ident">x_r</span> <span class="op">-</span> <span class="ident">f_m</span>) <span class="op">/</span> (<span class="ident">x_r</span> <span class="op">*</span> <span class="ident">q</span>));
<span class="comment">// p1 + area of left tail</span>
<span class="kw">let</span> <span class="ident">p3</span> <span class="op">=</span> <span class="ident">p2</span> <span class="op">+</span> <span class="ident">c</span> <span class="op">/</span> <span class="ident">lambda_l</span>;
<span class="comment">// p1 + area of right tail</span>
<span class="kw">let</span> <span class="ident">p4</span> <span class="op">=</span> <span class="ident">p3</span> <span class="op">+</span> <span class="ident">c</span> <span class="op">/</span> <span class="ident">lambda_r</span>;
<span class="comment">// return value</span>
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">y</span>: <span class="ident">i64</span>;
<span class="kw">let</span> <span class="ident">gen_u</span> <span class="op">=</span> <span class="ident">Uniform</span>::<span class="ident">new</span>(<span class="number">0.</span>, <span class="ident">p4</span>);
<span class="kw">let</span> <span class="ident">gen_v</span> <span class="op">=</span> <span class="ident">Uniform</span>::<span class="ident">new</span>(<span class="number">0.</span>, <span class="number">1.</span>);
<span class="kw">loop</span> {
<span class="comment">// Step 1: Generate `u` for selecting the region. If region 1 is</span>
<span class="comment">// selected, generate a triangularly distributed variate.</span>
<span class="kw">let</span> <span class="ident">u</span> <span class="op">=</span> <span class="ident">gen_u</span>.<span class="ident">sample</span>(<span class="ident">rng</span>);
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">v</span> <span class="op">=</span> <span class="ident">gen_v</span>.<span class="ident">sample</span>(<span class="ident">rng</span>);
<span class="kw">if</span> <span class="op">!</span>(<span class="ident">u</span> <span class="op">></span> <span class="ident">p1</span>) {
<span class="ident">y</span> <span class="op">=</span> <span class="ident">f64_to_i64</span>(<span class="ident">x_m</span> <span class="op">-</span> <span class="ident">p1</span> <span class="op">*</span> <span class="ident">v</span> <span class="op">+</span> <span class="ident">u</span>);
<span class="kw">break</span>;
}
<span class="kw">if</span> <span class="op">!</span>(<span class="ident">u</span> <span class="op">></span> <span class="ident">p2</span>) {
<span class="comment">// Step 2: Region 2, parallelograms. Check if region 2 is</span>
<span class="comment">// used. If so, generate `y`.</span>
<span class="kw">let</span> <span class="ident">x</span> <span class="op">=</span> <span class="ident">x_l</span> <span class="op">+</span> (<span class="ident">u</span> <span class="op">-</span> <span class="ident">p1</span>) <span class="op">/</span> <span class="ident">c</span>;
<span class="ident">v</span> <span class="op">=</span> <span class="ident">v</span> <span class="op">*</span> <span class="ident">c</span> <span class="op">+</span> <span class="number">1.0</span> <span class="op">-</span> (<span class="ident">x</span> <span class="op">-</span> <span class="ident">x_m</span>).<span class="ident">abs</span>() <span class="op">/</span> <span class="ident">p1</span>;
<span class="kw">if</span> <span class="ident">v</span> <span class="op">></span> <span class="number">1.</span> {
<span class="kw">continue</span>;
} <span class="kw">else</span> {
<span class="ident">y</span> <span class="op">=</span> <span class="ident">f64_to_i64</span>(<span class="ident">x</span>);
}
} <span class="kw">else</span> <span class="kw">if</span> <span class="op">!</span>(<span class="ident">u</span> <span class="op">></span> <span class="ident">p3</span>) {
<span class="comment">// Step 3: Region 3, left exponential tail.</span>
<span class="ident">y</span> <span class="op">=</span> <span class="ident">f64_to_i64</span>(<span class="ident">x_l</span> <span class="op">+</span> <span class="ident">v</span>.<span class="ident">ln</span>() <span class="op">/</span> <span class="ident">lambda_l</span>);
<span class="kw">if</span> <span class="ident">y</span> <span class="op"><</span> <span class="number">0</span> {
<span class="kw">continue</span>;
} <span class="kw">else</span> {
<span class="ident">v</span> <span class="kw-2">*</span><span class="op">=</span> (<span class="ident">u</span> <span class="op">-</span> <span class="ident">p2</span>) <span class="op">*</span> <span class="ident">lambda_l</span>;
}
} <span class="kw">else</span> {
<span class="comment">// Step 4: Region 4, right exponential tail.</span>
<span class="ident">y</span> <span class="op">=</span> <span class="ident">f64_to_i64</span>(<span class="ident">x_r</span> <span class="op">-</span> <span class="ident">v</span>.<span class="ident">ln</span>() <span class="op">/</span> <span class="ident">lambda_r</span>);
<span class="kw">if</span> <span class="ident">y</span> <span class="op">></span> <span class="number">0</span> <span class="op">&&</span> (<span class="ident">y</span> <span class="kw">as</span> <span class="ident">u64</span>) <span class="op">></span> <span class="self">self</span>.<span class="ident">n</span> {
<span class="kw">continue</span>;
} <span class="kw">else</span> {
<span class="ident">v</span> <span class="kw-2">*</span><span class="op">=</span> (<span class="ident">u</span> <span class="op">-</span> <span class="ident">p3</span>) <span class="op">*</span> <span class="ident">lambda_r</span>;
}
}
<span class="comment">// Step 5: Acceptance/rejection comparison.</span>
<span class="comment">// Step 5.0: Test for appropriate method of evaluating f(y).</span>
<span class="kw">let</span> <span class="ident">k</span> <span class="op">=</span> (<span class="ident">y</span> <span class="op">-</span> <span class="ident">m</span>).<span class="ident">abs</span>();
<span class="kw">if</span> <span class="op">!</span>(<span class="ident">k</span> <span class="op">></span> <span class="ident">SQUEEZE_THRESHOLD</span> <span class="op">&&</span> (<span class="ident">k</span> <span class="kw">as</span> <span class="ident">f64</span>) <span class="op"><</span> <span class="number">0.5</span> <span class="op">*</span> <span class="ident">npq</span> <span class="op">-</span> <span class="number">1.</span>) {
<span class="comment">// Step 5.1: Evaluate f(y) via the recursive relationship. Start the</span>
<span class="comment">// search from the mode.</span>
<span class="kw">let</span> <span class="ident">s</span> <span class="op">=</span> <span class="ident">p</span> <span class="op">/</span> <span class="ident">q</span>;
<span class="kw">let</span> <span class="ident">a</span> <span class="op">=</span> <span class="ident">s</span> <span class="op">*</span> (<span class="ident">n</span> <span class="op">+</span> <span class="number">1.</span>);
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">f</span> <span class="op">=</span> <span class="number">1.0</span>;
<span class="kw">if</span> <span class="ident">m</span> <span class="op"><</span> <span class="ident">y</span> {
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">i</span> <span class="op">=</span> <span class="ident">m</span>;
<span class="kw">loop</span> {
<span class="ident">i</span> <span class="op">+</span><span class="op">=</span> <span class="number">1</span>;
<span class="ident">f</span> <span class="kw-2">*</span><span class="op">=</span> <span class="ident">a</span> <span class="op">/</span> (<span class="ident">i</span> <span class="kw">as</span> <span class="ident">f64</span>) <span class="op">-</span> <span class="ident">s</span>;
<span class="kw">if</span> <span class="ident">i</span> <span class="op">=</span><span class="op">=</span> <span class="ident">y</span> {
<span class="kw">break</span>;
}
}
} <span class="kw">else</span> <span class="kw">if</span> <span class="ident">m</span> <span class="op">></span> <span class="ident">y</span> {
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">i</span> <span class="op">=</span> <span class="ident">y</span>;
<span class="kw">loop</span> {
<span class="ident">i</span> <span class="op">+</span><span class="op">=</span> <span class="number">1</span>;
<span class="ident">f</span> <span class="op">/</span><span class="op">=</span> <span class="ident">a</span> <span class="op">/</span> (<span class="ident">i</span> <span class="kw">as</span> <span class="ident">f64</span>) <span class="op">-</span> <span class="ident">s</span>;
<span class="kw">if</span> <span class="ident">i</span> <span class="op">=</span><span class="op">=</span> <span class="ident">m</span> {
<span class="kw">break</span>;
}
}
}
<span class="kw">if</span> <span class="ident">v</span> <span class="op">></span> <span class="ident">f</span> {
<span class="kw">continue</span>;
} <span class="kw">else</span> {
<span class="kw">break</span>;
}
}
<span class="comment">// Step 5.2: Squeezing. Check the value of ln(v) againts upper and</span>
<span class="comment">// lower bound of ln(f(y)).</span>
<span class="kw">let</span> <span class="ident">k</span> <span class="op">=</span> <span class="ident">k</span> <span class="kw">as</span> <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">rho</span> <span class="op">=</span> (<span class="ident">k</span> <span class="op">/</span> <span class="ident">npq</span>) <span class="op">*</span> ((<span class="ident">k</span> <span class="op">*</span> (<span class="ident">k</span> <span class="op">/</span> <span class="number">3.</span> <span class="op">+</span> <span class="number">0.625</span>) <span class="op">+</span> <span class="number">1.</span> <span class="op">/</span> <span class="number">6.</span>) <span class="op">/</span> <span class="ident">npq</span> <span class="op">+</span> <span class="number">0.5</span>);
<span class="kw">let</span> <span class="ident">t</span> <span class="op">=</span> <span class="op">-</span><span class="number">0.5</span> <span class="op">*</span> <span class="ident">k</span> <span class="op">*</span> <span class="ident">k</span> <span class="op">/</span> <span class="ident">npq</span>;
<span class="kw">let</span> <span class="ident">alpha</span> <span class="op">=</span> <span class="ident">v</span>.<span class="ident">ln</span>();
<span class="kw">if</span> <span class="ident">alpha</span> <span class="op"><</span> <span class="ident">t</span> <span class="op">-</span> <span class="ident">rho</span> {
<span class="kw">break</span>;
}
<span class="kw">if</span> <span class="ident">alpha</span> <span class="op">></span> <span class="ident">t</span> <span class="op">+</span> <span class="ident">rho</span> {
<span class="kw">continue</span>;
}
<span class="comment">// Step 5.3: Final acceptance/rejection test.</span>
<span class="kw">let</span> <span class="ident">x1</span> <span class="op">=</span> (<span class="ident">y</span> <span class="op">+</span> <span class="number">1</span>) <span class="kw">as</span> <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">f1</span> <span class="op">=</span> (<span class="ident">m</span> <span class="op">+</span> <span class="number">1</span>) <span class="kw">as</span> <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">z</span> <span class="op">=</span> (<span class="ident">f64_to_i64</span>(<span class="ident">n</span>) <span class="op">+</span> <span class="number">1</span> <span class="op">-</span> <span class="ident">m</span>) <span class="kw">as</span> <span class="ident">f64</span>;
<span class="kw">let</span> <span class="ident">w</span> <span class="op">=</span> (<span class="ident">f64_to_i64</span>(<span class="ident">n</span>) <span class="op">-</span> <span class="ident">y</span> <span class="op">+</span> <span class="number">1</span>) <span class="kw">as</span> <span class="ident">f64</span>;
<span class="kw">fn</span> <span class="ident">stirling</span>(<span class="ident">a</span>: <span class="ident">f64</span>) <span class="op">-</span><span class="op">></span> <span class="ident">f64</span> {
<span class="kw">let</span> <span class="ident">a2</span> <span class="op">=</span> <span class="ident">a</span> <span class="op">*</span> <span class="ident">a</span>;
(<span class="number">13860.</span> <span class="op">-</span> (<span class="number">462.</span> <span class="op">-</span> (<span class="number">132.</span> <span class="op">-</span> (<span class="number">99.</span> <span class="op">-</span> <span class="number">140.</span> <span class="op">/</span> <span class="ident">a2</span>) <span class="op">/</span> <span class="ident">a2</span>) <span class="op">/</span> <span class="ident">a2</span>) <span class="op">/</span> <span class="ident">a2</span>) <span class="op">/</span> <span class="ident">a</span> <span class="op">/</span> <span class="number">166320.</span>
}
<span class="kw">if</span> <span class="ident">alpha</span>
<span class="op">></span> <span class="ident">x_m</span> <span class="op">*</span> (<span class="ident">f1</span> <span class="op">/</span> <span class="ident">x1</span>).<span class="ident">ln</span>()
<span class="op">+</span> (<span class="ident">n</span> <span class="op">-</span> (<span class="ident">m</span> <span class="kw">as</span> <span class="ident">f64</span>) <span class="op">+</span> <span class="number">0.5</span>) <span class="op">*</span> (<span class="ident">z</span> <span class="op">/</span> <span class="ident">w</span>).<span class="ident">ln</span>()
<span class="op">+</span> ((<span class="ident">y</span> <span class="op">-</span> <span class="ident">m</span>) <span class="kw">as</span> <span class="ident">f64</span>) <span class="op">*</span> (<span class="ident">w</span> <span class="op">*</span> <span class="ident">p</span> <span class="op">/</span> (<span class="ident">x1</span> <span class="op">*</span> <span class="ident">q</span>)).<span class="ident">ln</span>()
<span class="comment">// We use the signs from the GSL implementation, which are</span>
<span class="comment">// different than the ones in the reference. According to</span>
<span class="comment">// the GSL authors, the new signs were verified to be</span>
<span class="comment">// correct by one of the original designers of the</span>
<span class="comment">// algorithm.</span>
<span class="op">+</span> <span class="ident">stirling</span>(<span class="ident">f1</span>)
<span class="op">+</span> <span class="ident">stirling</span>(<span class="ident">z</span>)
<span class="op">-</span> <span class="ident">stirling</span>(<span class="ident">x1</span>)
<span class="op">-</span> <span class="ident">stirling</span>(<span class="ident">w</span>)
{
<span class="kw">continue</span>;
}
<span class="kw">break</span>;
}
<span class="macro">assert</span><span class="macro">!</span>(<span class="ident">y</span> <span class="op">></span><span class="op">=</span> <span class="number">0</span>);
<span class="ident">result</span> <span class="op">=</span> <span class="ident">y</span> <span class="kw">as</span> <span class="ident">u64</span>;
}
<span class="comment">// Invert the result for p < 0.5.</span>
<span class="kw">if</span> <span class="ident">p</span> <span class="op">!</span><span class="op">=</span> <span class="self">self</span>.<span class="ident">p</span> {
<span class="self">self</span>.<span class="ident">n</span> <span class="op">-</span> <span class="ident">result</span>
} <span class="kw">else</span> {
<span class="ident">result</span>
}
}
}
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">test</span>)]</span>
<span class="kw">mod</span> <span class="ident">test</span> {
<span class="kw">use</span> <span class="kw">super</span>::<span class="ident">Binomial</span>;
<span class="kw">use</span> <span class="kw">crate</span>::<span class="ident">Distribution</span>;
<span class="kw">use</span> <span class="ident">rand</span>::<span class="ident">Rng</span>;
<span class="kw">fn</span> <span class="ident">test_binomial_mean_and_variance</span><span class="op"><</span><span class="ident">R</span>: <span class="ident">Rng</span><span class="op">></span>(<span class="ident">n</span>: <span class="ident">u64</span>, <span class="ident">p</span>: <span class="ident">f64</span>, <span class="ident">rng</span>: <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">R</span>) {
<span class="kw">let</span> <span class="ident">binomial</span> <span class="op">=</span> <span class="ident">Binomial</span>::<span class="ident">new</span>(<span class="ident">n</span>, <span class="ident">p</span>).<span class="ident">unwrap</span>();
<span class="kw">let</span> <span class="ident">expected_mean</span> <span class="op">=</span> <span class="ident">n</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">*</span> <span class="ident">p</span>;
<span class="kw">let</span> <span class="ident">expected_variance</span> <span class="op">=</span> <span class="ident">n</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">*</span> <span class="ident">p</span> <span class="op">*</span> (<span class="number">1.0</span> <span class="op">-</span> <span class="ident">p</span>);
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">results</span> <span class="op">=</span> [<span class="number">0.0</span>; <span class="number">1000</span>];
<span class="kw">for</span> <span class="ident">i</span> <span class="kw">in</span> <span class="ident">results</span>.<span class="ident">iter_mut</span>() {
<span class="kw-2">*</span><span class="ident">i</span> <span class="op">=</span> <span class="ident">binomial</span>.<span class="ident">sample</span>(<span class="ident">rng</span>) <span class="kw">as</span> <span class="ident">f64</span>;
}
<span class="kw">let</span> <span class="ident">mean</span> <span class="op">=</span> <span class="ident">results</span>.<span class="ident">iter</span>().<span class="ident">sum</span>::<span class="op"><</span><span class="ident">f64</span><span class="op">></span>() <span class="op">/</span> <span class="ident">results</span>.<span class="ident">len</span>() <span class="kw">as</span> <span class="ident">f64</span>;
<span class="macro">assert</span><span class="macro">!</span>((<span class="ident">mean</span> <span class="kw">as</span> <span class="ident">f64</span> <span class="op">-</span> <span class="ident">expected_mean</span>).<span class="ident">abs</span>() <span class="op"><</span> <span class="ident">expected_mean</span> <span class="op">/</span> <span class="number">50.0</span>);
<span class="kw">let</span> <span class="ident">variance</span> <span class="op">=</span>
<span class="ident">results</span>.<span class="ident">iter</span>().<span class="ident">map</span>(<span class="op">|</span><span class="ident">x</span><span class="op">|</span> (<span class="ident">x</span> <span class="op">-</span> <span class="ident">mean</span>) <span class="op">*</span> (<span class="ident">x</span> <span class="op">-</span> <span class="ident">mean</span>)).<span class="ident">sum</span>::<span class="op"><</span><span class="ident">f64</span><span class="op">></span>() <span class="op">/</span> <span class="ident">results</span>.<span class="ident">len</span>() <span class="kw">as</span> <span class="ident">f64</span>;
<span class="macro">assert</span><span class="macro">!</span>((<span class="ident">variance</span> <span class="op">-</span> <span class="ident">expected_variance</span>).<span class="ident">abs</span>() <span class="op"><</span> <span class="ident">expected_variance</span> <span class="op">/</span> <span class="number">10.0</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_binomial</span>() {
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">rng</span> <span class="op">=</span> <span class="kw">crate</span>::<span class="ident">test</span>::<span class="ident">rng</span>(<span class="number">351</span>);
<span class="ident">test_binomial_mean_and_variance</span>(<span class="number">150</span>, <span class="number">0.1</span>, <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">rng</span>);
<span class="ident">test_binomial_mean_and_variance</span>(<span class="number">70</span>, <span class="number">0.6</span>, <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">rng</span>);
<span class="ident">test_binomial_mean_and_variance</span>(<span class="number">40</span>, <span class="number">0.5</span>, <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">rng</span>);
<span class="ident">test_binomial_mean_and_variance</span>(<span class="number">20</span>, <span class="number">0.7</span>, <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">rng</span>);
<span class="ident">test_binomial_mean_and_variance</span>(<span class="number">20</span>, <span class="number">0.5</span>, <span class="kw-2">&</span><span class="kw-2">mut</span> <span class="ident">rng</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="kw">fn</span> <span class="ident">test_binomial_end_points</span>() {
<span class="kw">let</span> <span class="kw-2">mut</span> <span class="ident">rng</span> <span class="op">=</span> <span class="kw">crate</span>::<span class="ident">test</span>::<span class="ident">rng</span>(<span class="number">352</span>);
<span class="macro">assert_eq</span><span class="macro">!</span>(<span class="ident">rng</span>.<span class="ident">sample</span>(<span class="ident">Binomial</span>::<span class="ident">new</span>(<span class="number">20</span>, <span class="number">0.0</span>).<span class="ident">unwrap</span>()), <span class="number">0</span>);
<span class="macro">assert_eq</span><span class="macro">!</span>(<span class="ident">rng</span>.<span class="ident">sample</span>(<span class="ident">Binomial</span>::<span class="ident">new</span>(<span class="number">20</span>, <span class="number">1.0</span>).<span class="ident">unwrap</span>()), <span class="number">20</span>);
}
<span class="attribute">#[<span class="ident">test</span>]</span>
<span class="attribute">#[<span class="ident">should_panic</span>]</span>
<span class="kw">fn</span> <span class="ident">test_binomial_invalid_lambda_neg</span>() {
<span class="ident">Binomial</span>::<span class="ident">new</span>(<span class="number">20</span>, <span class="op">-</span><span class="number">10.0</span>).<span class="ident">unwrap</span>();
}
}
</pre></div>
</section><section id="search" class="content hidden"></section><section class="footer"></section><div id="rustdoc-vars" data-root-path="../../" data-current-crate="rand_distr" data-search-js="../../search-index.js"></div>
<script src="../../main.js"></script><script src="../../source-script.js"></script><script src="../../source-files.js"></script></body></html>