/
LogNormal.R
executable file
·296 lines (282 loc) · 10.5 KB
/
LogNormal.R
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
#' Create a LogNormal distribution
#'
#' A random variable created by exponentiating a [Normal()]
#' distribution. Taking the log of LogNormal data returns in
#' [Normal()] data.
#'
#' @param log_mu The location parameter, written \eqn{\mu} in textbooks.
#' Can be any real number. Defaults to `0`.
#' @param log_sigma The scale parameter, written \eqn{\sigma} in textbooks.
#' Can be any positive real number. Defaults to `1`.
#'
#' @return A `LogNormal` object.
#' @export
#'
#' @family continuous distributions
#'
#' @details
#'
#' We recommend reading this documentation on
#' <https://alexpghayes.github.io/distributions3/>, where the math
#' will render with additional detail and much greater clarity.
#'
#' In the following, let \eqn{X} be a LogNormal random variable with
#' success probability `p` = \eqn{p}.
#'
#' **Support**: \eqn{R^+}
#'
#' **Mean**: \eqn{\exp(\mu + \sigma^2/2)}
#'
#' **Variance**: \eqn{[\exp(\sigma^2)-1]\exp(2\mu+\sigma^2)}
#'
#' **Probability density function (p.d.f)**:
#'
#' \deqn{
#' f(x) = \frac{1}{x \sigma \sqrt{2 \pi}} \exp \left(-\frac{(\log x - \mu)^2}{2 \sigma^2} \right)
#' }{
#' f(x) = \frac{1}{x \sigma \sqrt{2 \pi}} \exp (-\frac{(\log x - \mu)^2}{2 \sigma^2})
#' }
#'
#' **Cumulative distribution function (c.d.f)**:
#'
#' \deqn{F(x) = \frac{1}{2} + \frac{1}{2\sqrt{pi}}\int_{-x}^x e^{-t^2} dt}
#'
#' **Moment generating function (m.g.f)**:
#' Undefined.
#'
#'
#' @examples
#'
#' set.seed(27)
#'
#' X <- LogNormal(0.3, 2)
#' X
#'
#' random(X, 10)
#'
#' pdf(X, 2)
#' log_pdf(X, 2)
#'
#' cdf(X, 4)
#' quantile(X, 0.7)
LogNormal <- function(log_mu = 0, log_sigma = 1) {
stopifnot(
"parameter lengths do not match (only scalars are allowed to be recycled)" =
length(log_mu) == length(log_sigma) | length(log_mu) == 1 | length(log_sigma) == 1
)
d <- data.frame(log_mu = log_mu, log_sigma = log_sigma)
class(d) <- c("LogNormal", "distribution")
d
}
#' @export
mean.LogNormal <- function(x, ...) {
ellipsis::check_dots_used()
mu <- x$log_mu
sigma <- x$log_sigma
rval <- exp(mu + sigma^2 / 2)
setNames(rval, names(x))
}
#' @export
variance.LogNormal <- function(x, ...) {
mu <- x$log_mu
sigma <- x$log_sigma
rval <- (exp(sigma^2) - 1) * exp(2 * mu + sigma^2)
setNames(rval, names(x))
}
#' @export
skewness.LogNormal <- function(x, ...) {
mu <- x$log_mu
sigma <- x$log_sigma
rval <- (exp(sigma^2) + 2) * sqrt(exp(sigma^2) - 1)
setNames(rval, names(x))
}
#' @export
kurtosis.LogNormal <- function(x, ...) {
mu <- x$log_mu
sigma <- x$log_sigma
rval <- exp(4 * sigma^2) + 2 * exp(3 * sigma^2) + 3 * exp(2 * sigma^2) - 6
setNames(rval, names(x))
}
#' Draw a random sample from a LogNormal distribution
#'
#' @inherit LogNormal examples
#'
#' @param x A `LogNormal` object created by a call to [LogNormal()].
#' @param n The number of samples to draw. Defaults to `1L`.
#' @param drop logical. Should the result be simplified to a vector if possible?
#' @param ... Unused. Unevaluated arguments will generate a warning to
#' catch mispellings or other possible errors.
#'
#' @family LogNormal distribution
#'
#' @return In case of a single distribution object or `n = 1`, either a numeric
#' vector of length `n` (if `drop = TRUE`, default) or a `matrix` with `n` columns
#' (if `drop = FALSE`).
#' @export
#'
random.LogNormal <- function(x, n = 1L, drop = TRUE, ...) {
n <- make_positive_integer(n)
if (n == 0L) {
return(numeric(0L))
}
FUN <- function(at, d) rlnorm(n = at, meanlog = d$log_mu, sdlog = d$log_sigma)
apply_dpqr(d = x, FUN = FUN, at = n, type = "random", drop = drop)
}
#' Evaluate the probability mass function of a LogNormal distribution
#'
#' Please see the documentation of [LogNormal()] for some properties
#' of the LogNormal distribution, as well as extensive examples
#' showing to how calculate p-values and confidence intervals.
#'
#' @inherit LogNormal examples
#'
#' @param d A `LogNormal` object created by a call to [LogNormal()].
#' @param x A vector of elements whose probabilities you would like to
#' determine given the distribution `d`.
#' @param drop logical. Should the result be simplified to a vector if possible?
#' @param elementwise logical. Should each distribution in \code{d} be evaluated
#' at all elements of \code{x} (\code{elementwise = FALSE}, yielding a matrix)?
#' Or, if \code{d} and \code{x} have the same length, should the evaluation be
#' done element by element (\code{elementwise = TRUE}, yielding a vector)? The
#' default of \code{NULL} means that \code{elementwise = TRUE} is used if the
#' lengths match and otherwise \code{elementwise = FALSE} is used.
#' @param ... Arguments to be passed to \code{\link[stats]{dlnorm}}.
#' Unevaluated arguments will generate a warning to catch mispellings or other
#' possible errors.
#'
#' @family LogNormal distribution
#'
#' @return In case of a single distribution object, either a numeric
#' vector of length `probs` (if `drop = TRUE`, default) or a `matrix` with
#' `length(x)` columns (if `drop = FALSE`). In case of a vectorized distribution
#' object, a matrix with `length(x)` columns containing all possible combinations.
#' @export
#'
pdf.LogNormal <- function(d, x, drop = TRUE, elementwise = NULL, ...) {
FUN <- function(at, d) dlnorm(x = at, meanlog = d$log_mu, sdlog = d$log_sigma, ...)
apply_dpqr(d = d, FUN = FUN, at = x, type = "density", drop = drop, elementwise = elementwise)
}
#' @rdname pdf.LogNormal
#' @export
log_pdf.LogNormal <- function(d, x, drop = TRUE, elementwise = NULL, ...) {
FUN <- function(at, d) dlnorm(x = at, meanlog = d$log_mu, sdlog = d$log_sigma, log = TRUE)
apply_dpqr(d = d, FUN = FUN, at = x, type = "logLik", drop = drop, elementwise = elementwise)
}
#' Evaluate the cumulative distribution function of a LogNormal distribution
#'
#' @inherit LogNormal examples
#'
#' @param d A `LogNormal` object created by a call to [LogNormal()].
#' @param x A vector of elements whose cumulative probabilities you would
#' like to determine given the distribution `d`.
#' @param drop logical. Should the result be simplified to a vector if possible?
#' @param elementwise logical. Should each distribution in \code{d} be evaluated
#' at all elements of \code{x} (\code{elementwise = FALSE}, yielding a matrix)?
#' Or, if \code{d} and \code{x} have the same length, should the evaluation be
#' done element by element (\code{elementwise = TRUE}, yielding a vector)? The
#' default of \code{NULL} means that \code{elementwise = TRUE} is used if the
#' lengths match and otherwise \code{elementwise = FALSE} is used.
#' @param ... Arguments to be passed to \code{\link[stats]{plnorm}}.
#' Unevaluated arguments will generate a warning to catch mispellings or other
#' possible errors.
#'
#' @family LogNormal distribution
#'
#' @return In case of a single distribution object, either a numeric
#' vector of length `probs` (if `drop = TRUE`, default) or a `matrix` with
#' `length(x)` columns (if `drop = FALSE`). In case of a vectorized distribution
#' object, a matrix with `length(x)` columns containing all possible combinations.
#' @export
#'
cdf.LogNormal <- function(d, x, drop = TRUE, elementwise = NULL, ...) {
FUN <- function(at, d) plnorm(q = at, meanlog = d$log_mu, sdlog = d$log_sigma, ...)
apply_dpqr(d = d, FUN = FUN, at = x, type = "probability", drop = drop, elementwise = elementwise)
}
#' Determine quantiles of a LogNormal distribution
#'
#' @inherit LogNormal examples
#' @inheritParams random.LogNormal
#'
#' @param probs A vector of probabilities.
#' @param drop logical. Should the result be simplified to a vector if possible?
#' @param elementwise logical. Should each distribution in \code{x} be evaluated
#' at all elements of \code{probs} (\code{elementwise = FALSE}, yielding a matrix)?
#' Or, if \code{x} and \code{probs} have the same length, should the evaluation be
#' done element by element (\code{elementwise = TRUE}, yielding a vector)? The
#' default of \code{NULL} means that \code{elementwise = TRUE} is used if the
#' lengths match and otherwise \code{elementwise = FALSE} is used.
#' @param ... Arguments to be passed to \code{\link[stats]{qlnorm}}.
#' Unevaluated arguments will generate a warning to catch mispellings or other
#' possible errors.
#'
#' @return In case of a single distribution object, either a numeric
#' vector of length `probs` (if `drop = TRUE`, default) or a `matrix` with
#' `length(probs)` columns (if `drop = FALSE`). In case of a vectorized
#' distribution object, a matrix with `length(probs)` columns containing all
#' possible combinations.
#' @export
#'
#' @family LogNormal distribution
#'
quantile.LogNormal <- function(x, probs, drop = TRUE, elementwise = NULL, ...) {
FUN <- function(at, d) qlnorm(p = at, meanlog = d$log_mu, sdlog = d$log_sigma, ...)
apply_dpqr(d = x, FUN = FUN, at = probs, type = "quantile", drop = drop, elementwise = elementwise)
}
#' Fit a Log Normal distribution to data
#'
#' @param d A `LogNormal` object created by a call to [LogNormal()].
#' @param x A vector of data.
#' @param ... Unused.
#'
#' @family LogNormal distribution
#'
#' @return A `LogNormal` object.
#' @export
#'
fit_mle.LogNormal <- function(d, x, ...) {
ss <- suff_stat(d, x, ...)
LogNormal(ss$mu, ss$sigma)
}
#' Compute the sufficient statistics for a Log-normal distribution from data
#'
#' @inheritParams fit_mle.LogNormal
#'
#' @return A named list of the sufficient statistics of the normal distribution:
#'
#' - `mu`: The sample mean of the log of the data.
#' - `sigma`: The sample standard deviation of the log of the data.
#' - `samples`: The number of samples in the data.
#'
#' @export
#'
suff_stat.LogNormal <- function(d, x, ...) {
valid_x <- x > 0
if (any(!valid_x)) stop("`x` must be a vector of positive real numbers")
log_x <- log(x)
list(mu = mean(log_x), sigma = sd(log_x), samples = length(x))
}
#' Return the support of the LogNormal distribution
#'
#' @param d An `LogNormal` object created by a call to [LogNormal()].
#' @param drop logical. Should the result be simplified to a vector if possible?
#' @param ... Currently not used.
#'
#' @return A vector of length 2 with the minimum and maximum value of the support.
#'
#' @export
support.LogNormal <- function(d, drop = TRUE, ...) {
ellipsis::check_dots_used()
min <- rep(0, length(d))
max <- rep(Inf, length(d))
make_support(min, max, d, drop = drop)
}
#' @exportS3Method
is_discrete.LogNormal <- function(d, ...) {
ellipsis::check_dots_used()
setNames(rep.int(FALSE, length(d)), names(d))
}
#' @exportS3Method
is_continuous.LogNormal <- function(d, ...) {
ellipsis::check_dots_used()
setNames(rep.int(TRUE, length(d)), names(d))
}