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  1. +201 −0 LICENSE
  2. +1 −0 README.md
  3. BIN rebar
  4. +3 −0 rebar.config
  5. +372 −0 src/bear.erl
  6. +75 −0 src/bear_scutil.erl
201 LICENSE
@@ -0,0 +1,201 @@
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1 README.md
@@ -0,0 +1 @@
+### bear : a set of statistics functions for erlang
BIN rebar
Binary file not shown.
3 rebar.config
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+{deps, []}.
+{erl_opts, [debug_info]}.
+{cover_enabled, true}.
372 src/bear.erl
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+%%%
+%%% Copyright 2011, Boundary
+%%%
+%%% Licensed under the Apache License, Version 2.0 (the "License");
+%%% you may not use this file except in compliance with the License.
+%%% You may obtain a copy of the License at
+%%%
+%%% http://www.apache.org/licenses/LICENSE-2.0
+%%%
+%%% Unless required by applicable law or agreed to in writing, software
+%%% distributed under the License is distributed on an "AS IS" BASIS,
+%%% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+%%% See the License for the specific language governing permissions and
+%%% limitations under the License.
+%%%
+
+
+%%%-------------------------------------------------------------------
+%%% File: bear.erl
+%%% @author joe williams <j@boundary.com>
+%%% @doc
+%%% statistics functions for calucating based on id and a list of values
+%%% @end
+%%%------------------------------------------------------------------
+
+-module(bear).
+
+-compile([export_all]).
+
+-export([
+ get_statistics/1,
+ get_statistics/2
+ ]).
+
+-define(HIST_BINS, 10).
+
+-define(STATS_MIN, 5).
+
+-record(scan_result, {n=0, sumX=0, sumXX=0, sumInv=0, sumLog, max, min}).
+-record(scan_result2, {x2=0, x3=0, x4=0}).
+
+-compile([native]).
+
+get_statistics(Values) when length(Values) < ?STATS_MIN ->
+ [
+ {min, 0.0},
+ {max, 0.0},
+ {arithmetic_mean, 0.0},
+ {geometric_mean, 0.0},
+ {harmonic_mean, 0.0},
+ {median, 0.0},
+ {variance, 0.0},
+ {standard_deviation, 0.0},
+ {skewness, 0.0},
+ {kurtosis, 0.0},
+ {percentile,
+ [
+ {75, 0.0},
+ {95, 0.0},
+ {99, 0.0},
+ {999, 0.0}
+ ]
+ },
+ {histogram, [{0, 0}]}
+ ];
+get_statistics(Values) ->
+ Scan_res = scan_values(Values),
+ Scan_res2 = scan_values2(Values, Scan_res),
+ Variance = variance(Scan_res, Scan_res2),
+ SortedValues = lists:sort(Values),
+ [
+ {min, Scan_res#scan_result.min},
+ {max, Scan_res#scan_result.max},
+ {arithmetic_mean, arithmetic_mean(Scan_res)},
+ {geometric_mean, geometric_mean(Scan_res)},
+ {harmonic_mean, harmonic_mean(Scan_res)},
+ {median, percentile(SortedValues, Scan_res, 0.5)},
+ {variance, Variance},
+ {standard_deviation, std_deviation(Scan_res, Scan_res2)},
+ {skewness, skewness(Scan_res, Scan_res2)},
+ {kurtosis, kurtosis(Scan_res, Scan_res2)},
+ {percentile,
+ [
+ {75, percentile(SortedValues, Scan_res, 0.75)},
+ {95, percentile(SortedValues, Scan_res, 0.95)},
+ {99, percentile(SortedValues, Scan_res, 0.99)},
+ {999, percentile(SortedValues, Scan_res, 0.999)}
+ ]
+ },
+ {histogram, get_histogram(Values, Scan_res, Scan_res2)}
+ ].
+
+get_statistics(Values, _) when length(Values) < ?STATS_MIN ->
+ 0.0;
+get_statistics(_, Values) when length(Values) < ?STATS_MIN ->
+ 0.0;
+get_statistics(Values1, Values2) when length(Values1) /= length(Values2) ->
+ 0.0;
+get_statistics(Values1, Values2) ->
+ [
+ {covariance, get_covariance(Values1, Values2)},
+ {tau, get_kendall_correlation(Values1, Values2)},
+ {rho, get_pearson_correlation(Values1, Values2)},
+ {r, get_spearman_correlation(Values1, Values2)}
+ ].
+
+%%%===================================================================
+%%% Internal functions
+%%%===================================================================
+
+scan_values([X|Values]) ->
+ scan_values(Values, #scan_result{n=1, sumX=X, sumXX=X*X,
+ sumLog=math_log(X),
+ max=X, min=X, sumInv=inverse(X)}).
+
+scan_values([X|Values],
+ #scan_result{n=N, sumX=SumX, sumXX=SumXX, sumLog=SumLog,
+ max=Max, min=Min, sumInv=SumInv}=Acc) ->
+ scan_values(Values,
+ Acc#scan_result{n=N+1, sumX=SumX+X, sumXX=SumXX+X*X,
+ sumLog=SumLog+math_log(X),
+ max=max(X,Max), min=min(X,Min),
+ sumInv=SumInv+inverse(X)});
+scan_values([], Acc) ->
+ Acc.
+
+scan_values2(Values, #scan_result{n=N, sumX=SumX}) ->
+ scan_values2(Values, SumX/N, #scan_result2{}).
+
+scan_values2([X|Values], Mean, #scan_result2{x2=X2, x3=X3, x4=X4}=Acc) ->
+ Diff = X-Mean,
+ Diff2 = Diff*Diff,
+ Diff3 = Diff2*Diff,
+ Diff4 = Diff2*Diff2,
+ scan_values2(Values, Mean, Acc#scan_result2{x2=X2+Diff2, x3=X3+Diff3,
+ x4=X4+Diff4});
+scan_values2([], _, Acc) ->
+ Acc.
+
+
+arithmetic_mean(#scan_result{n=N, sumX=Sum}) ->
+ Sum/N.
+
+geometric_mean(#scan_result{n=N, sumLog=SumLog}) ->
+ math:exp(SumLog/N).
+
+harmonic_mean(#scan_result{n=N, sumInv=Sum}) ->
+ N/Sum.
+
+percentile(SortedValues, #scan_result{n=N}, Percentile)
+ when is_list(SortedValues) ->
+ Element = round(Percentile * N),
+ lists:nth(Element, SortedValues).
+
+%% Two pass variance
+%% Results match those given by the 'var' function in R
+variance(#scan_result{n=N}, #scan_result2{x2=X2}) ->
+ X2/(N-1).
+
+std_deviation(Scan_res, Scan_res2) ->
+ math:sqrt(variance(Scan_res, Scan_res2)).
+
+%% http://en.wikipedia.org/wiki/Skewness
+%%
+%% skewness results should match this R function:
+%% skewness <- function(x) {
+%% m3 <- mean((x - mean(x))^3)
+%% skew <- m3 / (sd(x)^3)
+%% skew
+%% }
+skewness(#scan_result{n=N}=Scan_res, #scan_result2{x3=X3}=Scan_res2) ->
+ case math:pow(std_deviation(Scan_res,Scan_res2), 3) of
+ 0.0 ->
+ 0.0; %% Is this really the correct thing to do here?
+ Else ->
+ (X3/N)/Else
+ end.
+
+%% http://en.wikipedia.org/wiki/Kurtosis
+%%
+%% results should match this R function:
+%% kurtosis <- function(x) {
+%% m4 <- mean((x - mean(x))^4)
+%% kurt <- m4 / (sd(x)^4) - 3
+%% kurt
+%% }
+kurtosis(#scan_result{n=N}=Scan_res, #scan_result2{x4=X4}=Scan_res2) ->
+ case math:pow(std_deviation(Scan_res,Scan_res2), 4) of
+ 0.0 ->
+ 0.0; %% Is this really the correct thing to do here?
+ Else ->
+ ((X4/N)/Else) - 3
+ end.
+
+get_histogram(Values, Scan_res, Scan_res2) ->
+ Bins = get_hist_bins(Scan_res#scan_result.min,
+ Scan_res#scan_result.max,
+ std_deviation(Scan_res, Scan_res2),
+ length(Values)
+ ),
+
+ Dict = lists:foldl(fun (Value, Dict) ->
+ update_bin(Value, Bins, Dict)
+ end,
+ dict:from_list([{Bin, 0} || Bin <- Bins]),
+ Values),
+
+ lists:sort(dict:to_list(Dict)).
+
+update_bin(Value, [Bin|_Bins], Dict) when Value =< Bin ->
+ dict:update_counter(Bin, 1, Dict);
+update_bin(Values, [_Bin|Bins], Dict) ->
+ update_bin(Values, Bins, Dict).
+
+%% two pass covariance
+%% (http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Covariance)
+%% matches results given by excel's 'covar' function
+get_covariance(Values, _) when length(Values) < ?STATS_MIN ->
+ 0.0;
+get_covariance(_, Values) when length(Values) < ?STATS_MIN ->
+ 0.0;
+get_covariance(Values1, Values2) when length(Values1) /= length(Values2) ->
+ 0.0;
+get_covariance(Values1, Values2) ->
+ {SumX, SumY, N} = foldl2(fun (X, Y, {SumX, SumY, N}) ->
+ {SumX+X, SumY+Y, N+1}
+ end, {0,0,0}, Values1, Values2),
+ MeanX = SumX/N,
+ MeanY = SumY/N,
+ Sum = foldl2(fun (X, Y, Sum) ->
+ Sum + ((X - MeanX) * (Y - MeanY))
+ end,
+ 0, Values1, Values2),
+ Sum/N.
+
+get_kendall_correlation(Values, _) when length(Values) < ?STATS_MIN ->
+ 0.0;
+get_kendall_correlation(_, Values) when length(Values) < ?STATS_MIN ->
+ 0.0;
+get_kendall_correlation(Values1, Values2) when length(Values1) /= length(Values2) ->
+ 0.0;
+get_kendall_correlation(Values1, Values2) ->
+ bear_scutil:kendall_correlation(Values1, Values2).
+
+get_spearman_correlation(Values, _) when length(Values) < ?STATS_MIN ->
+ 0.0;
+get_spearman_correlation(_, Values) when length(Values) < ?STATS_MIN ->
+ 0.0;
+get_spearman_correlation(Values1, Values2) when length(Values1) /= length(Values2) ->
+ 0.0;
+get_spearman_correlation(Values1, Values2) ->
+ TR1 = ranks_of(Values1),
+ TR2 = ranks_of(Values2),
+ Numerator = 6 * foldl2(fun (X, Y, Acc) ->
+ Diff = X-Y,
+ Acc + Diff*Diff
+ end, 0, TR1,TR2),
+ N = length(Values1),
+ Denominator = math:pow(N,3)-N,
+ 1-(Numerator/Denominator).
+
+ranks_of(Values) when is_list(Values) ->
+ [Fst|Rest] = revsort(Values),
+ TRs = ranks_of(Rest, [], 2, Fst, 1),
+ Dict = gb_trees:from_orddict(TRs),
+ L = lists:foldl(fun (Val, Acc) ->
+ Rank = gb_trees:get(Val, Dict),
+ [Rank|Acc]
+ end, [], Values),
+ lists:reverse(L).
+
+ranks_of([E|Es],Acc, N, E, S) ->
+ ranks_of(Es, Acc, N+1, E, S);
+ranks_of([E|Es], Acc, N, P, S) ->
+ ranks_of(Es,[{P,(S+N-1)/2}|Acc], N+1, E, N);
+ranks_of([], Acc, N, P, S) ->
+ [{P,(S+N-1)/2}|Acc].
+
+
+get_pearson_correlation(Values, _) when length(Values) < ?STATS_MIN ->
+ 0.0;
+get_pearson_correlation(_, Values) when length(Values) < ?STATS_MIN ->
+ 0.0;
+get_pearson_correlation(Values1, Values2) when length(Values1) /= length(Values2) ->
+ 0.0;
+get_pearson_correlation(Values1, Values2) ->
+ {SumX, SumY, SumXX, SumYY, SumXY, N} =
+ foldl2(fun (X,Y,{SX, SY, SXX, SYY, SXY, N}) ->
+ {SX+X, SY+Y, SXX+X*X, SYY+Y*Y, SXY+X*Y, N+1}
+ end, {0,0,0,0,0,0}, Values1, Values2),
+ Numer = (N*SumXY) - (SumX * SumY),
+ case math:sqrt(((N*SumXX)-(SumX*SumX)) * ((N*SumYY)-(SumY*SumY))) of
+ 0.0 ->
+ 0.0; %% Is this really the correct thing to do here?
+ Denom ->
+ Numer/Denom
+ end.
+
+revsort(L) ->
+ lists:reverse(lists:sort(L)).
+
+%% Foldl over two lists
+foldl2(F, Acc, [I1|L1], [I2|L2]) when is_function(F,3) ->
+ foldl2(F, F(I1, I2, Acc), L1, L2);
+foldl2(_F, Acc, [], []) ->
+ Acc.
+
+%% wrapper for math:log/1 to avoid dividing by zero
+math_log(0) ->
+ 1;
+math_log(X) ->
+ math:log(X).
+
+%% wrapper for calculating inverse to avoid dividing by zero
+inverse(0) ->
+ 0;
+inverse(X) ->
+ 1/X.
+
+get_hist_bins(Min, Max, StdDev, Count) ->
+ BinWidth = get_bin_width(StdDev, Count),
+ BinCount = get_bin_count(Min, Max, BinWidth),
+ case get_bin_list(BinWidth, BinCount, []) of
+ List when length(List) =< 1 ->
+ [Max];
+ Bins ->
+ %% add Min to Bins
+ [Bin + Min || Bin <- Bins]
+ end.
+
+get_bin_list(Width, Bins, Acc) when Bins > length(Acc) ->
+ Bin = ((length(Acc) + 1) * Width ),
+ get_bin_list(Width, Bins, [round_bin(Bin)| Acc]);
+get_bin_list(_, _, Acc) ->
+ lists:usort(Acc).
+
+round_bin(Bin) ->
+ Base = case erlang:trunc(math:pow(10, round(math:log10(Bin) - 1))) of
+ 0 ->
+ 1;
+ Else ->
+ Else
+ end,
+ %io:format("bin ~p, base ~p~n", [Bin, Base]),
+ round_bin(Bin, Base).
+
+round_bin(Bin, Base) when Bin rem Base == 0 ->
+ Bin;
+round_bin(Bin, Base) ->
+ Bin + Base - (Bin rem Base).
+
+% the following is up for debate as far as what the best method
+% of choosing bin counts and widths. these seem to work *good enough*
+% in my testing
+
+% bin width based on Sturges
+% http://www.jstor.org/pss/2965501
+get_bin_width(StdDev, Count) ->
+ %io:format("stddev: ~p, count: ~p~n", [StdDev, Count]),
+ case round((3.5 * StdDev) / math:pow(Count, 0.3333333)) of
+ 0 ->
+ 1;
+ Else ->
+ Else
+ end.
+
+% based on the simple ceilng function at
+% http://en.wikipedia.org/wiki/Histograms#Number_of_bins_and_width
+% with a modification to attempt to get on bin beyond the max value
+get_bin_count(Min, Max, Width) ->
+ %io:format("min: ~p, max: ~p, width ~p~n", [Min, Max, Width]),
+ round((Max - Min) / Width) + 1.
75 src/bear_scutil.erl
@@ -0,0 +1,75 @@
+%% taken from http://crunchyd.com/scutil/
+%% All code here is MIT Licensed
+%% http://scutil.com/license.html
+
+-module(bear_scutil).
+
+-export([
+ kendall_correlation/2
+ ]).
+-compile([export_all]).
+-compile([native]).
+
+% seems to match the value returned by the 'cor' (method="kendal") R function
+% http://en.wikipedia.org/wiki/Kendall_tau_rank_correlation_coefficient
+kendall_correlation(List1, List2) when is_list(List1), is_list(List2) ->
+ {RA,_} = lists:unzip(tied_ordered_ranking(List1)),
+ {RB,_} = lists:unzip(tied_ordered_ranking(List2)),
+
+ Ordering = lists:keysort(1, lists:zip(RA,RB)),
+ {_,OrdB} = lists:unzip(Ordering),
+
+ N = length(List1),
+ P = lists:sum(kendall_right_of(OrdB, [])),
+
+ -(( (4*P) / (N * (N - 1))) - 1).
+
+%%%===================================================================
+%%% Internal functions
+%%%==================================================================
+
+simple_ranking(List) when is_list(List) ->
+ lists:zip(lists:seq(1,length(List)),lists:reverse(lists:sort(List))).
+
+tied_ranking(List) ->
+ tied_rank_worker(simple_ranking(List), [], no_prev_value).
+
+tied_ordered_ranking(List) when is_list(List) ->
+ tied_ordered_ranking(List, tied_ranking(List), []).
+
+tied_ordered_ranking([], [], Work) ->
+ lists:reverse(Work);
+
+tied_ordered_ranking([Front|Rem], Ranks, Work) ->
+ {value,Item} = lists:keysearch(Front,2,Ranks),
+ {IRank,Front} = Item,
+ tied_ordered_ranking(Rem, Ranks--[Item], [{IRank,Front}]++Work).
+
+kendall_right_of([], Work) ->
+ lists:reverse(Work);
+kendall_right_of([F|R], Work) ->
+ kendall_right_of(R, [kendall_right_of_item(F,R)]++Work).
+
+kendall_right_of_item(B, Rem) ->
+ length([R || R <- Rem, R < B]).
+
+tied_add_prev(Work, {FoundAt, NewValue}) ->
+ lists:duplicate( length(FoundAt), {lists:sum(FoundAt)/length(FoundAt), NewValue} ) ++ Work.
+
+tied_rank_worker([], Work, PrevValue) ->
+ lists:reverse(tied_add_prev(Work, PrevValue));
+
+tied_rank_worker([Item|Remainder], Work, PrevValue) ->
+ case PrevValue of
+ no_prev_value ->
+ {BaseRank,BaseVal} = Item,
+ tied_rank_worker(Remainder, Work, {[BaseRank],BaseVal});
+ {FoundAt,OldVal} ->
+ case Item of
+ {Id,OldVal} ->
+ tied_rank_worker(Remainder, Work, {[Id]++FoundAt,OldVal});
+ {Id,NewVal} ->
+ tied_rank_worker(Remainder, tied_add_prev(Work, PrevValue), {[Id],NewVal})
+
+ end
+ end.

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