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folsom_statistics.erl
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folsom_statistics.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: folsom_statistics.erl
%%% @author joe williams <j@boundary.com>
%%% @doc
%%% statistics functions for calucating based on id and a list of values
%%% @end
%%%------------------------------------------------------------------
-module(folsom_statistics).
-export([get_max/1,
get_min/1,
get_histogram/1,
get_variance/1,
get_standard_deviation/1,
get_covariance/2,
get_kurtosis/1,
get_skewness/1,
get_mean/1,
get_median/1,
get_percentile/2,
get_statistics/1]).
-define(HIST, [1, 5, 10, 20, 30, 40, 50, 100, 150,
200, 250, 300, 350, 400, 450, 500,
750, 1000, 1500, 2000, 3000, 4000,
5000, 10000, 20000, 30000, 40000,
50000, 99999999999999]).
-define(STATS_MIN, 5).
get_max([]) ->
0;
get_max(Values) ->
[Head | _] = lists:reverse(lists:sort(Values)),
Head.
get_min([]) ->
0;
get_min(Values) ->
[Head | _] = lists:sort(Values),
Head.
get_histogram(Values) ->
Bins = [{Bin, 0} || Bin <- ?HIST],
build_hist(Values, Bins).
% two pass variance
get_variance(Values) when length(Values) < ?STATS_MIN ->
0;
get_variance(Values) ->
Mean = get_mean(Values),
List = [(Value - Mean) * (Value - Mean) || Value <- Values],
Sum = lists:sum(List),
Sum / (length(Values) - 1).
get_standard_deviation(Values) when length(Values) < ?STATS_MIN ->
0;
get_standard_deviation(Values) ->
math:sqrt(get_variance(Values)).
% two pass covariance
get_covariance(Values, _) when length(Values) < ?STATS_MIN ->
0;
get_covariance(_, Values) when length(Values) < ?STATS_MIN ->
0;
get_covariance(Values1, Values2) ->
Mean1 = get_mean(Values1),
Mean2 = get_mean(Values2),
Zip = lists:zip(Values1, Values2),
List = [((X1 - Mean1) * (X2 - Mean2)) / length(Values1) || {X1, X2} <- Zip],
lists:sum(List).
get_kurtosis(Values) when length(Values) < ?STATS_MIN ->
0;
get_kurtosis(Values) ->
Mean = get_mean(Values),
StdDev = get_standard_deviation(Values),
Count = length(Values),
get_kurtosis(Values, Mean, StdDev, Count).
get_skewness(Values) when length(Values) < ?STATS_MIN ->
0;
get_skewness(Values) ->
Mean = get_mean(Values),
StdDev = get_standard_deviation(Values),
Count = length(Values),
get_skewness(Values, Mean, StdDev, Count).
get_mean(Values) when length(Values) < ?STATS_MIN ->
0;
get_mean(Values) ->
Sum = lists:sum(Values),
Sum / length(Values).
get_median(Values) when length(Values) < ?STATS_MIN ->
0;
get_median(Values) when is_list(Values) ->
get_percentile(Values, 0.5).
get_percentile(Values, _) when length(Values) < ?STATS_MIN ->
0;
get_percentile(Values, Percentile) when is_list(Values) ->
SortedValues = lists:sort(Values),
Element = round(Percentile * length(SortedValues)),
lists:nth(Element, SortedValues).
% calculates stats on a sample
get_statistics(Values) ->
[
{min, get_min(Values)},
{max, get_max(Values)},
{mean, get_mean(Values)},
{median, get_median(Values)},
{variance, get_variance(Values)},
{standard_deviation, get_standard_deviation(Values)},
{skewness, get_skewness(Values)},
{kurtosis, get_kurtosis(Values)},
{percentile,
[
{75, get_percentile(Values, 0.75)},
{95, get_percentile(Values, 0.95)},
{99, get_percentile(Values, 0.99)},
{999, get_percentile(Values, 0.999)}
]
},
{histogram, get_histogram(Values)}
].
%%%===================================================================
%%% Internal functions
%%%===================================================================
% these histogram functions are too complicated, find better solution
build_hist([Head | Tail], Hist) ->
{Bin, Count} = proplists:lookup(which_bin(Head, Hist, []), Hist),
List = proplists:delete(Bin, Hist),
NewHist = lists:append(List, [{Bin, Count + 1}]),
build_hist(Tail, NewHist);
build_hist([], Hist) ->
lists:sort(Hist).
which_bin(Value, [{Bin, _} = B | Tail], Acc) when Value =< Bin ->
which_bin(Value, Tail, lists:sort(lists:append(Acc, [B])));
which_bin(Value, [_ | Tail], Acc) ->
which_bin(Value, Tail, Acc);
which_bin(_, [], [{Bin, _} | _]) ->
Bin.
% my best estimation of excess kurtosis thus far
% http://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm
get_kurtosis([], _, _, _) ->
0;
get_kurtosis(Values, Mean, StdDev, Count) ->
List1 = [math:pow(Value - Mean, 4) || Value <- Values],
(lists:sum(List1) / ((Count - 1) * math:pow(StdDev, 4)) ) - 3.
% results match excel calculation in my testing
get_skewness([], _, _, _) ->
0;
get_skewness(Values, Mean, StdDev, Count) ->
List = [math:pow((Value - Mean) / StdDev, 3) * Count || Value <- Values],
lists:sum(List) / ( (Count - 1) * (Count - 2) ).