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mir.stat.distribution.beta_proportion

This module contains algorithms for the Beta Proportion Distribution.
An alternate parameterization of the mir.stat.distribution.beta distribuion in terms of the mean of the distribution and the sum of its shape parameters (also known as the sample size of the Beta distribution).
License:
Apache-2.0
Authors:
John Michael Hall
pure nothrow @nogc @safe T betaProportionPDF(T)(const T x, const T mu, const T kappa)
if (isFloatingPoint!T);
Computes the beta proportion probability density function (PDF).
Parameters:
T x value to evaluate PDF
T mu shape parameter #1
T kappa shape parameter #2
See Also:
Beta Proportion Distribution, betaPDF 
Examples: 
import mir.math.common: approxEqual;

assert(0.5.betaProportionPDF(0.5, 2) == 1);
assert(0.75.betaProportionPDF((1.0 / 3), 3).approxEqual(0.5));
assert(0.25.betaProportionPDF((1.0 / 9), 4.5).approxEqual(0.9228516));
pure nothrow @nogc @safe T betaProportionCDF(T)(const T x, const T mu, const T kappa)
if (isFloatingPoint!T);
Computes the beta proportion cumulatve distribution function (CDF).
Parameters:
T x value to evaluate CDF
T mu shape parameter #1
T kappa shape parameter #2
See Also:
Beta Proportion Distribution, betaCDF 
Examples: 
import mir.math.common: approxEqual;

assert(0.5.betaProportionCDF(0.5, 2).approxEqual(0.5));
assert(0.75.betaProportionCDF((1.0 / 3), 3).approxEqual(0.9375));
assert(0.25.betaProportionCDF((1.0 / 9), 4.5).approxEqual(0.8588867));
pure nothrow @nogc @safe T betaProportionCCDF(T)(const T x, const T mu, const T kappa)
if (isFloatingPoint!T);
Computes the beta proportion complementary cumulative distribution function (CCDF).
Parameters:
T x value to evaluate CCDF
T mu shape parameter #1
T kappa shape parameter #2
See Also:
Beta Proportion Distribution, betaCDF 
Examples: 
import mir.math.common: approxEqual;

assert(0.5.betaProportionCCDF(0.5, 2).approxEqual(0.5));
assert(0.75.betaProportionCCDF((1.0 / 3), 3).approxEqual(0.0625));
assert(0.25.betaProportionCCDF((1.0 / 9), 4.5).approxEqual(0.1411133));
pure nothrow @nogc @safe T betaProportionInvCDF(T)(const T p, const T mu, const T kappa)
if (isFloatingPoint!T);
Computes the beta proportion inverse cumulative distribution function (InvCDF).
Parameters:
T p value to evaluate InvCDF
T mu shape parameter #1
T kappa shape parameter #2
See Also:
Beta Proportion Distribution, betaInvCDF 
Examples: 
import mir.math.common: approxEqual;

assert(0.5.betaProportionInvCDF(0.5, 2).approxEqual(0.5));
assert(0.9375.betaProportionInvCDF((1.0 / 3), 3).approxEqual(0.75));
assert(0.8588867.betaProportionInvCDF((1.0 / 9), 4.5).approxEqual(0.25));
pure nothrow @nogc @safe T betaProportionLPDF(T)(const T x, const T mu, const T kappa)
if (isFloatingPoint!T);
Computes the beta proportion log probability density function (LPDF).
Parameters:
T x value to evaluate LPDF
T mu shape parameter #1
T kappa shape parameter #2
See Also:
Beta Proportion Distribution, betaLPDF 
Examples: 
import mir.math.common: approxEqual, log;

assert(0.5.betaProportionLPDF(0.5, 2).approxEqual(log(betaProportionPDF(0.5, 0.5, 2))));
assert(0.75.betaProportionLPDF((1.0 / 3), 3).approxEqual(log(betaProportionPDF(0.75, (1.0 / 3), 3))));
assert(0.25.betaProportionLPDF((1.0 / 9), 4.5).approxEqual(log(betaProportionPDF(0.25, (1.0 / 9), 4.5))));