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mir.stat.distribution.gamma

This module contains algorithms for the Gamma Distribution.
This module uses the shape/scale parameterization of the gamma distribution. To use the shape/rate parameterization, apply the inverse to the rate and pass it as the scale parameter.
License:
Apache-2.0
Authors:
Ilia Ki, John Michael Hall
pure nothrow @nogc @safe T gammaPDF(T)(const T x, const T shape, const T scale = 1)
if (isFloatingPoint!T);

pure nothrow @nogc @safe T gammaPDF(T)(const T x, const size_t shape, const T scale = 1)
if (isFloatingPoint!T);
Computes the gamma probability density function (PDF).
shape values less than 1 are supported when it is a floating point type.
If shape is passed as a size_t type (or a type convertible to that), then the PDF is calculated using the relationship with the poisson distribution (i.e. replacing the gamma function with the factorial).
Parameters:
T x value to evaluate PDF
T shape shape parameter
T scale scale parameter
See Also:
Gamma Distribution
Examples: 
import mir.test: shouldApprox;

2.0.gammaPDF(3.0).shouldApprox == 0.2706706;
2.0.gammaPDF(3.0, 4.0).shouldApprox == 0.01895408;
// Calling with `size_t` uses factorial function instead of gamma, but
// produces same results
2.0.gammaPDF(3).shouldApprox == 2.0.gammaPDF(3.0);
2.0.gammaPDF(3, 4.0).shouldApprox == 2.0.gammaPDF(3.0, 4.0);
pure nothrow @nogc @safe T gammaCDF(T)(const T x, const T shape, const T scale = 1)
if (isFloatingPoint!T);
Computes the gamma cumulative distribution function (CDF).
Parameters:
T x value to evaluate CDF
T shape shape parameter
T scale scale parameter
See Also:
Gamma Distribution
Examples: 
import mir.test: shouldApprox;

2.0.gammaCDF(5).shouldApprox == 0.05265302;
1.0.gammaCDF(5, 0.5).shouldApprox == 0.05265302;
pure nothrow @nogc @safe T gammaCCDF(T)(const T x, const T shape, const T scale = 1)
if (isFloatingPoint!T);
Computes the gamma complementary cumulative distribution function (CCDF).
Parameters:
T x value to evaluate CCDF
T shape shape parameter
T scale scale parameter
See Also:
Gamma Distribution
Examples: 
import mir.test: shouldApprox;

2.0.gammaCCDF(5).shouldApprox == 0.947347;
1.0.gammaCCDF(5, 0.5).shouldApprox == 0.947347;
pure nothrow @nogc @safe T gammaInvCDF(T)(const T p, const T shape, const T scale = 1)
if (isFloatingPoint!T);
Computes the gamma inverse cumulative distribution function (InvCDF).
Parameters:
T p value to evaluate InvCDF
T shape shape parameter
T scale scale parameter
See Also:
Gamma Distribution
Examples: 
import mir.test: shouldApprox;

0.05.gammaInvCDF(5).shouldApprox == 1.97015;
0.05.gammaInvCDF(5, 0.5).shouldApprox == 0.9850748;
pure nothrow @nogc @safe T gammaLPDF(T)(const T x, const T shape, const T scale = 1)
if (isFloatingPoint!T);

pure nothrow @nogc @safe T gammaLPDF(T)(const T x, const size_t shape, const T scale = 1)
if (isFloatingPoint!T);
Computes the gamma log probability density function (LPDF).
shape values less than 1 are supported when it is a floating point type.
If shape is passed as a size_t type (or a type convertible to that), then the LPDF is calculated using the relationship with the poisson distribution (i.e. replacing the logGamma function with the logFactorial).
Parameters:
T x value to evaluate LPDF
T shape shape parameter
T scale scale parameter
See Also:
Gamma Distribution
Examples: 
import mir.test: shouldApprox;

2.0.gammaLPDF(3.0).shouldApprox == -1.306853;
2.0.gammaLPDF(3.0, 4.0).shouldApprox == -3.965736;
// Calling with `size_t` uses log factorial function instead of log gamma,
// but produces same results
2.0.gammaLPDF(3).shouldApprox == 2.0.gammaLPDF(3.0);
2.0.gammaLPDF(3, 4.0).shouldApprox == 2.0.gammaLPDF(3.0, 4.0);