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mir.stat.distribution.uniform_discrete

This module contains algorithms for the Discrete Uniform Distribution.
License:
Apache-2.0
Authors:
John Michael Hall
pure nothrow @nogc @safe double uniformDiscretePMF(const size_t x, const size_t lower = 0, const size_t upper = 1);
Computes the discrete uniform probability mass function (PMF).
Parameters:
size_t x value to evaluate PMF
size_t lower lower bound
size_t upper upper bound
See Also:
Discrete Uniform Distribution
Examples: 
import mir.test: shouldApprox;

1.uniformDiscretePMF.shouldApprox == 0.5;
2.uniformDiscretePMF(1, 3).shouldApprox == 1.0 / 3;
pure nothrow @nogc @safe double uniformDiscreteCDF(const size_t x, const size_t lower = 0, const size_t upper = 1);
Computes the discrete uniform cumulative distribution function (CDF).
Parameters:
size_t x value to evaluate CDF
size_t lower lower bound
size_t upper upper bound
See Also:
Discrete Uniform Distribution
Examples: 
import mir.test: shouldApprox;

0.uniformDiscreteCDF.shouldApprox == 0.5;
1.uniformDiscreteCDF.shouldApprox == 1.0;

1.uniformDiscreteCDF(1, 3).shouldApprox == 1.0 / 3;
2.uniformDiscreteCDF(1, 3).shouldApprox == 2.0 / 3;
3.uniformDiscreteCDF(1, 3).shouldApprox == 1.0;
pure nothrow @nogc @safe double uniformDiscreteCCDF(const size_t x, const size_t lower = 0, const size_t upper = 1);
Computes the discrete uniform complementary cumulative distribution function (CCDF).
Parameters:
size_t x value to evaluate CCDF
size_t lower lower bound
size_t upper upper bound
See Also:
Discrete Uniform Distribution
Examples: 
import mir.test: shouldApprox;

0.uniformDiscreteCCDF.shouldApprox == 0.5;
1.uniformDiscreteCCDF.shouldApprox == 0.0;

1.uniformDiscreteCCDF(1, 3).shouldApprox == 2.0 / 3;
2.uniformDiscreteCCDF(1, 3).shouldApprox == 1.0 / 3;
3.uniformDiscreteCCDF(1, 3).shouldApprox == 0.0;
pure nothrow @nogc @safe size_t uniformDiscreteInvCDF(T)(const T p, const size_t lower = 0, const size_t upper = 1)
if (isFloatingPoint!T);
Computes the discrete uniform inverse cumulative distribution function (InvCDF)
Parameters:
T p value to evaluate InvCDF
size_t lower lower bound
size_t upper upper bound
See Also:
Discrete Uniform Distribution
Examples:
. 
import mir.test: should;

0.0.uniformDiscreteInvCDF.should == 0;
0.5.uniformDiscreteInvCDF.should == 0;
1.0.uniformDiscreteInvCDF.should == 1;

0.0.uniformDiscreteInvCDF(1, 3).should == 1;
0.2.uniformDiscreteInvCDF(1, 3).should == 1;
(1.0 / 3).uniformDiscreteInvCDF(1, 3).should == 1;
0.5.uniformDiscreteInvCDF(1, 3).should == 1;
(2.0 / 3).uniformDiscreteInvCDF(1, 3).should == 2;
1.0.uniformDiscreteInvCDF(1, 3).should == 3;
pure nothrow @nogc @safe double uniformDiscreteLPMF(const size_t x, const size_t lower = 0, const size_t upper = 1);
Computes the discrete uniform log probability distribution function (LPDF)
Parameters:
size_t x value to evaluate LPDF
size_t lower lower bound
size_t upper upper bound
See Also:
Discrete Uniform Distribution
Examples: 
import mir.math.common: log;
import mir.test: shouldApprox;

1.uniformDiscreteLPMF.shouldApprox == -log(2.0);
2.uniformDiscreteLPMF(1, 3).shouldApprox == -log(3.0);