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mir.stat.distribution.laplace

This module contains algorithms for the Laplace Distribution.
License:
Apache-2.0
Authors:
John Michael Hall
pure nothrow @nogc @safe T laplacePDF(T)(const T x)
if (isFloatingPoint!T);
Computes the Laplace probability density function (PDF).
Parameters:
T x value to evaluate PDF
See Also:
Laplace Distribution
pure nothrow @nogc @safe T laplacePDF(T)(const T x, const T location, const T scale)
if (isFloatingPoint!T);
Ditto, with location and scale parameters (by standardizing x).
Parameters:
T x value to evaluate PDF
T location location parameter
T scale scale parameter
Examples: 
import mir.test: shouldApprox;

laplacePDF(-2.0).shouldApprox == 0.06766764;
laplacePDF(-1.0).shouldApprox == 0.1839397;
laplacePDF(-0.5).shouldApprox == 0.3032653;
laplacePDF(0.0).shouldApprox == 0.5;
laplacePDF(0.5).shouldApprox == 0.3032653;
laplacePDF(1.0).shouldApprox == 0.1839397;
laplacePDF(2.0).shouldApprox == 0.06766764;

// Can also provide location/scale parameters
laplacePDF(-1.0, 2.0, 3.0).shouldApprox == 0.06131324;
laplacePDF(1.0, 2.0, 3.0).shouldApprox == 0.1194219;
laplacePDF(4.0, 2.0, 3.0).shouldApprox == 0.08556952;
pure nothrow @nogc @safe T laplaceCDF(T)(const T x)
if (isFloatingPoint!T);
Computes the Laplace cumulative distribution function (CDF).
Parameters:
T x value to evaluate CDF
See Also:
Laplace Distribution
pure nothrow @nogc @safe T laplaceCDF(T)(const T x, const T location, const T scale)
if (isFloatingPoint!T);
Ditto, with location and scale parameters (by standardizing x).
Parameters:
T x value to evaluate CDF
T location location parameter
T scale scale parameter
Examples: 
import mir.test: shouldApprox;

laplaceCDF(-2.0).shouldApprox == 0.06766764;
laplaceCDF(-1.0).shouldApprox == 0.1839397;
laplaceCDF(-0.5).shouldApprox == 0.3032653;
laplaceCDF(0.0).shouldApprox == 0.5;
laplaceCDF(0.5).shouldApprox == 0.6967347;
laplaceCDF(1.0).shouldApprox == 0.8160603;
laplaceCDF(2.0).shouldApprox == 0.9323324;

// Can also provide location/scale parameters
laplaceCDF(-1.0, 2.0, 3.0).shouldApprox == 0.1839397;
laplaceCDF(1.0, 2.0, 3.0).shouldApprox == 0.3582657;
laplaceCDF(4.0, 2.0, 3.0).shouldApprox == 0.7432914;
pure nothrow @nogc @safe T laplaceCCDF(T)(const T x)
if (isFloatingPoint!T);
Computes the Laplace complementary cumulative distribution function (CCDF).
Parameters:
T x value to evaluate CCDF
See Also:
Laplace Distribution
T laplaceCCDF(T)(const T x, const T location, const T scale)
if (isFloatingPoint!T);
Ditto, with location and scale parameters (by standardizing x).
Parameters:
T x value to evaluate CCDF
T location location parameter
T scale scale parameter
Examples: 
import mir.test: shouldApprox;

laplaceCCDF(-2.0).shouldApprox == 0.9323324;
laplaceCCDF(-1.0).shouldApprox == 0.8160603;
laplaceCCDF(-0.5).shouldApprox == 0.6967347;
laplaceCCDF(0.0).shouldApprox == 0.5;
laplaceCCDF(0.5).shouldApprox == 0.3032653;
laplaceCCDF(1.0).shouldApprox == 0.1839397;
laplaceCCDF(2.0).shouldApprox == 0.06766764;

// Can also provide location/scale parameters
laplaceCCDF(-1.0, 2.0, 3.0).shouldApprox == 0.8160603;
laplaceCCDF(1.0, 2.0, 3.0).shouldApprox == 0.6417343;
laplaceCCDF(4.0, 2.0, 3.0).shouldApprox == 0.2567086;
pure nothrow @nogc @safe T laplaceInvCDF(T)(const T p)
if (isFloatingPoint!T);
Computes the Laplace inverse cumulative distribution function (InvCDF).
Parameters:
T p value to evaluate InvCDF
See Also:
Laplace Distribution
T laplaceInvCDF(T)(const T p, const T location, const T scale)
if (isFloatingPoint!T);
Ditto, with location and scale parameters (by standardizing x).
Parameters:
T p value to evaluate InvCDF
T location location parameter
T scale scale parameter
See Also:
Logistic probability distribution
Examples: 
import mir.test: shouldApprox;

laplaceInvCDF(0.0).shouldApprox == -double.infinity;
laplaceInvCDF(0.25).shouldApprox == -0.6931472;
laplaceInvCDF(0.5).shouldApprox == 0.0;
laplaceInvCDF(0.75).shouldApprox == 0.6931472;
laplaceInvCDF(1.0).shouldApprox == double.infinity;

// Can also provide location/scale parameters
laplaceInvCDF(0.2, 2, 3).shouldApprox == -0.7488722;
laplaceInvCDF(0.4, 2, 3).shouldApprox == 1.330569;
laplaceInvCDF(0.6, 2, 3).shouldApprox == 2.669431;
laplaceInvCDF(0.8, 2, 3).shouldApprox == 4.748872;
pure nothrow @nogc @safe T laplaceLPDF(T)(const T x)
if (isFloatingPoint!T);
Computes the Laplace log probability density function (LPDF).
Parameters:
T x value to evaluate LPDF
See Also:
Laplace Distribution
T laplaceLPDF(T)(const T x, const T location, const T scale)
if (isFloatingPoint!T);
Ditto, with location and scale parameters (by standardizing x).
Parameters:
T x value to evaluate LPDF
T location location parameter
T scale scale parameter
See Also:
Laplace Distribution
Examples: 
import mir.math.common: log;
import mir.test: shouldApprox;

laplaceLPDF(-2.0).shouldApprox == log(0.06766764);
laplaceLPDF(-1.0).shouldApprox == log(0.1839397);
laplaceLPDF(-0.5).shouldApprox == log(0.3032653);
laplaceLPDF(0.0).shouldApprox == log(0.5);
laplaceLPDF(0.5).shouldApprox == log(0.3032653);
laplaceLPDF(1.0).shouldApprox == log(0.1839397);
laplaceLPDF(2.0).shouldApprox == log(0.06766764);

// Can also provide location/scale parameters
laplaceLPDF(-1.0, 2.0, 3.0).shouldApprox == log(0.06131324);
laplaceLPDF(1.0, 2.0, 3.0).shouldApprox == log(0.1194219);
laplaceLPDF(4.0, 2.0, 3.0).shouldApprox == log(0.08556952);