dstats.distrib

Probability distribution CDFs, PDFs/PMFs, and a few inverse CDFs.

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Functions

betaCDF double betaCDF(double x, double alpha, double beta)
betaCDFR double betaCDFR(double x, double alpha, double beta)
betaPDF double betaPDF(double x, double alpha, double beta)
binomialCDF double binomialCDF(ulong k, ulong n, double p): P(K <= k) where K is random variable.
binomialCDFR double binomialCDFR(ulong k, ulong n, double p): P(K >= k) where K is random variable.
binomialPMF double binomialPMF(ulong k, ulong n, double p)
cauchyCDF double cauchyCDF(double X, double X0 = 0, double gamma = 1)
cauchyCDFR double cauchyCDFR(double X, double X0 = 0, double gamma = 1)
cauchyPDF double cauchyPDF(double X, double X0 = 0, double gamma = 1)
chiSquareCDF double chiSquareCDF(double x, double v): χ² distribution function and its complement.
chiSquareCDFR double chiSquareCDFR(double x, double v)
chiSquarePDF double chiSquarePDF(double x, double v)
dirichletPDF double dirichletPDF(X x, A alpha): The Dirichlet probability density.
exponentialCDF double exponentialCDF(double x, double lambda)
exponentialCDFR double exponentialCDFR(double x, double lambda)
exponentialPDF double exponentialPDF(double x, double lambda)
fisherCDF double fisherCDF(double x, double df1, double df2)
fisherCDFR double fisherCDFR(double x, double df1, double df2): The Fisher distribution, its complement, and inverse.
gammaCDF double gammaCDF(double x, double rate, double shape)
gammaCDFR double gammaCDFR(double x, double rate, double shape)
gammaPDF double gammaPDF(double x, double rate, double shape)
hypergeometricCDF double hypergeometricCDF(long x, long n1, long n2, long n): P(X <= x), where X is random variable. Uses either direct summation, normal or binomial approximation depending on parameters.
hypergeometricCDFR double hypergeometricCDFR(ulong x, ulong n1, ulong n2, ulong n): P(X >= x), where X is random variable.
hypergeometricPMF double hypergeometricPMF(long x, long n1, long n2, long n)
invBetaCDF double invBetaCDF(double p, double alpha, double beta)
invBinomialCDF uint invBinomialCDF(double pVal, uint n, double p): Returns the value of k for the given p-value, n and p. If p-value does not exactly map to a value of k, the value for which binomialCDF(k, n, p) is closest to pVal is used.
invCauchyCDF double invCauchyCDF(double p, double X0 = 0, double gamma = 1)
invChiSquareCDFR double invChiSquareCDFR(double v, double p): Inverse of complemented χ² distribution
invExponentialCDF double invExponentialCDF(double p, double lambda)
invFisherCDFR double invFisherCDFR(double df1, double df2, double p): Inverse of complemented Fisher distribution
invGammaCDF double invGammaCDF(double p, double rate, double shape): This just calls invGammaCDFR w/ 1 - p b/c invGammaCDFR is more accurate, but this function is necessary for consistency.
invGammaCDFR double invGammaCDFR(double p, double rate, double shape)
invLaplaceCDF double invLaplaceCDF(double p, double mu = 0, double b = 1)
invNegBinomCDF ulong invNegBinomCDF(double pVal, ulong n, double p)
invNormalCDF double invNormalCDF(double p, double mean = 0, double sd = 1): Inverse of Normal distribution function
invPoissonCDF uint invPoissonCDF(double pVal, double lambda): Returns the value of k for the given p-value and lambda. If p-val doesn't exactly map to a value of k, the k for which poissonCDF(k, lambda) is closest to pVal is used.
invStudentsTCDF double invStudentsTCDF(double p, double df): Inverse of Student's t distribution * Given probability p and degrees of freedom df, finds the argument t such that the one-sided studentsDistribution(nu,t) is equal to p. Used to test whether two distributions have the same standard deviation. *
kolmogorovDistrib double kolmogorovDistrib(immutable double x): Kolmogorov distribution. Used in Kolmogorov-Smirnov testing.
laplaceCDF double laplaceCDF(double X, double mu = 0, double b = 1)
laplaceCDFR double laplaceCDFR(double X, double mu = 0, double b = 1)
laplacePDF double laplacePDF(double x, double mu = 0, double b = 1)
logNormalCDF double logNormalCDF(double x, double mu = 0, double sigma = 1)
logNormalCDFR double logNormalCDFR(double x, double mu = 0, double sigma = 1)
logNormalPDF double logNormalPDF(double x, double mu = 0, double sigma = 1)
negBinomCDF double negBinomCDF(ulong k, ulong n, double p): Negative binomial distribution.
negBinomCDFR double negBinomCDFR(ulong k, ulong n, double p): Probability that k or more failures precede the nth success.
negBinomPMF double negBinomPMF(ulong k, ulong n, double p)
normalCDF double normalCDF(double x, double mean = 0, double stdev = 1): P(X < x) for normal distribution where X is random var.
normalCDFR double normalCDFR(double x, double mean = 0, double stdev = 1): P(X > x) for normal distribution where X is random var.
normalPDF double normalPDF(double x, double mean = 0, double sd = 1)
paramFunctor ParamFunctor!(distrib) paramFunctor(ParameterTypeTuple!(distrib)[1..$] parameters): Takes a distribution function (CDF or PDF/PMF) as a template argument, and parameters as function arguments in the order that they appear in the function declaration and returns a functor that binds the supplied parameters to the distribution function. Assumes the non-parameter argument is the first argument to the distribution function.
parametrize double delegate(ParameterTypeTuple!(distrib)[0]) parametrize(ParameterTypeTuple!(distrib)[1..$] parameters): Takes a distribution function (CDF or PDF/PMF) as a template argument, and parameters as function arguments in the order that they appear in the function declaration and returns a delegate that binds the supplied parameters to the distribution function. Assumes the non-parameter argument is the first argument to the distribution function.
poissonCDF double poissonCDF(ulong k, double lambda): P(K <= k) where K is r.v.
poissonCDFR double poissonCDFR(ulong k, double lambda): P(K >= k) where K is r.v.
poissonPMF double poissonPMF(ulong k, double lambda)
studentsTCDF double studentsTCDF(double t, double df)
studentsTCDFR double studentsTCDFR(double t, double df)
studentsTPDF double studentsTPDF(double t, double df)
uniformCDF double uniformCDF(double X, double lower, double upper)
uniformCDFR double uniformCDFR(double X, double lower, double upper)
uniformPDF double uniformPDF(double X, double lower, double upper)
weibullCDF double weibullCDF(double x, double shape, double scale = 1)
weibullCDFR double weibullCDFR(double x, double shape, double scale = 1)
weibullPDF double weibullPDF(double x, double shape, double scale = 1)

Structs

ParamFunctor struct ParamFunctor(alias distrib)

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