--- name: "PDL::GSL::CDF" section: "3pm" platform: "linux" package: "pdl" version: "1:2.081-2" release: "Debian 12 (Bookworm)" platforms: ["linux"] url: "https://new.carta.tech/PDL::GSL::CDF" --- # PDL::GSL::CDF(3pm) PDL interface to GSL Cumulative Distribution Functions ## NAME PDL::GSL::CDF - PDL interface to GSL Cumulative Distribution Functions ## DESCRIPTION This is an interface to the Cumulative Distribution Function package present in the GNU Scientific Library. Let us have a continuous random number distributions are defined by a probability density function `p(x)`. The cumulative distribution function for the lower tail `P(x)` is defined by the integral of `p(x)`, and gives the probability of a variate taking a value less than `"x"`. These functions are named **cdf\_NNNNNNN\_P()**. The cumulative distribution function for the upper tail `Q(x)` is defined by the integral of `p(x)`, and gives the probability of a variate taking a value greater than `"x"`. These functions are named **cdf\_NNNNNNN\_Q()**. The upper and lower cumulative distribution functions are related by `"P(x) + Q(x) = 1"` and satisfy `"0 <= P(x) <= 1"` and `"0 <= Q(x) <= 1"`. The inverse cumulative distributions, `"x = Pinv(P)"` and `"x = Qinv(Q)"` give the values of `"x"` which correspond to a specific value of `"P"` or `"Q"`. They can be used to find confidence limits from probability values. These functions are named **cdf\_NNNNNNN\_Pinv()** and **cdf\_NNNNNNN\_Qinv()**. For discrete distributions the probability of sampling the integer value `"k"` is given by `p(k)`, where `"sum_k p(k) = 1"`. The cumulative distribution for the lower tail `P(k)` of a discrete distribution is defined as, where the sum is over the allowed range of the distribution less than or equal to `"k"`. The cumulative distribution for the upper tail of a discrete distribution `Q(k)` is defined as giving the sum of probabilities for all values greater than `"k"`. These two definitions satisfy the identity `"P(k) + Q(k) = 1"`. If the range of the distribution is `1` to `"n"` inclusive then `"P(n) = 1"`, `"Q(n) = 0"` while `"P(1) = p(1)"`, `"Q(1) = 1 - p(1)"`. ## SYNOPSIS ``` use PDL; use PDL::GSL::CDF; my $p = gsl_cdf_tdist_P( $t, $df ); my $t = gsl_cdf_tdist_Pinv( $p, $df ); ``` ## FUNCTIONS ### The Beta Distribution (gsl\_cdf\_beta\_\*) These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the beta distribution with parameters *a* and *b*. ### gsl\_cdf\_beta\_P ``` Signature: (double x(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_beta\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_beta\_Pinv ``` Signature: (double p(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_beta\_Pinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_beta\_Q ``` Signature: (double x(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_beta\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_beta\_Qinv ``` Signature: (double q(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_beta\_Qinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The Binomial Distribution (gsl\_cdf\_binomial\_\*) These functions compute the cumulative distribution functions P(k), Q(k) for the binomial distribution with parameters *p* and *n*. ### gsl\_cdf\_binomial\_P ``` Signature: (ushort k(); double p(); ushort n(); double [o]out()) ``` gsl\_cdf\_binomial\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_binomial\_Q ``` Signature: (ushort k(); double p(); ushort n(); double [o]out()) ``` gsl\_cdf\_binomial\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The Cauchy Distribution (gsl\_cdf\_cauchy\_\*) These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Cauchy distribution with scale parameter *a*. ### gsl\_cdf\_cauchy\_P ``` Signature: (double x(); double a(); double [o]out()) ``` gsl\_cdf\_cauchy\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_cauchy\_Pinv ``` Signature: (double p(); double a(); double [o]out()) ``` gsl\_cdf\_cauchy\_Pinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_cauchy\_Q ``` Signature: (double x(); double a(); double [o]out()) ``` gsl\_cdf\_cauchy\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_cauchy\_Qinv ``` Signature: (double q(); double a(); double [o]out()) ``` gsl\_cdf\_cauchy\_Qinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The Chi-squared Distribution (gsl\_cdf\_chisq\_\*) These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the chi-squared distribution with *nu* degrees of freedom. ### gsl\_cdf\_chisq\_P ``` Signature: (double x(); double nu(); double [o]out()) ``` gsl\_cdf\_chisq\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_chisq\_Pinv ``` Signature: (double p(); double nu(); double [o]out()) ``` gsl\_cdf\_chisq\_Pinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_chisq\_Q ``` Signature: (double x(); double nu(); double [o]out()) ``` gsl\_cdf\_chisq\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_chisq\_Qinv ``` Signature: (double q(); double nu(); double [o]out()) ``` gsl\_cdf\_chisq\_Qinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The Exponential Distribution (gsl\_cdf\_exponential\_\*) These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the exponential distribution with mean *mu*. ### gsl\_cdf\_exponential\_P ``` Signature: (double x(); double mu(); double [o]out()) ``` gsl\_cdf\_exponential\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_exponential\_Pinv ``` Signature: (double p(); double mu(); double [o]out()) ``` gsl\_cdf\_exponential\_Pinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_exponential\_Q ``` Signature: (double x(); double mu(); double [o]out()) ``` gsl\_cdf\_exponential\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_exponential\_Qinv ``` Signature: (double q(); double mu(); double [o]out()) ``` gsl\_cdf\_exponential\_Qinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The Exponential Power Distribution (gsl\_cdf\_exppow\_\*) These functions compute the cumulative distribution functions P(x), Q(x) for the exponential power distribution with parameters *a* and *b*. ### gsl\_cdf\_exppow\_P ``` Signature: (double x(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_exppow\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_exppow\_Q ``` Signature: (double x(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_exppow\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The F-distribution (gsl\_cdf\_fdist\_\*) These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the F-distribution with *nu1* and *nu2* degrees of freedom. ### gsl\_cdf\_fdist\_P ``` Signature: (double x(); double nua(); double nub(); double [o]out()) ``` gsl\_cdf\_fdist\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_fdist\_Pinv ``` Signature: (double p(); double nua(); double nub(); double [o]out()) ``` gsl\_cdf\_fdist\_Pinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_fdist\_Q ``` Signature: (double x(); double nua(); double nub(); double [o]out()) ``` gsl\_cdf\_fdist\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_fdist\_Qinv ``` Signature: (double q(); double nua(); double nub(); double [o]out()) ``` gsl\_cdf\_fdist\_Qinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The Flat (Uniform) Distribution (gsl\_cdf\_flat\_\*) These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for a uniform distribution from *a* to *b*. ### gsl\_cdf\_flat\_P ``` Signature: (double x(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_flat\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_flat\_Pinv ``` Signature: (double p(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_flat\_Pinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_flat\_Q ``` Signature: (double x(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_flat\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_flat\_Qinv ``` Signature: (double q(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_flat\_Qinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The Gamma Distribution (gsl\_cdf\_gamma\_\*) These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the gamma distribution with parameters *a* and *b*. ### gsl\_cdf\_gamma\_P ``` Signature: (double x(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_gamma\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_gamma\_Pinv ``` Signature: (double p(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_gamma\_Pinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_gamma\_Q ``` Signature: (double x(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_gamma\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_gamma\_Qinv ``` Signature: (double q(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_gamma\_Qinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The Gaussian Distribution (gsl\_cdf\_gaussian\_\*) These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Gaussian distribution with standard deviation *sigma*. ### gsl\_cdf\_gaussian\_P ``` Signature: (double x(); double sigma(); double [o]out()) ``` gsl\_cdf\_gaussian\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_gaussian\_Pinv ``` Signature: (double p(); double sigma(); double [o]out()) ``` gsl\_cdf\_gaussian\_Pinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_gaussian\_Q ``` Signature: (double x(); double sigma(); double [o]out()) ``` gsl\_cdf\_gaussian\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_gaussian\_Qinv ``` Signature: (double q(); double sigma(); double [o]out()) ``` gsl\_cdf\_gaussian\_Qinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The Geometric Distribution (gsl\_cdf\_geometric\_\*) These functions compute the cumulative distribution functions P(k), Q(k) for the geometric distribution with parameter *p*. ### gsl\_cdf\_geometric\_P ``` Signature: (ushort k(); double p(); double [o]out()) ``` gsl\_cdf\_geometric\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_geometric\_Q ``` Signature: (ushort k(); double p(); double [o]out()) ``` gsl\_cdf\_geometric\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The Type-1 Gumbel Distribution (gsl\_cdf\_gumbel1\_\*) These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Type-1 Gumbel distribution with parameters *a* and *b*. ### gsl\_cdf\_gumbel1\_P ``` Signature: (double x(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_gumbel1\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_gumbel1\_Pinv ``` Signature: (double p(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_gumbel1\_Pinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_gumbel1\_Q ``` Signature: (double x(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_gumbel1\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_gumbel1\_Qinv ``` Signature: (double q(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_gumbel1\_Qinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The Type-2 Gumbel Distribution (gsl\_cdf\_gumbel2\_\*) These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Type-2 Gumbel distribution with parameters *a* and *b*. ### gsl\_cdf\_gumbel2\_P ``` Signature: (double x(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_gumbel2\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_gumbel2\_Pinv ``` Signature: (double p(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_gumbel2\_Pinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_gumbel2\_Q ``` Signature: (double x(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_gumbel2\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_gumbel2\_Qinv ``` Signature: (double q(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_gumbel2\_Qinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The Hypergeometric Distribution (gsl\_cdf\_hypergeometric\_\*) These functions compute the cumulative distribution functions P(k), Q(k) for the hypergeometric distribution with parameters *n1*, *n2* and *t*. ### gsl\_cdf\_hypergeometric\_P ``` Signature: (ushort k(); ushort na(); ushort nb(); ushort t(); double [o]out()) ``` gsl\_cdf\_hypergeometric\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_hypergeometric\_Q ``` Signature: (ushort k(); ushort na(); ushort nb(); ushort t(); double [o]out()) ``` gsl\_cdf\_hypergeometric\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The Laplace Distribution (gsl\_cdf\_laplace\_\*) These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Laplace distribution with width *a*. ### gsl\_cdf\_laplace\_P ``` Signature: (double x(); double a(); double [o]out()) ``` gsl\_cdf\_laplace\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_laplace\_Pinv ``` Signature: (double p(); double a(); double [o]out()) ``` gsl\_cdf\_laplace\_Pinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_laplace\_Q ``` Signature: (double x(); double a(); double [o]out()) ``` gsl\_cdf\_laplace\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_laplace\_Qinv ``` Signature: (double q(); double a(); double [o]out()) ``` gsl\_cdf\_laplace\_Qinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The Logistic Distribution (gsl\_cdf\_logistic\_\*) These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the logistic distribution with scale parameter *a*. ### gsl\_cdf\_logistic\_P ``` Signature: (double x(); double a(); double [o]out()) ``` gsl\_cdf\_logistic\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_logistic\_Pinv ``` Signature: (double p(); double a(); double [o]out()) ``` gsl\_cdf\_logistic\_Pinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_logistic\_Q ``` Signature: (double x(); double a(); double [o]out()) ``` gsl\_cdf\_logistic\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_logistic\_Qinv ``` Signature: (double q(); double a(); double [o]out()) ``` gsl\_cdf\_logistic\_Qinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The Lognormal Distribution (gsl\_cdf\_lognormal\_\*) These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the lognormal distribution with parameters *zeta* and *sigma*. ### gsl\_cdf\_lognormal\_P ``` Signature: (double x(); double zeta(); double sigma(); double [o]out()) ``` gsl\_cdf\_lognormal\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_lognormal\_Pinv ``` Signature: (double p(); double zeta(); double sigma(); double [o]out()) ``` gsl\_cdf\_lognormal\_Pinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_lognormal\_Q ``` Signature: (double x(); double zeta(); double sigma(); double [o]out()) ``` gsl\_cdf\_lognormal\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_lognormal\_Qinv ``` Signature: (double q(); double zeta(); double sigma(); double [o]out()) ``` gsl\_cdf\_lognormal\_Qinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_negative\_binomial\_P ``` Signature: (ushort k(); double p(); double n(); double [o]out()) ``` gsl\_cdf\_negative\_binomial\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_negative\_binomial\_Q ``` Signature: (ushort k(); double p(); double n(); double [o]out()) ``` gsl\_cdf\_negative\_binomial\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The Pareto Distribution (gsl\_cdf\_pareto\_\*) These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Pareto distribution with exponent *a* and scale *b*. ### gsl\_cdf\_pareto\_P ``` Signature: (double x(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_pareto\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_pareto\_Pinv ``` Signature: (double p(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_pareto\_Pinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_pareto\_Q ``` Signature: (double x(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_pareto\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_pareto\_Qinv ``` Signature: (double q(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_pareto\_Qinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The Pascal Distribution (gsl\_cdf\_pascal\_\*) These functions compute the cumulative distribution functions P(k), Q(k) for the Pascal distribution with parameters *p* and *n*. ### gsl\_cdf\_pascal\_P ``` Signature: (ushort k(); double p(); ushort n(); double [o]out()) ``` gsl\_cdf\_pascal\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_pascal\_Q ``` Signature: (ushort k(); double p(); ushort n(); double [o]out()) ``` gsl\_cdf\_pascal\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The Poisson Distribution (gsl\_cdf\_poisson\_\*) These functions compute the cumulative distribution functions P(k), Q(k) for the Poisson distribution with parameter *mu*. ### gsl\_cdf\_poisson\_P ``` Signature: (ushort k(); double mu(); double [o]out()) ``` gsl\_cdf\_poisson\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_poisson\_Q ``` Signature: (ushort k(); double mu(); double [o]out()) ``` gsl\_cdf\_poisson\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The Rayleigh Distribution (gsl\_cdf\_rayleigh\_\*) These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Rayleigh distribution with scale parameter *sigma*. ### gsl\_cdf\_rayleigh\_P ``` Signature: (double x(); double sigma(); double [o]out()) ``` gsl\_cdf\_rayleigh\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_rayleigh\_Pinv ``` Signature: (double p(); double sigma(); double [o]out()) ``` gsl\_cdf\_rayleigh\_Pinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_rayleigh\_Q ``` Signature: (double x(); double sigma(); double [o]out()) ``` gsl\_cdf\_rayleigh\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_rayleigh\_Qinv ``` Signature: (double q(); double sigma(); double [o]out()) ``` gsl\_cdf\_rayleigh\_Qinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The t-distribution (gsl\_cdf\_tdist\_\*) These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the t-distribution with *nu* degrees of freedom. ### gsl\_cdf\_tdist\_P ``` Signature: (double x(); double nu(); double [o]out()) ``` gsl\_cdf\_tdist\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_tdist\_Pinv ``` Signature: (double p(); double nu(); double [o]out()) ``` gsl\_cdf\_tdist\_Pinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_tdist\_Q ``` Signature: (double x(); double nu(); double [o]out()) ``` gsl\_cdf\_tdist\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_tdist\_Qinv ``` Signature: (double q(); double nu(); double [o]out()) ``` gsl\_cdf\_tdist\_Qinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The Unit Gaussian Distribution (gsl\_cdf\_ugaussian\_\*) These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the unit Gaussian distribution. ### gsl\_cdf\_ugaussian\_P ``` Signature: (double x(); double [o]out()) ``` gsl\_cdf\_ugaussian\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_ugaussian\_Pinv ``` Signature: (double p(); double [o]out()) ``` gsl\_cdf\_ugaussian\_Pinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_ugaussian\_Q ``` Signature: (double x(); double [o]out()) ``` gsl\_cdf\_ugaussian\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_ugaussian\_Qinv ``` Signature: (double q(); double [o]out()) ``` gsl\_cdf\_ugaussian\_Qinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### The Weibull Distribution (gsl\_cdf\_weibull\_\*) These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Weibull distribution with scale *a* and exponent *b*. ### gsl\_cdf\_weibull\_P ``` Signature: (double x(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_weibull\_P processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_weibull\_Pinv ``` Signature: (double p(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_weibull\_Pinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_weibull\_Q ``` Signature: (double x(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_weibull\_Q processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ### gsl\_cdf\_weibull\_Qinv ``` Signature: (double q(); double a(); double b(); double [o]out()) ``` gsl\_cdf\_weibull\_Qinv processes bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays. ## AUTHOR Copyright (C) 2009 Maggie J. Xiong \ The GSL CDF module was written by J. Stover. All rights reserved. There is no warranty. You are allowed to redistribute this software / documentation as described in the file COPYING in the PDL distribution.