GSL-FFI-RANDIST¶

Gaussian Distribution¶

gsl-ran-gaussian Function¶

Signature:

(rng, sigma) => (variate)

Parameters:

rng – Random number generator. An instance of <gsl-rng*>.
sigma – Standard deviation. A <c-double>.

Result variate:

Sample from a Gaussian distribution with mean = 0 and standard deviation = sigma. A <c-double>.

gsl-ran-gaussian-pdf Function¶

Signature:

(x, sigma) => (pdf)

Parameters:

x – Value. A <c-double>.
sigma – Standard deviation. A <c-double>.

Result pdf:

Probability density function. A <c-double>.

gsl-ran-gaussian-ziggurat Function¶

Signature:

(rng, sigma) => (sample)

Parameters:

rng – Random number generator. An instance of <gsl-rng*>.
sigma – Standard deviation. A <c-double>.

Result sample:

Sample from a Gaussian distribution with mean = 0 and standard deviation = sigma. A <c-double>.

gsl-ran-gaussian-ratio-method Function¶

Signature:

(rng, sigma) => (sample)

Parameters:

rng – Random number generator. An instance of <gsl-rng*>
sigma – Standard deviation. A <c-double>

Result sample:

Sample from a Gaussian distribution with mean = 0 and standard deviation = sigma. A <c-double>

gsl-cdf-gaussian-p Function¶

Signature:

(x, sigma) => (cd)

Parameters:

x – Value. A <c-double>
sigma – Standard deviation. A <c-double>

Result cd:

Cumulative distribution function. A <c-double>

gsl-cdf-gaussian-q Function¶

Signature:

(x, sigma) => (cd)

Parameters:

x – Value. A <c-double>
sigma – Standard deviation. A <c-double>

Result cd:

Cumulative distribution function. A <c-double>

gsl-cdf-gaussian-pinv Function¶

Signature:

(p, sigma) => (x)

Parameters:

p – Probability. A <c-double>
sigma – Standard deviation. A <c-double>

Result x:

Value. A <c-double>

gsl-cdf-gaussian-qinv Function¶

Signature:

(p, sigma) => (x)

Parameters:

p – Probability. A <c-double>
sigma – Standard deviation. A <c-double>

Result x:

Value. A <c-double>

Unit Gaussian Distribution¶

gsl-ran-ugaussian Function¶

Signature:

(rng) => (sample)

Parameters:

rng – Random number generator. An instance of <gsl-rng*>

Result sample:

Sample from a standard Gaussian distribution with mean = 0 and standard deviation = 1. A <c-double>

gsl-ran-ugaussian-pdf Function¶

Signature:

=> (pdf)

Parameters:

x – Value. A <c-double>

Result pdf:

Probability density function. A <c-double>

Tail distributions¶

Gaussian tail¶

gsl-ran-gaussian-tail Function¶

Signature:

(rng, a, sigma) => (variate)

Parameters:

rng – Random number generator. An instance of <gsl-rng*>.
a – An <c-double>.
sigma – Standard deviation. A <c-double>.

Result variate:

A <c-double>.

gsl-ran-gaussian-tail-pdf Function¶

Signature:

(x, a, sigma) => (pd)

Parameters:

rng – Random number generator. An instance of <gsl-rng*>.
x – An <c-double>.
a – An <c-double>.
sigma – Standard deviation. A <c-double>.

Result pd:

A <c-double>.

Exponential¶

gsl-ran-exponential Function¶

Signature:

(rng, mu) => (variate)

Parameters:

rng – Random number generator. An instance of <gsl-rng*>.
mu – Mean. A <c-double>.

Result variate:

Sample from an exponential distribution with mean = mu. A <c-double>.

gsl-ran-exponential-pdf Function¶

Signature:

(x, mu) => (pdf)

Parameters:

x – Value. A <c-double>.
mu – Mean. A <c-double>.

Result pdf:

Probability density function. A <c-double>.

gsl-cdf-exponential-p Function¶

Signature:

(x, mu) => (cd)

Parameters:

x – Value. A <c-double>.
mu – Mean. A <c-double>.

Result cd:

Cumulative distribution function. A <c-double>

gsl-cdf-exponential-q Function¶

Signature:

(x, mu) => (cd)

Parameters:

x – Value. A <c-double>.
mu – Mean. A <c-double>.

Result cd:

Cumulative distribution function. A <c-double>

gsl-cdf-exponential-pinv Function¶

Signature:

(p, mu) => (x)

Parameters:

p – Probability. A <c-double>.
mu – Mean. A <c-double>.

Result x:

Value. A <c-double>

gsl-cdf-exponential-qinv Function¶

Signature:

(p, mu) => (x)

Parameters:

p – Probability. A <c-double>.
mu – Mean. A <c-double>.

Result x:

Value. A <c-double>

Laplace¶

gsl-ran-laplace Function¶

Signature:

(rng, a) => (variate)

Parameters:

rng – Random number generator. An instance of <gsl-rng*>.
a – Scale parameter. A <c-double>.

Result variate:

Sample from a Laplace distribution. A <c-double>.

gsl-ran-laplace-pdf Function¶

Signature:

(x, a) => (pdf)

Parameters:

x – Value. A <c-double>.
a – Scale parameter. A <c-double>.

Result pdf:

Probability density function. A <c-double>.

gsl-cdf-laplace-p Function¶

Signature:

gsl-cdf-laplace-p(x, a) => (cd)

Parameters:

x – Value. A <c-double>.
a – Scale parameter. A <c-double>.

Result cd:

Cumulative distribution function. A <c-double>.

gsl-cdf-laplace-q Function¶

Signature:

gsl-cdf-laplace-q(x, a) => (cd)

Parameters:

x – Value. A <c-double>.
a – Scale parameter. A <c-double>.

Result cd:

Cumulative distribution function. A <c-double>.

gsl-cdf-laplace-pinv Function¶

Signature:

gsl-cdf-laplace-pinv(p, a) => (x)

Parameters:

p – Probability. A <c-double>.
a – Scale parameter. A <c-double>.

Result x:

Value. A <c-double>.

gsl-cdf-laplace-qinv Function¶

Signature:

gsl-cdf-laplace-qinv(p, a) => (x)

Parameters:

p – Probability. A <c-double>.
a – Scale parameter. A <c-double>.

Result x:

Value. A <c-double>.

Exponentiated power¶

gsl-ran-exppow Function¶

Signature:

gsl-ran-exppow(rng, a, b) => (variate)

Parameters:

rng – Random number generator. An instance of <gsl-rng*>.
a – Scale parameter. A <c-double>.
b –

Shape parameter. A <c-double>.

result variate:

Sample from an exponentiated power distribution with scale = a and shape = b. A <c-double>.

gsl-ran-exppow-pdf Function¶

Signature:

gsl-ran-exppow(x, a, b) => (pdf)

Parameters:

x – Value. A <c-double>.
a – Scale parameter. A <c-double>.
b – Shape parameter. A <c-double>.

Result pdf:

Probability density function. A <c-double>

gsl-cdf-exppow-p Function¶

Signature:

gsl-cdf-exppow-p (x, a, b) => (cd)

Parameters:

x – Value. A <c-double>.
a – A <c-double>.
b – A <c-double>.

Result cd:

A <c-double>

gsl-cdf-exppow-q Function¶

Signature:

gsl-cdf-exppow-q (x, a, b) => (cd)

Parameters:

x – Value. A <c-double>.
a – A <c-double>.
b – A <c-double>.

Result cd:

A <c-double>

Cauchy¶

gsl-ran-cauchy Function¶

Signature:

(rng, a) => (variate)

Parameters:

rng – Random number generator. An instance of <gsl-rng*>.
a – Location parameter. A <c-double>.

Result variate:

Sample from a Cauchy distribution with location = x0 and scale = gamma. A <c-double>.

gsl-ran-cauchy-pdf Function¶

Signature:

(x, a) => (pdf)

Parameters:

x – Value. A <c-double>.
a – Location parameter. A <c-double>.

Result pdf:

Probability density function. A <c-double>

gsl-cdf-cauchy-p Function¶

Signature:

gsl-cdf-cauchy-p(x, a) => (cd)

Parameters:

x – Value. A <c-double>.
a – Scale parameter. A <c-double>.

Result cd:

Cumulative distribution function. A <c-double>.

gsl-cdf-cauchy-q Function¶

Signature:

gsl-cdf-cauchy-q(x, a) => (cd)

Parameters:

x – Value. A <c-double>.
a – Scale parameter. A <c-double>.

Result cd:

Cumulative distribution function. A <c-double>.

gsl-cdf-cauchy-pinv Function¶

Signature:

gsl-cdf-cauchy-pinv(p, a) => (x)

Parameters:

p – Probability. A <c-double>.
a – Scale parameter. A <c-double>.

Result x:

Value. A <c-double>.

gsl-cdf-cauchy-qinv Function¶

Signature:

gsl-cdf-cauchy-qinv(p, a) => (x)

Parameters:

p – Probability. A <c-double>.
a – Scale parameter. A <c-double>.

Result x:

Value. A <c-double>.

Rayleigh¶

gsl-ran-rayleigh Function¶

Signature:

gsl-ran-rayleigh(rng, sigma) => (variate)

Parameters:

rng – Random number generator. An instance of <gsl-rng*>.

sigma – Scale parameter. A <c-double>.

Result variate:

Sample from a Rayleigh distribution with scale = sigma. A <c-double>.

gsl-ran-rayleigh-pdf Function¶

Signature:

gsl-ran-rayleigh-pdf(x, sigma) => (pdf)

Parameters:

x – Value. A <c-double>.
sigma – Scale parameter. A <c-double>.

Result pdf:

Probability density function. A <c-double>

gsl-cdf-rayleigh-p Function¶

Signature:

gsl-ran-rayleigh-p(x, sigma) => (cd)

Parameters:

x – Value. A <c-double>.
sigma – Scale parameter. A <c-double>.

Result cd:

Cumulative distribution function. A <c-double>

gsl-cdf-rayleigh-q Function¶

Signature:

gsl-ran-rayleigh-q(x, sigma) => (cd)

Parameters:

x – Value. A <c-double>.
sigma – Scale parameter. A <c-double>.

Result cd:

Cumulative distribution function. A <c-double>

gsl-cdf-rayleigh-pinv Function¶

Signature:

gsl-ran-rayleigh-pinv(p, sigma) => (x)

Parameters:

p – Probability. A <c-double>.
sigma – Scale parameter. A <c-double>.

Result x:

Value. A <c-double>

gsl-cdf-rayleigh-qinv Function¶

Signature:

gsl-ran-rayleigh-qinv(p, sigma) => (x)

Parameters:

p – Probability. A <c-double>.
sigma – Scale parameter. A <c-double>.

Result x:

Value. A <c-double>

Rayleigh tail¶

gsl-ran-rayleigh-tail Function¶

Signature:

gsl-ran-rayleigh-tail(rng, a, sigma) => (variate)

Parameters:

rng – Random number generator. An instance of <gsl-rng*>.
a – An <c-double>.
sigma – Scale parameter. A <c-double>.

Result variate:

A <c-double>.

gsl-ran-rayleigh-tail-pdf Function¶

Signature:

gsl-ran-rayleigh-tail-pdf(x, a, sigma) => (pd)

Parameters:

rng – Random number generator. An instance of <gsl-rng*>.
x – An <c-double>.
a – An <c-double>.
sigma – Scale parameter. A <c-double>.

Result pd:

A <c-double>

The Landau distribution¶

gsl-ran-landau Function¶

Signature:

gsl-ran-landau(rng) => (variate)

Parameters:

rng – Random number generator. An instance of <gsl-rng*>.

Result variate:

A <c-double>

gsl-ran-landau-pdf Function¶

Signature:

gsl-ran-landau-pdf(x) => (pd)

Parameters:

x – An <c-double>.

Result pd:

A <c-double>

The Levy alpha-Stable distribution¶

gsl-ran-levy Function¶

Signature:

gsl-ran-levy(rng, c, alpha) => (variate)

Parameters:

rng – Random number generator. An instance of <gsl-rng*>.
c – Scale. An instance of <gsl-rng*>.
alpha – Exponent. An instance of <c-double>.

Result variate:

A <c-double>

The Levy alpha-Stable distribution¶

gsl-ran-levy-skew Function¶

Signature:

gsl-ran-levy-skew(rng, c, alpha, beta) => (variate)

Parameters:

rng – Random number generator. An instance of <gsl-rng*>.
c – Scale. An instance of <gsl-rng*>.
alpha – Exponent. An instance of <c-double>.
beta – Skew. An instance of <c-double>.

Result variate:

A <c-double>

Gamma Distribution¶

gsl-ran-gamma Function¶

Signature:

(rng, a, b) => (variate)

Parameters:

rng – Random number generator. An instance of <gsl-rng*>.
a – Shape parameter. A <c-double>.
b – Scale parameter. A <c-double>.

Result variate:

Sample from a gamma distribution with shape = a and scale = b. A <c-double>.

gsl-ran-gamma-knuth Function¶

Signature:

(rng, a, b) => (variate)

Parameters:

rng – Random number generator. An instance of <gsl-rng*>.
a – Shape parameter. A <c-double>.
b – Scale parameter. A <c-double>.

Result variate:

Sample from a gamma distribution with shape = a and scale = b. A <c-double>.

gsl-ran-gamma-pdf Function¶

Signature:

(x, a, b) => (pdf)

Parameters:

x – Value. A <c-double>.
a – Shape parameter. A <c-double>.
b – Scale parameter. A <c-double>.

Result pdf:

Probability density function. A <c-double>

gsl-cdf-gamma-p Function¶

Signature:

(x, a, b) => (cd)

Parameters:

x – Value. A <c-double>.
a – Scale parameter. A <c-double>.
b – Scale parameter. A <c-double>.

Result cd:

Cumulative distribution function. A <c-double>

gsl-cdf-gamma-q Function¶

Signature:

(x, a, b) => (cd)

Parameters:

x – Value. A <c-double>.
a – Scale parameter. A <c-double>.
b – Scale parameter. A <c-double>.

Result cd:

A <c-double>

gsl-cdf-gamma-pinv Function¶

Signature:

(x, a, b) => (cd)

Parameters:

x – Value. A <c-double>.
a – Scale parameter. A <c-double>.
b – Scale parameter. A <c-double>.

Result cd:

A <c-double>

gsl-cdf-gamma-qinv Function¶

Signature:

(x, a, b) => (cd)

Parameters:

x – Value. A <c-double>.
a – Scale parameter. A <c-double>.
b – Scale parameter. A <c-double>.

Result cd:

A <c-double>

The Flat Distribution¶

gsl-ran-flat Function¶

Signature:

(rng, a, b) => (variate)

Parameters:

rng – Random number generator. An instance of <gsl-rng*>.
a – Shape parameter. A <c-double>.
b – Scale parameter. A <c-double>.

Result variate:

A <c-double>.

gsl-ran-flat-pdf Function¶

Signature:

(x, a, b) => (pdf)

Parameters:

x – Value. A <c-double>.
a – A <c-double>.
b – A <c-double>.

Result pdf:

A <c-double>

gsl-cdf-flat-q Function¶

Signature:

(x, sigma) => (cd)

Parameters:

x – Value. A <c-double>.
sigma – Scale parameter. A <c-double>.

Result cd:

Cumulative distribution function. A <c-double>

gsl-cdf-flat-p Function¶

Signature:

(x, a, b) => (cd)

Parameters:

x – Value. A <c-double>.
a – A <c-double>.
b – A <c-double>.

Result cd:

Cumulative distribution function. A <c-double>

gsl-cdf-flat-q Function

Signature:

(x, a, b) => (cd)

Parameters:

x – Value. A <c-double>.
a – A <c-double>.
b – A <c-double>.

Result cd:

A <c-double>

gsl-cdf-flat-pinv Function¶

Signature:

(x, a, b) => (cd)

Parameters:

x – Value. A <c-double>.
a – A <c-double>.
b – A <c-double>.

Result cd:

A <c-double>

gsl-cdf-flat-qinv Function¶

Signature:

(x, a, b) => (cd)

Parameters:

x – Value. A <c-double>.
a – Scale parameter. A <c-double>.
b – Scale parameter. A <c-double>.

Result cd:

A <c-double>

The Lognormal Distribution¶

gsl-ran-lognormal Function¶

Signature:

gsl-ran-lognormal rng zeta sigma => (variate)

Parameters:

rng – Random number generator. An instance of <gsl-rng*>.
zeta – A <c-double>.
sigma – A <c-double>.

Result variate:

A <c-double>.

gsl-ran-lognormal-pdf Function¶

Signature:

gsl-ran-lognormal-pdf x zeta sigma => (pdf)

Parameters:

x – Value. A <c-double>.
zeta – A <c-double>.
sigma – A <c-double>.

Result pdf:

A <c-double>

gsl-cdf-lognormal-p Function¶

Signature:

gsl-cdf-lognormal-p x zeta sigma => (cd)

Parameters:

x – A <c-double>.
zeta – A <c-double>.
sigma – A <c-double>.

Result cd:

A <c-double>

gsl-cdf-lognormal-q Function¶

Signature:

gsl-cdf-lognormal-q x zeta sigma => (cd)

Parameters:

x – Value. A <c-double>.
zeta – A <c-double>.
sigma – A <c-double>.

Result cd:

A <c-double>

gsl-cdf-lognormal-pinv Function¶

Signature:

gsl-cdf-lognormal-pinv p zeta sigma => (cd)

Parameters:

p – A <c-double>.
zeta – A <c-double>.
sigma – A <c-double>.

Result cd:

A <c-double>

gsl-cdf-lognormal-qinv Function¶

Signature:

gsl-cdf-lognormal-qinv q zeta sigma => (cd)

Parameters:

q – A <c-double>.
zeta – A <c-double>.
sigma – A <c-double>.

Result cd:

A <c-double>

The Chi-Square Distribution¶

gsl-ran-chisq Function¶

Signature:

gsl-ran-chisq rng nu => (variate)

Parameters:

rng – Random number generator. An instance of <gsl-rng*>.
nu – Degrees of freedom. A <c-double>.

Result variate:

A <c-double>.

gsl-ran-chisq-pdf Function¶

Signature:

gsl-ran-chisq-pdf x nu => (pdf)

Parameters:

x – Value. A <c-double>.
nu – Degrees of freedom. A <c-double>.

Result pdf:

A <c-double>.

gsl-cdf-chisq-p Function¶

Signature:

gsl-cdf-chisq-p x nu => (cd)

Parameters:

x – Value. A <c-double>.
nu – Degrees of freedom. A <c-double>.

Result cd:

A <c-double>

gsl-cdf-chisq-q Function¶

Signature:

gsl-cdf-chisq-q x nu => (cd)

Parameters:

x – Value. A <c-double>.
nu – Degrees of freedom. A <c-double>.

Result cd:

A <c-double>

gsl-cdf-chisq-pinv Function¶

Signature:

gsl-cdf-chisq-pinv p nu => (x)

Parameters:

p – Probability. A <c-double>.
nu – Degrees of freedom. A <c-double>.

Result x:

A <c-double>

gsl-cdf-chisq-qinv Function¶

Signature:

gsl-cdf-chisq-qinv q nu => (x)

Parameters:

q – Probability. A <c-double>.
nu – Degrees of freedom. A <c-double>.

Result x:

A <c-double>