Random number distributionsFor more information about the functions see the documentation of GSL.
| Function | Description |
|---|---|
| gaussian(x,σ) | probability density p(x) for a Gaussian distribution with standard deviation σ |
| ugaussian(x) | unit Gaussian distribution. They are equivalent to the functions above with a standard deviation of σ = 1 |
| gaussianP(x,σ) | cumulative distribution functions P(x) for the Gaussian distribution with standard deviation σ |
| gaussianQ(x,σ) | cumulative distribution functions Q(x) for the Gaussian distribution with standard deviation σ |
| gaussianPinv(P,σ) | inverse cumulative distribution functions P(x) for the Gaussian distribution with standard deviation σ |
| gaussianQinv(Q,σ) | inverse cumulative distribution functions Q(x) for the Gaussian distribution with standard deviation σ |
| ugaussianP(x) | cumulative distribution function P(x) for the unit Gaussian distribution |
| ugaussianQ(x) | cumulative distribution function Q(x) for the unit Gaussian distribution |
| ugaussianPinv(P) | inverse cumulative distribution function P(x) for the unit Gaussian distribution |
| ugaussianQinv(Q) | inverse cumulative distribution function Q(x) for the unit Gaussian distribution |
| gaussiantail(x,a,σ) | probability density p(x) for a Gaussian tail distribution with standard deviation σ and lower limit a |
| ugaussiantail(x,a) | tail of a unit Gaussian distribution. They are equivalent to the functions above with a standard deviation of σ = 1 |
| gaussianbi(x,y,σx,σy,ρ) | probability density p(x,y) for a bivariate gaussian distribution with standard deviations σx, σy and correlation coefficient ρ |
| exponential(x,μ) | probability density p(x) for an exponential distribution with mean μ |
| exponentialP(x,μ) | cumulative distribution function P(x) for an exponential distribution with mean μ |
| exponentialQ(x,μ) | cumulative distribution function Q(x) for an exponential distribution with mean μ |
| exponentialPinv(P,μ) | inverse cumulative distribution function P(x) for an exponential distribution with mean μ |
| exponentialQinv(Q,μ) | inverse cumulative distribution function Q(x) for an exponential distribution with mean μ |
| laplace(x,a) | probability density p(x) for a Laplace distribution with width a |
| laplaceP(x,a) | cumulative distribution function P(x) for a Laplace distribution with width a |
| laplaceQ(x,a) | cumulative distribution function Q(x) for a Laplace distribution with width a |
| laplacePinv(P,a) | inverse cumulative distribution function P(x) for an Laplace distribution with width a |
| laplaceQinv(Q,a) | inverse cumulative distribution function Q(x) for an Laplace distribution with width a |
| exppow(x,a,b) | probability density p(x) for an exponential power distribution with scale parameter a and exponent b |
| exppowP(x,a,b) | cumulative probability density P(x) for an exponential power distribution with scale parameter a and exponent b |
| exppowQ(x,a,b) | cumulative probability density Q(x) for an exponential power distribution with scale parameter a and exponent b |
| cauchy(x,a) | probability density p(x) for a Cauchy (Lorentz) distribution with scale parameter a |
| cauchyP(x,a) | cumulative distribution function P(x) for a Cauchy distribution with scale parameter a |
| cauchyQ(x,a) | cumulative distribution function Q(x) for a Cauchy distribution with scale parameter a |
| cauchyPinv(P,a) | inverse cumulative distribution function P(x) for a Cauchy distribution with scale parameter a |
| cauchyQinv(Q,a) | inverse cumulative distribution function Q(x) for a Cauchy distribution with scale parameter a |
| rayleigh(x,σ) | probability density p(x) for a Rayleigh distribution with scale parameter σ |
| rayleighP(x,σ) | cumulative distribution function P(x) for a Rayleigh distribution with scale parameter σ |
| rayleighQ(x,σ) | cumulative distribution function Q(x) for a Rayleigh distribution with scale parameter σ |
| rayleighPinv(P,σ) | inverse cumulative distribution function P(x) for a Rayleigh distribution with scale parameter σ |
| rayleighQinv(Q,σ) | inverse cumulative distribution function Q(x) for a Rayleigh distribution with scale parameter σ |
| rayleigh_tail(x,a,σ) | probability density p(x) for a Rayleigh tail distribution with scale parameter σ and lower limit a |
| landau(x) | probability density p(x) for the Landau distribution |
| gammapdf(x,a,b) | probability density p(x) for a gamma distribution with parameters a and b |
| gammaP(x,a,b) | cumulative distribution function P(x) for a gamma distribution with parameters a and b |
| gammaQ(x,a,b) | cumulative distribution function Q(x) for a gamma distribution with parameters a and b |
| gammaPinv(P,a,b) | inverse cumulative distribution function P(x) for a gamma distribution with parameters a and b |
| gammaQinv(Q,a,b) | inverse cumulative distribution function Q(x) for a gamma distribution with parameters a and b |
| flat(x,a,b) | probability density p(x) for a uniform distribution from a to b |
| flatP(x,a,b) | cumulative distribution function P(x) for a uniform distribution from a to b |
| flatQ(x,a,b) | cumulative distribution function Q(x) for a uniform distribution from a to b |
| flatPinv(P,a,b) | inverse cumulative distribution function P(x) for a uniform distribution from a to b |
| flatQinv(Q,a,b) | inverse cumulative distribution function Q(x) for a uniform distribution from a to b |
| lognormal(x,ζ,σ) | probability density p(x) for a lognormal distribution with parameters ζ and σ |
| lognormalP(x,ζ,σ) | cumulative distribution function P(x) for a lognormal distribution with parameters ζ and σ |
| lognormalQ(x,ζ,σ) | cumulative distribution function Q(x) for a lognormal distribution with parameters ζ and σ |
| lognormalPinv(P,ζ,σ) | inverse cumulative distribution function P(x) for a lognormal distribution with parameters ζ and σ |
| lognormalQinv(Q,ζ,σ) | inverse cumulative distribution function Q(x) for a lognormal distribution with parameters ζ and σ |
| chisq(x,ν) | probability density p(x) for a χ2 distribution with ν degrees of freedom |
| chisqP(x,ν) | cumulative distribution function P(x) for a χ2 distribution with ν degrees of freedom |
| chisqQ(x,ν) | cumulative distribution function Q(x) for a χ2 distribution with ν degrees of freedom |
| chisqPinv(P,ν) | inverse cumulative distribution function P(x) for a χ2 distribution with ν degrees of freedom |
| chisqQinv(Q,ν) | inverse cumulative distribution function Q(x) for a χ2 distribution with ν degrees of freedom |
| fdist(x,ν1,ν2) | probability density p(x) for an F-distribution with ν1 and ν2 degrees of freedom |
| fdistP(x,ν1,ν2) | cumulative distribution function P(x) for an F-distribution with ν1 and ν2 degrees of freedom |
| fdistQ(x,ν1,ν2) | cumulative distribution function Q(x) for an F-distribution with ν1 and ν2 degrees of freedom |
| fdistPinv(P,ν1,ν2) | inverse cumulative distribution function P(x) for an F-distribution with ν1 and ν2 degrees of freedom |
| fdistQinv(Q,ν1,ν2) | inverse cumulative distribution function Q(x) for an F-distribution with ν1 and ν2 degrees of freedom |
| tdist(x,ν) | probability density p(x) for a t-distribution with ν degrees of freedom |
| tdistP(x,ν) | cumulative distribution function P(x) for a t-distribution with ν degrees of freedom |
| tdistQ(x,ν) | cumulative distribution function Q(x) for a t-distribution with ν degrees of freedom |
| tdistPinv(P,ν) | inverse cumulative distribution function P(x) for a t-distribution with ν degrees of freedom |
| tdistQinv(Q,ν) | inverse cumulative distribution function Q(x) for a t-distribution with ν degrees of freedom |
| betapdf(x,a,b) | probability density p(x) for a beta distribution with parameters a and b |
| betaP(x,a,b) | cumulative distribution function P(x) for a beta distribution with parameters a and b |
| betaQ(x,a,b) | cumulative distribution function Q(x) for a beta distribution with parameters a and b |
| betaPinv(P,a,b) | inverse cumulative distribution function P(x) for a beta distribution with parameters a and b |
| betaQinv(Q,a,b) | inverse cumulative distribution function Q(x) for a beta distribution with parameters a and b |
| logistic(x,a) | probability density p(x) for a logistic distribution with scale parameter a |
| logisticP(x,a) | cumulative distribution function P(x) for a logistic distribution with scale parameter a |
| logisticQ(x,a) | cumulative distribution function Q(x) for a logistic distribution with scale parameter a |
| logisticPinv(P,a) | inverse cumulative distribution function P(x) for a logistic distribution with scale parameter a |
| logisticQinv(Q,a) | inverse cumulative distribution function Q(x) for a logistic distribution with scale parameter a |
| pareto(x,a,b) | probability density p(x) for a Pareto distribution with exponent a and scale b |
| paretoP(x,a,b) | cumulative distribution function P(x) for a Pareto distribution with exponent a and scale b |
| paretoQ(x,a,b) | cumulative distribution function Q(x) for a Pareto distribution with exponent a and scale b |
| paretoPinv(P,a,b) | inverse cumulative distribution function P(x) for a Pareto distribution with exponent a and scale b |
| paretoQinv(Q,a,b) | inverse cumulative distribution function Q(x) for a Pareto distribution with exponent a and scale b |
| weibull(x,a,b) | probability density p(x) for a Weibull distribution with scale a and exponent b |
| weibullP(x,a,b) | cumulative distribution function P(x) for a Weibull distribution with scale a and exponent b |
| weibullQ(x,a,b) | cumulative distribution function Q(x) for a Weibull distribution with scale a and exponent b |
| weibullPinv(P,a,b) | inverse cumulative distribution function P(x) for a Weibull distribution with scale a and exponent b |
| weibullQinv(Q,a,b) | inverse cumulative distribution function Q(x) for a Weibull distribution with scale a and exponent b |
| gumbel1(x,a,b) | probability density p(x) for a Type-1 Gumbel distribution with parameters a and b |
| gumbel1P(x,a,b) | cumulative distribution function P(x) for a Type-1 Gumbel distribution with parameters a and b |
| gumbel1Q(x,a,b) | cumulative distribution function Q(x) for a Type-1 Gumbel distribution with parameters a and b |
| gumbel1Pinv(P,a,b) | inverse cumulative distribution function P(x) for a Type-1 Gumbel distribution with parameters a and b |
| gumbel1Qinv(Q,a,b) | inverse cumulative distribution function Q(x) for a Type-1 Gumbel distribution with parameters a and b |
| gumbel2(x,a,b) | probability density p(x) at X for a Type-2 Gumbel distribution with parameters A and B |
| gumbel2P(x,a,b) | cumulative distribution function P(x) for a Type-2 Gumbel distribution with parameters a and b |
| gumbel2Q(x,a,b) | cumulative distribution function Q(x) for a Type-2 Gumbel distribution with parameters a and b |
| gumbel2Pinv(P,a,b) | inverse cumulative distribution function P(x) for a Type-2 Gumbel distribution with parameters a and b |
| gumbel2Qinv(Q,a,b) | inverse cumulative distribution function Q(x) for a Type-2 Gumbel distribution with parameters a and b |
| poisson(k,μ) | probability p(k) of obtaining k from a Poisson distribution with mean μ |
| poissonP(k,μ) | cumulative distribution functions P(k) for a Poisson distribution with mean μ |
| poissonQ(k,μ) | cumulative distribution functions Q(k) for a Poisson distribution with mean μ |
| bernoulli(k,p) | probability p(k) of obtaining k from a Bernoulli distribution with probability parameter p |
| binomial(k,p,n) | probability p(k) of obtaining p from a binomial distribution with parameters p and n |
| binomialP(k,p,n) | cumulative distribution functions P(k) for a binomial distribution with parameters p and n |
| binomialQ(k,p,n) | cumulative distribution functions Q(k) for a binomial distribution with parameters p and n |
| nbinomial(k,p,n) | probability p(k) of obtaining k from a negative binomial distribution with parameters p and n |
| nbinomialP(k,p,n) | cumulative distribution functions P(k) for a negative binomial distribution with parameters p and n |
| nbinomialQ(k,p,n) | cumulative distribution functions Q(k) for a negative binomial distribution with parameters p and n |
| pascal(k,p,n) | probability p(k) of obtaining k from a Pascal distribution with parameters p and n |
| pascalP(k,p,n) | cumulative distribution functions P(k) for a Pascal distribution with parameters p and n |
| pascalQ(k,p,n) | cumulative distribution functions Q(k) for a Pascal distribution with parameters p and n |
| geometric(k,p) | probability p(k) of obtaining k from a geometric distribution with probability parameter p |
| geometricP(k,p) | cumulative distribution functions P(k) for a geometric distribution with parameter p |
| geometricQ(k,p) | cumulative distribution functions Q(k) for a geometric distribution with parameter p |
| hypergeometric(k,n1,n2,t) | probability p(k) of obtaining k from a hypergeometric distribution with parameters n1, n2, t |
| hypergeometricP(k,n1,n2,t) | cumulative distribution function P(k) for a hypergeometric distribution with parameters n1, n2, t |
| hypergeometricQ(k,n1,n2,t) | cumulative distribution function Q(k) for a hypergeometric distribution with parameters n1, n2, t |
| logarithmic(k,p) | probability p(k) of obtaining K from a logarithmic distribution with probability parameter p |