## Random number distributions

FunctionDescription
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,σxy,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,ν12)probability density p(x) for an F-distribution with ν1 and ν2 degrees of freedom
fdistP(x,ν12)cumulative distribution function P(x) for an F-distribution with ν1 and ν2 degrees of freedom
fdistQ(x,ν12)cumulative distribution function Q(x) for an F-distribution with ν1 and ν2 degrees of freedom
fdistPinv(P,ν12)inverse cumulative distribution function P(x) for an F-distribution with ν1 and ν2 degrees of freedom
fdistQinv(Q,ν12)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