g05kh allows for the generation of multiple, independent, sequences of pseudorandom numbers using the leap-frog method.

g05kj allows for the generation of multiple, independent, sequences of pseudorandom numbers using the skip-ahead method.

The base pseudorandom number sequence defined by state is advanced $n$ places.

g05kk allows for the generation of multiple, independent, sequences of pseudorandom numbers using the skip-ahead method. The base pseudorandom number sequence defined by state is advanced $2^n$ places.

g05nc performs a pseudorandom permutation of a vector of integers.

g05nd selects a pseudorandom sample without replacement from an integer vector.

g05pd generates a given number of terms of a type I $\text{AGARCH}\left(p,q\right)$ process (see Engle and Ng (1993)).

g05pe generates a given number of terms of a type II $\text{AGARCH}\left(p,q\right)$ process (see Engle and Ng (1993)).

g05pf generates a given number of terms of a GJR $\text{GARCH}\left(p,q\right)$ process (see Glosten et al. (1993)).

g05pg generates a given number of terms of an exponential $\text{GARCH}\left(p,q\right)$ process (see Engle and Ng (1993)).

g05ph generates a realization of a univariate time series from an autoregressive moving average (ARMA) model. The realization may be continued or a new realization generated at subsequent calls to g05ph.

g05pj generates a realization of a multivariate time series from a vector autoregressive moving average (VARMA) model. The realization may be continued or a new realization generated at subsequent calls to g05pj.

g05pm simulates from an exponential smoothing model, where the model uses either single exponential, double exponential or a Holt–Winters method.

g05px generates a random orthogonal matrix.

g05py generates a random correlation matrix with given eigenvalues.

g05pz generates a random two-way table.

g05rc sets up a reference vector and generates an array of pseudorandom numbers from a Student's $t$ copula with $\nu$ degrees of freedom and covariance matrix $\frac{\nu }{\nu -2}C$.

g05rd sets up a reference vector and generates an array of pseudorandom numbers from a Normal (Gaussian) copula with covariance matrix $C$.

g05ry sets up a reference vector and generates an array of pseudorandom numbers from a multivariate Student's $t$ distribution with $\nu$ degrees of freedom, mean vector $a$ and covariance matrix $\frac{\nu }{\nu -2}C$.

g05rz sets up a reference vector and generates an array of pseudorandom numbers from a multivariate Normal distribution with mean vector $a$ and covariance matrix $C$.

g05sa generates a vector of pseudorandom numbers taken from a uniform distribution between $0$ and $1$.

g05sb generates a vector of pseudorandom numbers taken from a beta distribution with parameters $a$ and $b$.

g05sc generates a vector of pseudorandom numbers from a Cauchy distribution with median $a$ and semi-interquartile range $b$.

g05sd generates a vector of pseudorandom numbers taken from a ${\chi }^2$-distribution with $\nu$ degrees of freedom.

g05se generates a vector of pseudorandom numbers taken from a Dirichlet distribution.

g05sf generates a vector of pseudorandom numbers from a (negative) exponential distribution with mean $a$.

g05sg generates a vector of pseudorandom numbers from an exponential mix distribution composed of $m$ exponential distributions each having a mean $a_i$ and weight $w_i$.

g05sh generates a vector of pseudorandom numbers taken from an $F$ (or Fisher's variance ratio) distribution with $\mu$ and $\nu$ degrees of freedom.

g05sj generates a vector of pseudorandom numbers taken from a gamma distribution with parameters $a$ and $b$.

g05sk generates a vector of pseudorandom numbers taken from a Normal (Gaussian) distribution with mean $\mu$ and variance ${\sigma }^2$.

g05sl generates a vector of pseudorandom numbers from a logistic distribution with mean $a$ and spread $b$.

g05sm generates a vector of pseudorandom numbers from a log-normal distribution with parameters $\mu$ and ${\sigma }^2$.

g05sn generates a vector of pseudorandom numbers taken from a Student's $t$-distribution with $\nu$ degrees of freedom.

g05sp generates a vector of pseudorandom numbers from a triangular distribution with parameters $x_{\min }$, $x_{\mathrm{med}}$ and $x_{\max }$.

g05sq generates a vector of pseudorandom numbers uniformly distributed over the interval $\left[a,b\right]$.

g05sr generates a vector of pseudorandom numbers from a von Mises distribution with concentration parameter $\kappa$.

g05ss generates a vector of pseudorandom numbers from a two parameter Weibull distribution with shape parameter $a$ and scale parameter $b$.

g05ta generates a vector of pseudorandom integers from the discrete binomial distribution with parameters $m$ and $p$.

g05tb generates a vector of pseudorandom logical values – true with probability $p$ and false with probability $\left(1-p\right)$.

g05tc generates a vector of pseudorandom integers from the discrete geometric distribution with probability $p$ of success at a trial.

g05td generates a vector of pseudorandom integers from a discrete distribution with a given PDF (probability density function) or CDF (cumulative distribution function) $p$.

g05te generates a vector of pseudorandom integers from the discrete hypergeometric distribution of the number of specified items in a sample of size $l$, taken from a population of size $k$ with $m$ specified items in it.

g05tf generates a vector of pseudorandom integers from the discrete logarithmic distribution with parameter $a$.

g05tg generates a sequence of $n$ variates, each consisting of $k$ pseudorandom integers, from the discrete multinomial distribution with $k$ outcomes and $m$ trials, where the outcomes have probabilities $p_1,p_2,\dots ,p_k$ respectively.

g05th generates a vector of pseudorandom integers from the discrete negative binomial distribution with parameter $m$ and probability $p$ of success at a trial.

g05tj generates a vector of pseudorandom integers from the discrete Poisson distribution with mean $\lambda$.

g05tk generates a vector of pseudorandom integers, each from a discrete Poisson distribution with differing parameter.

g05tl generates a vector of pseudorandom integers uniformly distributed over the interval $\left[a,b\right]$.

g05yl initializes a quasi-random generator prior to calling g05ym (G05YJF not in this release) (G05YKF not in this release).

g05ym generates a uniformly distributed low-discrepancy sequence as proposed by Sobol, Faure or Niederreiter. It must be preceded by a call to one of the initialization methods g05yl or g05yn.

g05yn initializes a scrambled quasi-random generator prior to calling g05ym (G05YJF not in this release) (G05YKF not in this release). It must be preceded by a call to one of the pseudorandom initialization methods (G05KFF not in this release) (G05KGF not in this release).