# NAG FL InterfaceG05 (Rand)Random Number Generators

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G05 (Rand) Chapter Introduction – A description of the Chapter and an overview of the algorithms available.

Routine
Mark of
Introduction

Purpose
g05kff 22 nagf_rand_init_repeat
Initializes a pseudorandom number generator to give a repeatable sequence
g05kgf 22 nagf_rand_init_nonrepeat
Initializes a pseudorandom number generator to give a non-repeatable sequence
g05khf 22 nagf_rand_init_leapfrog
Primes a pseudorandom number generator for generating multiple streams using leap-frog
Primes a pseudorandom number generator for generating multiple streams using skip-ahead
Primes a pseudorandom number generator for generating multiple streams using skip-ahead, skipping ahead a power of $2$
g05ncf 22 nagf_rand_permute
Pseudorandom permutation of an integer vector
g05ndf 22 nagf_rand_sample
Pseudorandom sample from an integer vector
g05nef 23 nagf_rand_sample_wgt
Pseudorandom sample, without replacement, unequal weights
g05pdf 22 nagf_rand_times_garch_asym1
Generates a realization of a time series from a GARCH process with asymmetry of the form ${\left({\epsilon }_{t-1}+\gamma \right)}^{2}$
g05pef 22 nagf_rand_times_garch_asym2
Generates a realization of a time series from a GARCH process with asymmetry of the form ${\left(|{\epsilon }_{t-1}|+\gamma {\epsilon }_{t-1}\right)}^{2}$
g05pff 22 nagf_rand_times_garch_gjr
Generates a realization of a time series from an asymmetric Glosten, Jagannathan and Runkle (GJR) GARCH process
g05pgf 22 nagf_rand_times_garch_exp
Generates a realization of a time series from an exponential GARCH (EGARCH) process
g05phf 22 nagf_rand_times_arma
Generates a realization of a time series from an ARMA model
g05pjf 22 nagf_rand_times_mv_varma
Generates a realization of a multivariate time series from a VARMA model
g05pmf 22 nagf_rand_times_smooth_exp
Generates a realization of a time series from an exponential smoothing model
g05pvf 25 nagf_rand_kfold_xyw
Permutes a matrix, vector, vector triplet into a form suitable for $K$-fold cross validation
g05pwf 25 nagf_rand_subsamp_xyw
Permutes a matrix, vector, vector triplet into a form suitable for random sub-sampling validation
g05pxf 22 nagf_rand_matrix_orthog
Generates a random orthogonal matrix
g05pyf 22 nagf_rand_matrix_corr
Generates a random correlation matrix
g05pzf 22 nagf_rand_matrix_2waytable
Generates a random two-way table
g05rcf 22 nagf_rand_copula_students_t
Generates a matrix of pseudorandom numbers from a Student's $t$-copula
g05rdf 22 nagf_rand_copula_normal
Generates a matrix of pseudorandom numbers from a Gaussian copula
g05ref 23 nagf_rand_copula_clayton_bivar
Generates a matrix of pseudorandom numbers from a bivariate Clayton/Cook–Johnson copula
g05rff 23 nagf_rand_copula_frank_bivar
Generates a matrix of pseudorandom numbers from a bivariate Frank copula
g05rgf 23 nagf_rand_copula_plackett_bivar
Generates a matrix of pseudorandom numbers from a bivariate Plackett copula
g05rhf 23 nagf_rand_copula_clayton
Generates a matrix of pseudorandom numbers from a multivariate Clayton/Cook–Johnson copula
g05rjf 23 nagf_rand_copula_frank
Generates a matrix of pseudorandom numbers from a multivariate Frank copula
g05rkf 23 nagf_rand_copula_gumbel
Generates a matrix of pseudorandom numbers from a Gumbel–Hougaard copula
g05ryf 22 nagf_rand_multivar_students_t
Generates a matrix of pseudorandom numbers from a multivariate Student's $t$-distribution
g05rzf 22 nagf_rand_multivar_normal
Generates a matrix of pseudorandom numbers from a multivariate Normal distribution
g05saf 22 nagf_rand_dist_uniform01
Generates a vector of pseudorandom numbers from a uniform distribution over $\left(0,1\right]$
g05sbf 22 nagf_rand_dist_beta
Generates a vector of pseudorandom numbers from a beta distribution
g05scf 22 nagf_rand_dist_cauchy
Generates a vector of pseudorandom numbers from a Cauchy distribution
g05sdf 22 nagf_rand_dist_chisq
Generates a vector of pseudorandom numbers from a ${\chi }^{2}$ distribution
g05sef 22 nagf_rand_dist_dirichlet
Generates a vector of pseudorandom numbers from a Dirichlet distribution
g05sff 22 nagf_rand_dist_exp
Generates a vector of pseudorandom numbers from an exponential distribution
g05sgf 22 nagf_rand_dist_expmix
Generates a vector of pseudorandom numbers from an exponential mix distribution
g05shf 22 nagf_rand_dist_f
Generates a vector of pseudorandom numbers from an $F$-distribution
g05sjf 22 nagf_rand_dist_gamma
Generates a vector of pseudorandom numbers from a gamma distribution
g05skf 22 nagf_rand_dist_normal
Generates a vector of pseudorandom numbers from a Normal distribution
g05slf 22 nagf_rand_dist_logistic
Generates a vector of pseudorandom numbers from a logistic distribution
g05smf 22 nagf_rand_dist_lognormal
Generates a vector of pseudorandom numbers from a log-normal distribution
g05snf 22 nagf_rand_dist_students_t
Generates a vector of pseudorandom numbers from a Student's $t$-distribution
g05spf 22 nagf_rand_dist_triangular
Generates a vector of pseudorandom numbers from a triangular distribution
g05sqf 22 nagf_rand_dist_uniform
Generates a vector of pseudorandom numbers from a uniform distribution over $\left[a,b\right]$
g05srf 22 nagf_rand_dist_vonmises
Generates a vector of pseudorandom numbers from a von Mises distribution
g05ssf 22 nagf_rand_dist_weibull
Generates a vector of pseudorandom numbers from a Weibull distribution
g05taf 22 nagf_rand_int_binomial
Generates a vector of pseudorandom integers from a binomial distribution
g05tbf 22 nagf_rand_logical
Generates a vector of pseudorandom logical values
g05tcf 22 nagf_rand_int_geom
Generates a vector of pseudorandom integers from a geometric distribution
g05tdf 22 nagf_rand_int_general
Generates a vector of pseudorandom integers from a general discrete distribution
g05tef 22 nagf_rand_int_hypergeom
Generates a vector of pseudorandom integers from a hypergeometric distribution
g05tff 22 nagf_rand_int_log
Generates a vector of pseudorandom integers from a logarithmic distribution
g05tgf 22 nagf_rand_int_multinomial
Generates a vector of pseudorandom integers from a multinomial distribution
g05thf 22 nagf_rand_int_negbin
Generates a vector of pseudorandom integers from a negative binomial distribution
g05tjf 22 nagf_rand_int_poisson
Generates a vector of pseudorandom integers from a Poisson distribution
g05tkf 22 nagf_rand_int_poisson_varmean
Generates a vector of pseudorandom integers from a Poisson distribution with varying mean
g05tlf 22 nagf_rand_int_uniform
Generates a vector of pseudorandom integers from a uniform distribution
g05xaf 24 nagf_rand_bb_init
Initializes the Brownian bridge generator
g05xbf 24 nagf_rand_bb
Generate paths for a free or non-free Wiener process using the Brownian bridge algorithm
g05xcf 24 nagf_rand_bb_inc_init
Initializes the generator which backs out the increments of sample paths generated by a Brownian bridge algorithm
g05xdf 24 nagf_rand_bb_inc
Backs out the increments from sample paths generated by a Brownian bridge algorithm
g05xef 24 nagf_rand_bb_make_bridge_order
Creates a Brownian bridge construction order out of a set of input times
g05yjf 21 nagf_rand_quasi_normal
Generates a Normal quasi-random number sequence
g05ykf 21 nagf_rand_quasi_lognormal
Generates a log-normal quasi-random number sequence
g05ylf 22 nagf_rand_quasi_init
Initializes a quasi-random number generator
g05ymf 22 nagf_rand_quasi_uniform
Generates a uniform quasi-random number sequence
g05ynf 22 nagf_rand_quasi_init_scrambled
Initializes a scrambled quasi-random number generator
g05zmf 24 nagf_rand_field_1d_user_setup
Setup for simulating one-dimensional random fields, user-defined variogram
g05znf 24 nagf_rand_field_1d_predef_setup
Setup for simulating one-dimensional random fields
g05zpf 24 nagf_rand_field_1d_generate
Generates realizations of a one-dimensional random field
g05zqf 24 nagf_rand_field_2d_user_setup
Setup for simulating two-dimensional random fields, user-defined variogram
g05zrf 24 nagf_rand_field_2d_predef_setup
Setup for simulating two-dimensional random fields, preset variogram
g05zsf 24 nagf_rand_field_2d_generate
Generates realizations of a two-dimensional random field
g05ztf 24 nagf_rand_field_fracbm_generate
Generates realizations of fractional Brownian motion