rand_exp SYNOPSIS Generate exponentially distributed random numbers USAGE X = rand_exp([Rand_Type g,] beta [,num]) DESCRIPTION This function generates random numbers that are distributed according to an exponential distribution with parameter beta > 0. The distribution's probability density is given by P(x,beta) = (1/beta) exp(-x/beta) The optional parameter `g' may be used to specify the underlying random number generator. See the documentation for the `rand_new' function for more information. The `num' parameter indicates that `num' random values are to be generated and returned as an array. NOTES The exponential generator is commonly used to simulate waiting times between events. SEE ALSO rand_new, rand_uniform -------------------------------------------------------------- rand_int SYNOPSIS Generate random integers USAGE X = rand_int ([Rand_Type g,] imin, imax [,num]) DESCRIPTION This function may be used to generate a random integer `X' such that `imin <= X <= imax'. The optional parameter `g' may be used to specify the underlying random number generator. See the documentation for the `rand_new' function for more information. The `num' parameter indicates that `num' random values are to be generated and returned as an array. SEE ALSO rand_uniform, rand, rand_new -------------------------------------------------------------- rand_tdist SYNOPSIS Generate random numbers from the Student t distribution USAGE X = rand_tdist ([Rand_Type g,] nu [,num]) DESCRIPTION This function generates random numbers that are distributed according to the Student-t distribution with nu>0.0 degrees of freedom. The optional parameter `g' may be used to specify the underlying random number generator. See the documentation for the `rand_new' function for more information. The `num' parameter indicates that `num' random values are to be generated and returned as an array. SEE ALSO rand_uniform, rand_new, rand_chisq, rand_fdist -------------------------------------------------------------- rand_fdist SYNOPSIS Generate random numbers from the F distribution USAGE X = rand_fdist ([Rand_Type g,], nu1, nu2 [,num]) DESCRIPTION This function generates random numbers that are distributed according to the F-distribution, which is the ratio of two chi-squared distributed variates whose degrees of freedom are given by `nu1' (numerator) and `nu2' (denominator). The optional parameter `g' may be used to specify the underlying random number generator. See the documentation for the `rand_new' function for more information. The `num' parameter indicates that `num' random values are to be generated and returned as an array. SEE ALSO rand_uniform, rand_chisq, rand_tdist, rand_gauss, rand_new -------------------------------------------------------------- rand_chisq SYNOPSIS Generate Chi-Square distributed random numbers USAGE X = rand_fdist ([Rand_Type g,] nu, [,num]) DESCRIPTION This function generates random numbers that are distributed according to the Chi-squared distribution with `nu > 0' degrees of freedom. The optional parameter `g' may be used to specify the underlying random number generator. See the documentation for the `rand_new' function for more information. The `num' parameter indicates that `num' random values are to be generated and returned as an array. SEE ALSO rand_uniform, rand_fdist, rand_tdist, rand_gauss, rand_new -------------------------------------------------------------- rand_flat SYNOPSIS Generate uniformly distributed random numbers USAGE X = rand_fdist ([Rand_Type g,] xmin, xmax [,num]) DESCRIPTION This function generates random double-precision floating point numbers that are uniformly distributed in the range `xmin<=X0.0'. The optional parameter `g' may be used to specify the underlying random number generator. See the documentation for the `rand_new' function for more information. The `num' parameter indicates that `num' random values are to be generated and returned as an array. SEE ALSO rand_beta, rand_uniform, rand_binomial, rand_new -------------------------------------------------------------- rand_binomial SYNOPSIS Generate random numbers from the binomial distribution USAGE X = rand_binomial ([Rand_Type g,], p, n, [,num]) DESCRIPTION This function generates binomial distributed random numbers according to the probability density P(x;p,n) = n!/(k!*(n-k)!) * p^k * (1-p)^(n-k) where `n' is a non-negative integer and `0<=p<=1'. The optional parameter `g' may be used to specify the underlying random number generator. See the documentation for the `rand_new' function for more information. The `num' parameter indicates that `num' random values are to be generated and returned as an array. SEE ALSO rand_gamma, rand_poisson, rand_uniform, rand_new -------------------------------------------------------------- rand_poisson SYNOPSIS Generate Poisson distributed random numbers USAGE k = rand_poisson ([Rand_Type g,] mu [,num]) DESCRIPTION This function generates random unsigned integers that are poisson-distributed according to the probability distribution P(k;mu) = mu^k/k! * exp(-mu) where `mu>0.0'. The optional parameter `g' may be used to specify the underlying random number generator. See the documentation for the `rand_new' function for more information. The `num' parameter indicates that `num' random values are to be generated and returned as an array. SEE ALSO rand_gauss, rand_uniform, rand_binomial, rand_new -------------------------------------------------------------- rand_geometric SYNOPSIS Generate random numbers from the geometric distribution USAGE k = rand_geometric ([Rand_Type g,] p [,num]) DESCRIPTION This function generates random numbers that are distributed according to a geometric distribution with a probability density P(k; p) = p*(1-p)^(k-1) where `0<=p<=1' The optional parameter `g' may be used to specify the underlying random number generator. See the documentation for the `rand_new' function for more information. The `num' parameter indicates that `num' random values are to be generated and returned as an array. SEE ALSO rand_poisson, rand_exp, rand_gauss, rand_uniform, rand_new -------------------------------------------------------------- rand_cauchy SYNOPSIS Generate random numbers from the Cauchy distribution USAGE X = rand_cauchy ([Rand_Type g,] gamma [,num]) DESCRIPTION This function generates random numbers that are distributed according to a cauchy-distribution with a probability density P(x; gamma) = 1/(PI*gamma)/(1+(x/gamma)^2) where `gamma>=0.0'. The optional parameter `g' may be used to specify the underlying random number generator. See the documentation for the `rand_new' function for more information. The `num' parameter indicates that `num' random values are to be generated and returned as an array. SEE ALSO rand_gauss, rand_poisson, rand_exp, rand_new -------------------------------------------------------------- rand_beta SYNOPSIS Generate random numbers from the beta distribution USAGE X = rand_fdist ([Rand_Type g,] a, b [,num]) DESCRIPTION This function generates random numbers that are distributed according to a Beta-distribution with a probability density P(x; a,b) = x^(a-1)*(1-x)^(b-1)/B(a,b) where `a, b > 0'. SEE ALSO rand_gamma, rand_binomial, rand_chisq -------------------------------------------------------------- rand_gauss SYNOPSIS Generate gaussian-distributed random numbers USAGE X = rand_gauss ([Rand_Type g,] sigma [,num]) DESCRIPTION This function generates gaussian random numbers with the specified sigma and mean of 0 according to the probability density P(x; sigma) = 1/sqrt(2*PI*sigma^2) * exp(-0.5*x^2/sigma^2) The optional parameter `g' may be used to specify the underlying random number generator. See the documentation for the `rand_new' function for more information. The `num' parameter indicates that `num' random values are to be generated and returned as an array. NOTES This implementation utilizes the Box-Muller algorithm. SEE ALSO rand_uniform, rand_poisson, rand_chisq, rand_gauss, rand_new -------------------------------------------------------------- rand SYNOPSIS Generate random integers numbers USAGE X = rand ([Rand_Type g,] [,num]) DESCRIPTION This function generates unsigned 32 bit randomly distributed integers on the closed interval 0<=X<=0xFFFFFFFFUL. The optional parameter `g' may be used to specify the underlying random number generator. See the documentation for the `rand_new' function for more information. The `num' parameter indicates that `num' random values are to be generated and returned as an array. SEE ALSO rand_new, rand_int, rand_uniform, rand_flat -------------------------------------------------------------- rand_uniform_pos SYNOPSIS Generate uniform positive random numbers USAGE X = rand_uniform_pos ([Rand_Type] [num]) DESCRIPTION This function generates uniformly distributed random numbers in open interval `0