Randist.i

   1 %module "Math::GSL::Randist"
   2 %include "typemaps.i"
   3
   4 void gsl_ran_dir_2d (const gsl_rng * r, double *OUTPUT, double *OUTPUT);
   5 void gsl_ran_dir_2d_trig_method (const gsl_rng * r, double *OUTPUT, double *OUTPUT);
   6 void gsl_ran_dir_3d (const gsl_rng * r, double *OUTPUT, double *OUTPUT, double *OUTPUT);
   7 void gsl_ran_bivariate_gaussian (const gsl_rng * r, double sigma_x, double sigma_y, double rho, double *OUTPUT, double *OUTPUT);
   8
   9 %typemap(in) void * {
  10     AV *tempav;
  11     I32 len;
  12     int i,x;
  13     SV  **tv;
  14
  15     if (!SvROK($input))
  16         croak("Argument $argnum is not a reference.");
  17     if (SvTYPE(SvRV($input)) != SVt_PVAV)
  18         croak("Argument $argnum is not an array.");
  19
  20     tempav = (AV*)SvRV($input);
  21     len = av_len(tempav);
  22     $1 = (int **) malloc((len+2)*sizeof(int *));
  23     for (i = 0; i <= len; i++) {
  24         tv = av_fetch(tempav, i, 0);
  25         x  = SvIV(*tv);
  26         memset((int*)($1+i), x , 1);
  27         //printf("curr = %d\n", (int)($1+i) );
  28     }
  29 };
  30 %typemap(freearg) void * {
  31     free($1);
  32 }
  33
  34 %{
  35     #include "gsl/gsl_randist.h"
  36 %}
  37 %include "gsl/gsl_randist.h"
  38
  39 %perlcode %{
  40
  41 our @EXPORT_OK = qw/gsl_ran_bernoulli gsl_ran_bernoulli_pdf gsl_ran_beta
  42                     gsl_ran_beta_pdf gsl_ran_binomial gsl_ran_binomial_knuth
  43                     gsl_ran_binomial_tpe gsl_ran_binomial_pdf gsl_ran_exponential
  44                     gsl_ran_exponential_pdf gsl_ran_exppow gsl_ran_exppow_pdf
  45                     gsl_ran_cauchy gsl_ran_cauchy_pdf gsl_ran_chisq
  46                     gsl_ran_chisq_pdf gsl_ran_dirichlet gsl_ran_dirichlet_pdf
  47                     gsl_ran_dirichlet_lnpdf gsl_ran_erlang gsl_ran_erlang_pdf
  48                     gsl_ran_fdist gsl_ran_fdist_pdf gsl_ran_flat
  49                     gsl_ran_flat_pdf gsl_ran_gamma gsl_ran_gamma_int
  50                     gsl_ran_gamma_pdf gsl_ran_gamma_mt gsl_ran_gamma_knuth
  51                     gsl_ran_gaussian gsl_ran_gaussian_ratio_method gsl_ran_gaussian_ziggurat
  52                     gsl_ran_gaussian_pdf gsl_ran_ugaussian gsl_ran_ugaussian_ratio_method
  53                     gsl_ran_ugaussian_pdf gsl_ran_gaussian_tail gsl_ran_gaussian_tail_pdf
  54                     gsl_ran_ugaussian_tail gsl_ran_ugaussian_tail_pdf gsl_ran_bivariate_gaussian
  55                     gsl_ran_bivariate_gaussian_pdf gsl_ran_landau gsl_ran_landau_pdf
  56                     gsl_ran_geometric gsl_ran_geometric_pdf gsl_ran_hypergeometric
  57                     gsl_ran_hypergeometric_pdf gsl_ran_gumbel1 gsl_ran_gumbel1_pdf
  58                     gsl_ran_gumbel2 gsl_ran_gumbel2_pdf gsl_ran_logistic
  59                     gsl_ran_logistic_pdf gsl_ran_lognormal gsl_ran_lognormal_pdf
  60                     gsl_ran_logarithmic gsl_ran_logarithmic_pdf gsl_ran_multinomial
  61                     gsl_ran_multinomial_pdf gsl_ran_multinomial_lnpdf
  62                     gsl_ran_negative_binomial gsl_ran_negative_binomial_pdf gsl_ran_pascal
  63                     gsl_ran_pascal_pdf gsl_ran_pareto gsl_ran_pareto_pdf
  64                     gsl_ran_poisson gsl_ran_poisson_array
  65                     gsl_ran_poisson_pdf gsl_ran_rayleigh gsl_ran_rayleigh_pdf
  66                     gsl_ran_rayleigh_tail gsl_ran_rayleigh_tail_pdf gsl_ran_tdist
  67                     gsl_ran_tdist_pdf gsl_ran_laplace gsl_ran_laplace_pdf
  68                     gsl_ran_levy gsl_ran_levy_skew gsl_ran_weibull
  69                     gsl_ran_weibull_pdf gsl_ran_dir_2d gsl_ran_dir_2d_trig_method
  70                     gsl_ran_dir_3d gsl_ran_dir_nd gsl_ran_shuffle
  71                     gsl_ran_choose gsl_ran_sample
  72                     gsl_ran_discrete_t gsl_ran_discrete_free gsl_ran_discrete_preproc
  73                     gsl_ran_discrete gsl_ran_discrete_pdf
  74                 /;
  75
  76 our %EXPORT_TAGS = (
  77         all                 => [  @EXPORT_OK ],
  78         logarithmic         => [ gsl_ran_logarithmic , gsl_ran_logarithmic_pdf ],
  79         choose              => [ gsl_ran_choose ],
  80         exponential         => [ gsl_ran_exponential , gsl_ran_exponential_pdf ],
  81         gumbel1             => [ gsl_ran_gumbel1 , gsl_ran_gumbel1_pdf ],
  82         exppow              => [ gsl_ran_exppow , gsl_ran_exppow_pdf ],
  83         sample              => [ gsl_ran_sample ],
  84         logistic            => [ gsl_ran_logistic , gsl_ran_logistic_pdf ],
  85         gaussian            => [
  86                                  gsl_ran_gaussian , gsl_ran_gaussian_ratio_method , gsl_ran_gaussian_ziggurat,
  87                                  gsl_ran_gaussian_pdf , gsl_ran_gaussian_tail , gsl_ran_gaussian_tail_pdf
  88                                ],
  89         poisson             => [ gsl_ran_poisson , gsl_ran_poisson_array , gsl_ran_poisson_pdf ],
  90         binomial            => [ gsl_ran_binomial , gsl_ran_binomial_knuth , gsl_ran_binomial_tpe ,
  91                                  gsl_ran_binomial_pdf ],
  92         fdist               => [ gsl_ran_fdist , gsl_ran_fdist_pdf ],
  93         chisq               => [ gsl_ran_chisq , gsl_ran_chisq_pdf ],
  94         gamma               => [ gsl_ran_gamma , gsl_ran_gamma_int , gsl_ran_gamma_pdf , gsl_ran_gamma_mt , gsl_ran_gamma_knuth ],
  95         hypergeometric      => [ gsl_ran_hypergeometric , gsl_ran_hypergeometric_pdf ],
  96         dirichlet           => [ gsl_ran_dirichlet , gsl_ran_dirichlet_pdf , gsl_ran_dirichlet_lnpdf ],
  97         negative            => [ gsl_ran_negative_binomial , gsl_ran_negative_binomial_pdf ],
  98         flat                => [ gsl_ran_flat , gsl_ran_flat_pdf ],
  99         geometric           => [ gsl_ran_geometric , gsl_ran_geometric_pdf ],
 100         discrete            => [ gsl_ran_discrete , gsl_ran_discrete_pdf],
 101         tdist               => [ gsl_ran_tdist , gsl_ran_tdist_pdf ],
 102         ugaussian           => [ gsl_ran_ugaussian , gsl_ran_ugaussian_ratio_method , gsl_ran_ugaussian_pdf ,
 103                                  gsl_ran_ugaussian_tail , gsl_ran_ugaussian_tail_pdf ],
 104         rayleigh            => [ gsl_ran_rayleigh , gsl_ran_rayleigh_pdf , gsl_ran_rayleigh_tail ,
 105                                  gsl_ran_rayleigh_tail_pdf ],
 106         dir                 => [ gsl_ran_dir_2d , gsl_ran_dir_2d_trig_method , gsl_ran_dir_3d , gsl_ran_dir_nd ],
 107         pascal              => [ gsl_ran_pascal , gsl_ran_pascal_pdf ],
 108         gumbel2             => [ gsl_ran_gumbel2 , gsl_ran_gumbel2_pdf ],
 109         shuffle             => [ gsl_ran_shuffle ],
 110         landau              => [ gsl_ran_landau , gsl_ran_landau_pdf ],
 111         bernoulli           => [ gsl_ran_bernoulli , gsl_ran_bernoulli_pdf ],
 112         weibull             => [ gsl_ran_weibull , gsl_ran_weibull_pdf ],
 113         multinomial         => [ gsl_ran_multinomial , gsl_ran_multinomial_pdf , gsl_ran_multinomial_lnpdf ],
 114         beta                => [ gsl_ran_beta , gsl_ran_beta_pdf ],
 115         lognormal           => [ gsl_ran_lognormal , gsl_ran_lognormal_pdf ],
 116         laplace             => [ gsl_ran_laplace , gsl_ran_laplace_pdf ],
 117         erlang              => [ gsl_ran_erlang , gsl_ran_erlang_pdf ],
 118         cauchy              => [ gsl_ran_cauchy , gsl_ran_cauchy_pdf ],
 119         levy                => [ gsl_ran_levy , gsl_ran_levy_skew ],
 120         bivariate           => [ gsl_ran_bivariate_gaussian , gsl_ran_bivariate_gaussian_pdf ],
 121         pareto              => [ gsl_ran_pareto , gsl_ran_pareto_pdf ]
 122 );
 123
 124 __END__
 125
 126 =head1 NAME
 127
 128 Math::GSL::Randist - Probability Distributions
 129
 130 =head1 SYNOPSIS
 131
 132 use Math::GSL::Randist qw/:all/;
 133
 134 =head1 DESCRIPTION
 135
 136  Here is a list of all the functions included in this module :
 137
 138 =over
 139
 140 =item gsl_ran_bernoulli($r, $p) - This function returns either 0 or 1, the result of a Bernoulli trial with probability $p. The probability distribution for a Bernoulli trial is, p(0) = 1 - $p and  p(1) = $p. $r is a gsl_rng structure.
 141
 142 =item gsl_ran_bernoulli_pdf($k, $p) - This function computes the probability p($k) of obtaining $k from a Bernoulli distribution with probability parameter $p, using the formula given above.
 143
 144 =item gsl_ran_beta($r, $a, $b) - This function returns a random variate from the beta distribution. The distribution function is, p($x) dx = {Gamma($a+$b) \ Gamma($a) Gamma($b)} $x**{$a-1} (1-$x)**{$b-1} dx for 0 <= $x <= 1.$r is a gsl_rng structure.
 145
 146 =item gsl_ran_beta_pdf($x, $a, $b) - This function computes the probability density p($x) at $x for a beta distribution with parameters $a and $b, using the formula given above.
 147
 148 =item gsl_ran_binomial($k, $p, $n) - This function returns a random integer from the binomial distribution, the number of successes in n independent trials with probability $p. The probability distribution for binomial variates is p($k) = {$n! \ $k! ($n-$k)! } $p**$k (1-$p)^{$n-$k} for 0 <= $k <= $n.
 149
 150 =item gsl_ran_binomial_knuth
 151
 152 =item gsl_ran_binomial_tpe
 153
 154 =item gsl_ran_binomial_pdf($k, $p, $n) - This function computes the probability p($k) of obtaining $k from a binomial distribution with parameters $p and $n, using the formula given above.
 155
 156 =item gsl_ran_exponential($r, $mu) - This function returns a random variate from the exponential distribution with mean $mu. The distribution is, p($x) dx = {1 \ $mu} exp(-$x/$mu) dx for $x >= 0. $r is a gsl_rng structure.
 157
 158 =item gsl_ran_exponential_pdf($x, $mu) - This function computes the probability density p($x) at $x for an exponential distribution with mean $mu, using the formula given above.
 159
 160 =item gsl_ran_exppow($r, $a, $b) - This function returns a random variate from the exponential power distribution with scale parameter $a and exponent $b. The distribution is, p(x) dx = {1 / 2 $a Gamma(1+1/$b)} exp(-|$x/$a|**$b) dx for $x >= 0. For $b = 1 this reduces to the Laplace distribution. For $b = 2 it has the same form as a gaussian distribution, but with $a = sqrt(2) sigma. $r is a gsl_rng structure.
 161
 162 =item gsl_ran_exppow_pdf($x, $a, $b) - This function computes the probability density p($x) at $x for an exponential power distribution with scale parameter $a and exponent $b, using the formula given above.
 163
 164 =item gsl_ran_cauchy($r, $a) - This function returns a random variate from the Cauchy distribution with scale parameter $a. The probability distribution for Cauchy random variates is, p(x) dx = {1 / a pi (1 + (x/$a)**2) } dx for x in the range -infinity to +infinity. The Cauchy distribution is also known as the Lorentz distribution. $r is a gsl_rng structure.
 165
 166 =item gsl_ran_cauchy_pdf($x, $a) - This function computes the probability density p($x) at $x for a Cauchy distribution with scale parameter $a, using the formula given above.
 167
 168 =item gsl_ran_chisq($r, $nu) - This function returns a random variate from the chi-squared distribution with $nu degrees of freedom. The distribution function is, p(x) dx = {1 / 2 Gamma($nu/2) } (x/2)**{$nu/2 - 1} exp(-x/2) dx for $x >= 0. $r is a gsl_rng structure.
 169
 170 =item gsl_ran_chisq_pdf($x, $nu) - This function computes the probability density p($x) at $x for a chi-squared distribution with $nu degrees of freedom, using the formula given above.
 171
 172 =item gsl_ran_dirichlet
 173
 174 =item gsl_ran_dirichlet_pdf
 175
 176 =item gsl_ran_dirichlet_lnpdf
 177
 178 =item gsl_ran_erlang
 179
 180 =item gsl_ran_erlang_pdf
 181
 182 =item gsl_ran_fdist($r, $nu1, $nu2) - This function returns a random variate from the F-distribution with degrees of freedom nu1 and nu2. The distribution function is, p(x) dx = { Gamma(($nu_1 + $nu_2)/2) / Gamma($nu_1/2) Gamma($nu_2/2) } $nu_1**{$nu_1/2} $nu_2**{$nu_2/2} x**{$nu_1/2 - 1} ($nu_2 + $nu_1 x)**{-$nu_1/2 -$nu_2/2} for $x >= 0. $r is a gsl_rng structure.
 183
 184 =item gsl_ran_fdist_pdf($x, $nu1, $nu2) - This function computes the probability density p(x) at x for an F-distribution with nu1 and nu2 degrees of freedom, using the formula given above.
 185
 186 =item gsl_ran_flat($r, $a, $b) - This function returns a random variate from the flat (uniform) distribution from a to b. The distribution is, p(x) dx = {1 / ($b-$a)} dx if $a <= x < $b and 0 otherwise. $r is a gsl_rng structure.
 187
 188 =item gsl_ran_flat_pdf($x, $a, $b) - This function computes the probability density p($x) at $x for a uniform distribution from $a to $b, using the formula given above.
 189
 190 =item gsl_ran_gamma($r, $a, $b) - This function returns a random variate from the flat (uniform) distribution from $a to $b. The distribution is, p(x) dx = {1 / ($b-$a)} dx if $a <= x < $b and 0 otherwise. $r is a gsl_rng structure.
 191
 192 =item gsl_ran_gamma_int
 193
 194 =item gsl_ran_gamma_pdf($x, $a, $b) - This function computes the probability density p($x) at $x for a uniform distribution from $a to $b, using the formula given above.
 195
 196 =item gsl_ran_gamma_mt
 197
 198 =item gsl_ran_gamma_knuth
 199
 200 =item gsl_ran_gaussian($r, $sigma) - This function returns a Gaussian random variate, with mean zero and standard deviation $sigma. The probability distribution for Gaussian random variates is, p(x) dx = {1 / sqrt{2 pi $sigma**2}} exp(-x**2 / 2 $sigma**2) dx for x in the range -infinity to +infinity. $r is a gsl_rng structure.
 201
 202 =item gsl_ran_gaussian_ratio_method($r, $sigma) - This function computes a Gaussian random variate using the alternative Kinderman-Monahan-Leva ratio method.
 203
 204 =item gsl_ran_gaussian_ziggurat($r, $sigma) - This function computes a Gaussian random variate using the alternative Marsaglia-Tsang ziggurat ratio method. The Ziggurat algorithm is the fastest available algorithm in most cases. $r is a gsl_rng structure.
 205
 206 =item gsl_ran_gaussian_pdf($x, $sigma) - This function computes the probability density p($x) at $x for a Gaussian distribution with standard deviation sigma, using the formula given above.
 207
 208 =item gsl_ran_ugaussian($r) - This function computes results for the unit Gaussian distribution. It is equivalent to the gaussian functions above with a standard deviation of one, sigma = 1. $r is a gsl_rng structure.
 209
 210 =item gsl_ran_ugaussian_ratio_method($r) - This function computes results for the unit Gaussian distribution. It is equivalent to the gaussian functions above with a standard deviation of one, sigma = 1. $r is a gsl_rng structure.
 211
 212 =item gsl_ran_ugaussian_pdf($x) - This function computes results for the unit Gaussian distribution. It is equivalent to the gaussian functions above with a standard deviation of one, sigma = 1.
 213
 214 =item gsl_ran_gaussian_tail($r, $a, $sigma) - This function provides random variates from the upper tail of a Gaussian distribution with standard deviation sigma. The values returned are larger than the lower limit a, which must be positive. The probability distribution for Gaussian tail random variates is, p(x) dx = {1 / N($a; $sigma) sqrt{2 pi sigma**2}} exp(- x**2/(2 sigma**2)) dx for x > $a where N($a; $sigma) is the normalization constant, N($a; $sigma) = (1/2) erfc($a / sqrt(2 $sigma**2)). $r is a gsl_rng structure.
 215
 216 =item gsl_ran_gaussian_tail_pdf($x, $a, $gaussian) - This function computes the probability density p($x) at $x for a Gaussian tail distribution with standard deviation sigma and lower limit $a, using the formula given above.
 217
 218 =item gsl_ran_ugaussian_tail($r, $a) - This functions compute results for the tail of a unit Gaussian distribution. It is equivalent to the functions above with a standard deviation of one, $sigma = 1. $r is a gsl_rng structure.
 219
 220 =item gsl_ran_ugaussian_tail_pdf($x, $a) - This functions compute results for the tail of a unit Gaussian distribution. It is equivalent to the functions above with a standard deviation of one, $sigma = 1.
 221
 222 =item gsl_ran_bivariate_gaussian($r, $sigma_x, $sigma_y, $rho) - This function generates a pair of correlated Gaussian variates, with mean zero, correlation coefficient rho and standard deviations $sigma_x and $sigma_y in the x and y directions. The first value returned is x and the second y. The probability distribution for bivariate Gaussian random variates is, p(x,y) dx dy = {1 / 2 pi $sigma_x $sigma_y sqrt{1-$rho**2}} exp (-(x**2/$sigma_x**2 + y**2/$sigma_y**2 - 2 $rho x y/($sigma_x $sigma_y))/2(1- $rho**2)) dx dy for x,y in the range -infinity to +infinity. The correlation coefficient $rho should lie between 1 and -1. $r is a gsl_rng structure.
 223
 224 =item gsl_ran_bivariate_gaussian_pdf($x, $y, $sigma_x, $sigma_y, $rho) - This function computes the probability density p($x,$y) at ($x,$y) for a bivariate Gaussian distribution with standard deviations $sigma_x, $sigma_y and correlation coefficient $rho, using the formula given above.
 225
 226 =item gsl_ran_landau($r) - This function returns a random variate from the Landau distribution. The probability distribution for Landau random variates is defined analytically by the complex integral, p(x) = (1/(2 \pi i)) \int_{c-i\infty}^{c+i\infty} ds exp(s log(s) + x s) For numerical purposes it is more convenient to use the following equivalent form of the integral, p(x) = (1/\pi) \int_0^\infty dt \exp(-t \log(t) - x t) \sin(\pi t). $r is a gsl_rng structure.
 227
 228 =item gsl_ran_landau_pdf($x) - This function computes the probability density p($x) at $x for the Landau distribution using an approximation to the formula given above.
 229
 230 =item gsl_ran_geometric($r, $p) - This function returns a random integer from the geometric distribution, the number of independent trials with probability $p until the first success. The probability distribution for geometric variates is, p(k) =  p (1-$p)^(k-1) for k >= 1. Note that the distribution begins with k=1 with this definition. There is another convention in which the exponent k-1 is replaced by k. $r is a gsl_rng structure.
 231
 232 =item gsl_ran_geometric_pdf($k, $p) - This function computes the probability p($k) of obtaining $k from a geometric distribution with probability parameter p, using the formula given above.
 233
 234 =item gsl_ran_hypergeometric($r, $n1, $n2, $t) - This function returns a random integer from the hypergeometric distribution. The probability distribution for hypergeometric random variates is, p(k) =  C(n_1, k) C(n_2, t - k) / C(n_1 + n_2, t) where C(a,b) = a!/(b!(a-b)!) and t <= n_1 + n_2. The domain of k is max(0,t-n_2), ..., min(t,n_1). If a population contains n_1 elements of “type 1” and n_2 elements of “type 2” then the hypergeometric distribution gives the probability of obtaining k elements of “type 1” in t samples from the population without replacement. $r is a gsl_rng structure.
 235
 236 =item gsl_ran_hypergeometric_pdf($k, $n1, $n2, $t) - This function computes the probability p(k) of obtaining k from a hypergeometric distribution with parameters $n1, $n2 $t, using the formula given above.
 237
 238 =item gsl_ran_gumbel1($r, $a, $b) - This function returns a random variate from the Type-1 Gumbel distribution. The Type-1 Gumbel distribution function is, p(x) dx = a b \exp(-(b \exp(-ax) + ax)) dx for -\infty < x < \infty. $r is a gsl_rng structure.
 239
 240 =item gsl_ran_gumbel1_pdf($x, $a, $b) - This function computes the probability density p($x) at $x for a Type-1 Gumbel distribution with parameters $a and $b, using the formula given above.
 241
 242 =item gsl_ran_gumbel2($r, $a, $b) - This function returns a random variate from the Type-2 Gumbel distribution. The Type-2 Gumbel distribution function is, p(x) dx = a b x^{-a-1} \exp(-b x^{-a}) dx for 0 < x < \infty. $r is a gsl_rng structure.
 243
 244 =item gsl_ran_gumbel2_pdf($x, $a, $b) - This function computes the probability density p($x) at $x for a Type-2 Gumbel distribution with parameters $a and $b, using the formula given above.
 245
 246 =item gsl_ran_logistic($r, $a) - This function returns a random variate from the logistic distribution. The distribution function is, p(x) dx = { \exp(-x/a) \over a (1 + \exp(-x/a))^2 } dx for -\infty < x < +\infty. $r is a gsl_rng structure.
 247
 248 =item gsl_ran_logistic_pdf($x, $a) - This function computes the probability density p($x) at $x for a logistic distribution with scale parameter $a, using the formula given above.
 249
 250 =item gsl_ran_lognormal($r, $zeta, $sigma) - This function returns a random variate from the lognormal distribution. The distribution function is, p(x) dx = {1 \over x \sqrt{2 \pi \sigma^2} } \exp(-(\ln(x) - \zeta)^2/2 \sigma^2) dx for x > 0. $r is a gsl_rng structure.
 251
 252 =item gsl_ran_lognormal_pdf($x, $zeta, $sigma) - This function computes the probability density p($x) at $x for a lognormal distribution with parameters $zeta and $sigma, using the formula given above.
 253
 254 =item gsl_ran_logarithmic($r, $p) - This function returns a random integer from the logarithmic distribution. The probability distribution for logarithmic random variates is, p(k) = {-1 \over \log(1-p)} {(p^k \over k)} for k >= 1. $r is a gsl_rng structure.
 255
 256 =item gsl_ran_logarithmic_pdf($k, $p) - This function computes the probability p($k) of obtaining $k from a logarithmic distribution with probability parameter $p, using the formula given above.
 257
 258 =item gsl_ran_multinomial
 259
 260 =item gsl_ran_multinomial_pdf
 261
 262 =item gsl_ran_multinomial_lnpdf
 263
 264 =item gsl_ran_negative_binomial($r, $p, $n) - This function returns a random integer from the negative binomial distribution, the number of failures occurring before n successes in independent trials with probability p of success. The probability distribution for negative binomial variates is, p(k) = {\Gamma(n + k) \over \Gamma(k+1) \Gamma(n) } p^n (1-p)^k Note that n is not required to be an integer.
 265
 266 =item gsl_ran_negative_binomial_pdf($k, $p, $n) - This function computes the probability p($k) of obtaining $k from a negative binomial distribution with parameters $p and $n, using the formula given above.
 267
 268 =item gsl_ran_pascal($r, $p, $n) - This function returns a random integer from the Pascal distribution. The Pascal distribution is simply a negative binomial distribution with an integer value of $n. p($k) = {($n + $k - 1)! \ $k! ($n - 1)! } $p**$n (1-$p)**$k for $k >= 0. $r is gsl_rng structure
 269
 270 =item gsl_ran_pascal_pdf($k, $p, $n) - This function computes the probability p($k) of obtaining $k from a Pascal distribution with parameters $p and $n, using the formula given above.
 271
 272 =item gsl_ran_pareto($r, $a, $b) - This function returns a random variate from the Pareto distribution of order $a. The distribution function is p($x) dx = ($a/$b) / ($x/$b)^{$a+1} dx for $x >= $b. $r is a gsl_rng structure
 273
 274 =item gsl_ran_pareto_pdf($x, $a, $b) - This function computes the probability density p(x) at x for a Pareto distribution with exponent a and scale b, using the formula given above.
 275
 276 =item gsl_ran_poisson($r, $mu) -This function returns a random integer from the Poisson distribution with mean $mu. $r is a gsl_rng structure. The probability distribution for Poisson variates is, p(k) = {$mu**$k \ $k!} exp(-$mu) for $k >= 0. $r is a gsl_rng structure
 277
 278 =item gsl_ran_poisson_array
 279
 280 =item gsl_ran_poisson_pdf($k, $mu) - This function computes the probability p($k) of obtaining $k from a Poisson distribution with mean $mu, using the formula given above.
 281
 282 =item gsl_ran_rayleigh($r, $sigma) - This function returns a random variate from the Rayleigh distribution with scale parameter sigma. The distribution is, p(x) dx = {x \over \sigma^2} \exp(- x^2/(2 \sigma^2)) dx for x > 0. $r is a gsl_rng structure
 283
 284 =item gsl_ran_rayleigh_pdf($x, $sigma) - This function computes the probability density p($x) at $x for a Rayleigh distribution with scale parameter sigma, using the formula given above.
 285
 286 =item gsl_ran_rayleigh_tail($r, $a, $sigma) - This function returns a random variate from the tail of the Rayleigh distribution with scale parameter $sigma and a lower limit of $a. The distribution is, p(x) dx = {x \over \sigma^2} \exp ((a^2 - x^2) /(2 \sigma^2)) dx for x > a. $r is a gsl_rng structure
 287
 288 =item gsl_ran_rayleigh_tail_pdf($x, $a, $sigma) - This function computes the probability density p($x) at $x for a Rayleigh tail distribution with scale parameter $sigma and lower limit $a, using the formula given above.
 289
 290 =item gsl_ran_tdist($r, $nu) - This function returns a random variate from the t-distribution. The distribution function is, p(x) dx = {\Gamma((\nu + 1)/2) \over \sqrt{\pi \nu} \Gamma(\nu/2)} (1 + x^2/\nu)^{-(\nu + 1)/2} dx for -\infty < x < +\infty.
 291
 292 =item gsl_ran_tdist_pdf($x, $nu) - This function computes the probability density p($x) at $x for a t-distribution with nu degrees of freedom, using the formula given above.
 293
 294 =item gsl_ran_laplace($r, $a) - This function returns a random variate from the Laplace distribution with width $a. The distribution is, p(x) dx = {1 \over 2 a}  \exp(-|x/a|) dx for -\infty < x < \infty.
 295
 296 =item gsl_ran_laplace_pdf($x, $a) - This function computes the probability density p($x) at $x for a Laplace distribution with width $a, using the formula given above.
 297
 298 =item gsl_ran_levy($r, $c, $alpha) - This function returns a random variate from the Levy symmetric stable distribution with scale $c and exponent $alpha. The symmetric stable probability distribution is defined by a fourier transform, p(x) = {1 \over 2 \pi} \int_{-\infty}^{+\infty} dt \exp(-it x - |c t|^alpha) There is no explicit solution for the form of p(x) and the library does not define a corresponding pdf function. For \alpha = 1 the distribution reduces to the Cauchy distribution. For \alpha = 2 it is a Gaussian distribution with \sigma = \sqrt{2} c. For \alpha < 1 the tails of the distribution become extremely wide. The algorithm only works for 0 < alpha <= 2. $r is a gsl_rng structure
 299
 300 =item gsl_ran_levy_skew($r, $c, $alpha, $beta) - This function returns a random variate from the Levy skew stable distribution with scale $c, exponent $alpha and skewness parameter $beta. The skewness parameter must lie in the range [-1,1]. The Levy skew stable probability distribution is defined by a fourier transform, p(x) = {1 \over 2 \pi} \int_{-\infty}^{+\infty} dt \exp(-it x - |c t|^alpha (1-i beta sign(t) tan(pi alpha/2))) When \alpha = 1 the term \tan(\pi \alpha/2) is replaced by -(2/\pi)\log|t|. There is no explicit solution for the form of p(x) and the library does not define a corresponding pdf function. For $alpha = 2 the distribution reduces to a Gaussian distribution with $sigma = sqrt(2) $c and the skewness parameter has no effect. For $alpha < 1 the tails of the distribution become extremely wide. The symmetric distribution corresponds to $beta = 0. The algorithm only works for 0 < $alpha <= 2. The Levy alpha-stable distributions have the property that if N alpha-stable variates are drawn from the distribution p(c, \alpha, \beta) then the sum Y = X_1 + X_2 + \dots + X_N will also be distributed as an alpha-stable variate, p(N^(1/\alpha) c, \alpha, \beta). $r is a gsl_rng structure
 301
 302 =item gsl_ran_weibull($r, $a, $b) - This function returns a random variate from the Weibull distribution. The distribution function is, p(x) dx = {b \over a^b} x^{b-1}  \exp(-(x/a)^b) dx for x >= 0. $r is a gsl_rng structure
 303
 304 =item gsl_ran_weibull_pdf($x, $a, $b) - This function computes the probability density p($x) at $x for a Weibull distribution with scale $a and exponent $b, using the formula given above.
 305
 306 =item gsl_ran_dir_2d($r) - This function returns two values. The first is $x and the second is $y of a random direction vector v = ($x,$y) in two dimensions. The vector is normalized such that |v|^2 = $x^2 + $y^2 = 1. $r is a gsl_rng structure
 307
 308 =item gsl_ran_dir_2d_trig_method($r)  - This function returns two values. The first is $x and the second is $y of a random direction vector v = ($x,$y) in two dimensions. The vector is normalized such that |v|^2 = $x^2 + $y^2 = 1. $r is a gsl_rng structure
 309
 310 =item gsl_ran_dir_3d($r) - This function returns three values. The first is $x, the second $y and the third $z of a random direction vector v = ($x,$y,$z) in three dimensions. The vector is normalized such that |v|^2 = x^2 + y^2 + z^2 = 1. The method employed is due to Robert E. Knop (CACM 13, 326 (1970)), and explained in Knuth, v2, 3rd ed, p136. It uses the surprising fact that the distribution projected along any axis is actually uniform (this is only true for 3 dimensions).
 311
 312 =item gsl_ran_dir_nd
 313
 314 =item gsl_ran_shuffle
 315
 316 =item gsl_ran_choose
 317
 318 =item gsl_ran_sample
 319
 320 =item gsl_ran_discrete_preproc
 321
 322 =item gsl_ran_discrete($r, $g) - After gsl_ran_discrete_preproc has been called, you use this function to get the discrete random numbers. $r is a gsl_rng structure and $g is a gsl_ran_discrete structure
 323 =item gsl_ran_discrete_pdf($k, $g) - Returns the probability P[$k] of observing the variable $k. Since P[$k] is not stored as part of the lookup table, it must be recomputed; this computation takes O(K), so if K is large and you care about the original array P[$k] used to create the lookup table, then you should just keep this original array P[$k] around. $r is a gsl_rng structure and $g is a gsl_ran_discrete structure
 324
 325 =item gsl_ran_discrete_free($g) - De-allocates the gsl_ran_discrete pointed to by g.
 326
 327 =back
 328
 329  You have to add the functions you want to use inside the qw /put_funtion_here /.
 330  You can also write use Math::GSL::Randist qw/:name_of_tag/; to use all avaible functions of the module.
 331  Other tags are also avaible, here is a complete list of all tags for this module :
 332
 333 =over
 334
 335 =item logarithmic
 336
 337 =item choose
 338
 339 =item exponential
 340
 341 =item gumbel1
 342
 343 =item exppow
 344
 345 =item sample
 346
 347 =item logistic
 348
 349 =item gaussian
 350
 351 =item poisson
 352
 353 =item binomial
 354
 355 =item fdist
 356
 357 =item chisq
 358
 359 =item gamma
 360
 361 =item hypergeometric
 362
 363 =item dirichlet
 364
 365 =item negative
 366
 367 =item flat
 368
 369 =item geometric
 370
 371 =item discrete
 372
 373 =item tdist
 374
 375 =item ugaussian
 376
 377 =item rayleigh
 378
 379 =item dir
 380
 381 =item pascal
 382
 383 =item gumbel2
 384
 385 =item shuffle
 386
 387 =item landau
 388
 389 =item bernoulli
 390
 391 =item weibull
 392
 393 =item multinomial
 394
 395 =item beta
 396
 397 =item lognormal
 398
 399 =item laplace
 400
 401 =item erlang
 402
 403 =item cauchy
 404
 405 =item levy
 406
 407 =item bivariate
 408
 409 =item pareto
 410
 411 =back
 412
 413  For example the beta tag contains theses functions : gsl_ran_beta, gsl_ran_beta_pdf.
 414
 415 For more informations on the functions, we refer you to the GSL offcial documentation:
 416 L<http://www.gnu.org/software/gsl/manual/html_node/>
 417  Tip : search on google: site:http://www.gnu.org/software/gsl/manual/html_node/ name_of_the_function_you_want
 418
 419  You might also want to write
 420  use Math::GSL::RNG qw/:all/;
 421  since a lot of the functions of Math::GSL::Randist take as argument a structure that is created by Math::GSL::RNG.
 422  Refer to Math::GSL::RNG documentation to see how to create such a structure.
 423
 424  Math::GSL::CDF also contains a structure named gsl_ran_discrete_t. An example is given in the EXAMPLES part on how to use the function related to this structure.
 425
 426
 427 =head1 EXAMPLES
 428
 429     use Math::GSL::Randist qw/:all/;
 430     print gsl_ran_exponential_pdf(5,2) . "\n";
 431
 432     use Math::GSL::Randist qw/:all/;
 433     $x= Math::GSL::gsl_ran_discrete_t::new;
 434
 435
 436 =head1 AUTHORS
 437
 438 Jonathan Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>
 439
 440 =head1 COPYRIGHT AND LICENSE
 441
 442 Copyright (C) 2008 Jonathan Leto and Thierry Moisan
 443
 444 This program is free software; you can redistribute it and/or modify it
 445 under the same terms as Perl itself.
 446
 447 =cut
 448 %}