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Math::GSL::Randist(3) User Contributed Perl DocumentationMath::GSL::Randist(3)

NAME
Math::GSL::Randist - Probability	Distributions

SYNOPSIS
use Math::GSL::RNG;
use Math::GSL::Randist qw/:all/;

my $rng = Math::GSL::RNG->new(); my$coinflip = gsl_ran_bernoulli($rng->raw(), .5); DESCRIPTION Here is a list of all the functions included in this module. For all sampling methods, the first argument$r is a raw	gsl_rnd	structure
retrieve	by calling raw() on an Math::GSL::RNG object.

Bernoulli
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.

gsl_ran_bernoulli_pdf($k,$p)
This	function computes the probability p($k) of obtaining$k	from a
Bernoulli distribution with probability parameter $p, using the formula given above. Beta gsl_ran_beta($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.$r is a gsl_rng structure. gsl_ran_beta_pdf($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.

Binomial
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.  Uses	Binomial Triangle Parallelogram	Exponential algorithm.

gsl_ran_binomial_knuth($k,$p, $n) Alternative and original implementation for gsl_ran_binomial using Knuth's algorithm. gsl_ran_binomial_tpe($k,	$p,$n)
Same	as gsl_ran_binomial.

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	$n, using the formula given above. Exponential gsl_ran_exponential($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.

gsl_ran_exponential_pdf($x,$mu)
This	function computes the probability density p($x) at$x for an
exponential distribution with mean $mu, using the formula given above. Exponential Power gsl_ran_exppow($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.

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
$b, using the formula given above. Cauchy gsl_ran_cauchy($r, $scale) This function returns a random variate from the Cauchy distribution with$scale.	The probability	distribution for Cauchy	random
variates is,

p(x) dx = {1 / $scale pi (1 + (x/$$scale)**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.

gsl_ran_cauchy_pdf($x,$scale)
This	function computes the probability density p($x) at$x for a
Cauchy distribution with $scale, using the formula given above. Chi-Squared gsl_ran_chisq($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.

gsl_ran_chisq_pdf($x,$nu)
This	function computes the probability density p($x) at$x for a
chi-squared distribution with $nu degrees of freedom, using the formula given above. Dirichlet gsl_ran_dirichlet($r, $alpha) This function returns an array of K (where K = length of$alpha
array) random variates from a Dirichlet distribution	of order K-1.
The distribution function is

p(\theta_1, ..., \theta_K)	d\theta_1 ... d\theta_K	=
(1/Z) \prod_{i=1}^K \theta_i^{\alpha_i - 1} \delta(1 -\sum_{i=1}^K \theta_i) d\theta_1 ... d\theta_K

for theta_i >= 0 and	alpha_i	> 0. The delta function	ensures	that
\sum	\theta_i = 1. The normalization	factor Z is

Z = {\prod_{i=1}^K	\Gamma(\alpha_i)} / {\Gamma( \sum_{i=1}^K \alpha_i)}

The random variates are generated by	sampling K values from gamma
distributions with parameters a=alpha_i, b=1, and renormalizing.
See A.M. Law, W.D. Kelton, Simulation Modeling and Analysis (1991).

gsl_ran_dirichlet_pdf($theta,$alpha)
This	function computes the probability density p(\theta_1, ... ,
\theta_K) at	theta[K] for a Dirichlet distribution with parameters
alpha[K], using the formula given above. $alpha and$theta should
be array references of the same size.  Theta	should be normalized
to sum to 1.

gsl_ran_dirichlet_lnpdf($theta,$alpha)
This	function computes the logarithm	of the probability density
p(\theta_1, ...  , \theta_K)	for a Dirichlet	distribution with
parameters alpha[K].	$alpha and$theta should be array references
of the same size.  Theta should be normalized to sum	to 1.

Erlang
gsl_ran_erlang($r,$scale, $shape) Equivalent to gsl_ran_gamma($r, $shape,$scale) where $shape is an integer. gsl_ran_erlang_pdf Equivalent to gsl_ran_gamma_pdf($r, $shape,$scale) where $shape is an integer. F-distribution gsl_ran_fdist($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.	$r is a gsl_rng structure. gsl_ran_fdist_pdf($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.

Uniform/Flat	distribution
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.

gsl_ran_flat_pdf($x,$a,	$b) This function computes the probability density p($x)	at $x for a uniform distribution from$a	to $b, using the formula given above. Gamma gsl_ran_gamma($r, $shape,$scale)
This	function returns a random variate from the gamma distribution.
The distribution function is,
p(x) dx = {1 \over	\Gamma($shape)$scale^$shape} x^{$shape-1}	e^{-x/$scale} dx for x > 0. Uses Marsaglia-Tsang method. Can also be called as gsl_ran_gamma_mt. gsl_ran_gamma_pdf($x, $shape,$scale)
This	function computes the probability density p($x) at$x for a
gamma distribution with parameters $shape and$scale, using the
formula given above.

gsl_ran_gamma($r,$shape, $scale) Same as gsl_ran_gamma. gsl_ran_gamma_knuth($r, $shape,$scale)
Alternative implementation for gsl_ran_gamma, using algorithm in
Knuth volume	2.

Gaussian/Normal
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.  Uses Box-Mueller (polar)
method.

gsl_ran_gaussian_ratio_method($r,$sigma)
This	function computes a Gaussian random variate using the
alternative Kinderman-Monahan-Leva ratio method.

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. $r is a gsl_rng structure. gsl_ran_gaussian_pdf($x,	$sigma) This function computes the probability density p($x)	at $x for a Gaussian distribution with standard deviation sigma, using the formula given above. gsl_ran_ugaussian($r)
gsl_ran_ugaussian_ratio_method($r) gsl_ran_ugaussian_pdf($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.

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. $r is a gsl_rng structure. gsl_ran_bivariate_gaussian_pdf($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 $rho, using the formula given above. Gaussian Tail gsl_ran_gaussian_tail($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.

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.

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.

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, $sigma = 1. Landau gsl_ran_landau($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). $r is a gsl_rng structure. gsl_ran_landau_pdf($x)
This	function computes the probability density p($x) at$x for the
Landau distribution using an	approximation to the formula given
above.

Geometric
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. $r is a gsl_rng structure. gsl_ran_geometric_pdf($k, $p) This function computes the probability p($k)	of obtaining $k from a geometric distribution with probability parameter p, using the formula given above. Hypergeometric gsl_ran_hypergeometric($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.

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	$t, using the formula given above. Gumbel gsl_ran_gumbel1($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. $r is a gsl_rng structure. gsl_ran_gumbel1_pdf($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.

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.

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 $b, using the formula given above. Logistic gsl_ran_logistic($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.

gsl_ran_logistic_pdf($x,$a)
This	function computes the probability density p($x) at$x for a
logistic distribution with scale parameter $a, using the formula given above. Lognormal gsl_ran_lognormal($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. $r is a gsl_rng structure. gsl_ran_lognormal_pdf($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.

Logarithmic
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. $r is a gsl_rng structure. gsl_ran_logarithmic_pdf($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.

Multinomial
gsl_ran_multinomial($r,$P, $N) This function computes and returns a random sample n[] from the multinomial distribution formed by N trials from an underlying distribution p[K]. The distribution function for n[] is, P(n_1, n_2, ..., n_K) = (N!/(n_1! n_2! ... n_K!)) p_1^n_1 p_2^n_2 ... p_K^n_K where (n_1, n_2, ..., n_K) are nonnegative integers with sum_{k=1}^K n_k = N, and (p_1, p_2, ..., p_K) is a probability distribution with \sum p_i = 1. If the array p[K] is not normalized then its entries will be treated as weights and normalized appropriately. Random variates are generated using the conditional binomial method (see C.S. Davis, The computer generation of multinomial random variates, Comp. Stat. Data Anal. 16 (1993) 205-217 for details). gsl_ran_multinomial_pdf($counts,	$P) This function returns the probability for the multinomial distribution P(counts, counts, ..., counts[K]) with parameters p[K]. gsl_ran_multinomial_lnpdf($counts, $P) This function returns the logarithm of the probability for the multinomial distribution P(counts, counts, ..., counts[K]) with parameters p[K]. Negative Binomial gsl_ran_negative_binomial($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.

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 $n, using the formula given above. Pascal gsl_ran_pascal($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

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 $n, using the formula given above. Pareto gsl_ran_pareto($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

gsl_ran_pareto_pdf($x,$a, $b) This function computes the probability density p(x) at x for a Pareto distribution with exponent a and scale b, using the formula given above. Poisson gsl_ran_poisson($r, $lambda) This function returns a random integer from the Poisson distribution with mean$lambda. $r is a gsl_rng structure. The probability distribution for Poisson variates is, p(k) = {$lambda**$k \$k!} exp(-$lambda) for$k >= 0.	$r is a gsl_rng structure. gsl_ran_poisson_pdf($k, $lambda) This function computes the probability p($k)	of obtaining $k from a Poisson distribution with mean$lambda, using the formula given
above.

Rayleigh
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. $r is a gsl_rng structure gsl_ran_rayleigh_pdf($x,	$sigma) This function computes the probability density p($x)	at $x for a Rayleigh distribution with scale parameter sigma, using the formula given above. gsl_ran_rayleigh_tail($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. $r is a gsl_rng structure gsl_ran_rayleigh_tail_pdf($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.

Student-t
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.

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.

Laplace
gsl_ran_laplace($r,$a)
This	function returns a random variate from the Laplace
distribution	with width $a. The distribution is, p(x) dx = {1 \over 2 a} \exp(-|x/a|) dx for -\infty < x < \infty. gsl_ran_laplace_pdf($x, $a) This function computes the probability density p($x)	at $x for a Laplace distribution with width$a, using the formula given above.

Levy
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

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

Weibull
gsl_ran_weibull($r,$scale, $exponent) This function returns a random variate from the Weibull distribution with$scale and	$exponent (aka scale). The distribution function is p(x) dx = {$exponent \over $scale^$exponent} x^{$exponent-1} \exp(-(x/$scale)^$exponent) dx for x >= 0.$r is a gsl_rng structure

gsl_ran_weibull_pdf($x,$scale, $exponent) This function computes the probability density p($x)	at $x for a Weibull distribution with$scale and	$exponent, using the formula given above. Spherical Vector gsl_ran_dir_2d($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. $r is a gsl_rng structure gsl_ran_dir_2d_trig_method($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. $r is a gsl_rng structure gsl_ran_dir_3d($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).

gsl_ran_dir_nd (Not yet implemented )
This	function returns a random direction vector v =
(x_1,x_2,...,x_n) in	n dimensions. The vector is normalized such
that

|v|^2 = x_1^2 + x_2^2 + ... + x_n^2 = 1.

The method uses the fact that a multivariate	Gaussian distribution
is spherically symmetric. Each component is generated to have a
Gaussian distribution, and then the components are normalized. The
method is described by Knuth, v2, 3rd ed, p135-136, and attributed
to G. W. Brown, Modern Mathematics for the Engineer (1956).

Shuffling and Sampling
gsl_ran_shuffle
Please use the "shuffle" method in the GSL::RNG module OO
interface.

gsl_ran_choose
Please use the "choose" method in the GSL::RNG module OO interface.

gsl_ran_sample
Please use the "sample" method in the GSL::RNG module OO interface.

gsl_ran_discrete_preproc
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

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 $g is a gsl_ran_discrete structure gsl_ran_discrete_free($g)
De-allocates	the gsl_ran_discrete pointed to	by g.

You have to add	the functions you want to use inside the qw /put_funtion_here /.
You can	also write use Math::GSL::Randist qw/:all/; to use all avaible functions of the	module.
Other tags are also avaible, here is a complete	list of	all tags for this module :

logarithmic
choose
exponential
gumbel1
exppow
sample
logistic
gaussian
poisson
binomial
fdist
chisq
gamma
hypergeometric
dirichlet
negative
flat
geometric
discrete
tdist
ugaussian
rayleigh
dir
pascal
gumbel2
shuffle
landau
bernoulli
weibull
multinomial
beta
lognormal
laplace
erlang
cauchy
levy
bivariate
pareto

For example the	beta tag contains theses functions : gsl_ran_beta, gsl_ran_beta_pdf.

For more	informations on	the functions, we refer	you to the GSL offcial
documentation: <http://www.gnu.org/software/gsl/manual/html_node/>

You might also want to write

use Math::GSL::RNG qw/:all/;

since a lot of the functions of Math::GSL::Randist take as argument a
structure that is created by Math::GSL::RNG.  Refer to Math::GSL::RNG
documentation to	see how	to create such a structure.

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.

EXAMPLES
use Math::GSL::Randist qw/:all/;
print gsl_ran_exponential_pdf(5,2) .	"\n";

use Math::GSL::Randist qw/:all/;
my \$x = Math::GSL::gsl_ran_discrete_t::new;

AUTHORS
Jonathan	"Duke" Leto <jonathan@leto.net>	and Thierry Moisan
<thierry.moisan@gmail.com>