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Math::GSL::Randist(3) |
User Contributed Perl Documentation |
Math::GSL::Randist(3) |
Math::GSL::Randist - Probability Distributions
use Math::GSL::RNG;
use Math::GSL::Randist qw/:all/;
my $rng = Math::GSL::RNG->new();
my $coinflip = gsl_ran_bernoulli($rng->raw(), .5);
Here is a list of all the functions included in this module. For all sampling
methods, the first argument $r is a raw gsl_rnd
structure retrieve by calling raw() on an Math::GSL::RNG object.
- gsl_ran_bernoulli($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 $p, using the formula given above.
- gsl_ran_beta($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 $b, using the
formula given above.
- gsl_ran_binomial($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 $n, using the
formula given above.
- gsl_ran_exponential($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
$mu, using the formula given above.
- gsl_ran_exppow($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
$b, using the formula given above.
- gsl_ran_cauchy($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
$scale, using the formula given above.
- gsl_ran_chisq($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
$nu degrees of freedom, using the formula given
above.
- gsl_ran_dirichlet($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
$theta should be array references of the same
size. Theta should be normalized to sum to 1.
- gsl_ran_erlang($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 $shape is an
integer.
- gsl_ran_fdist($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, $nu2)
- This function computes the probability density p(x) at x for an
F-distribution with nu1 and nu2 degrees of freedom, using the formula
given above.
- gsl_ran_flat($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 $b, using the
formula given above.
- gsl_ran_gamma($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, $scale)
- Alternative implementation for gsl_ran_gamma, using algorithm in Knuth
volume 2.
- gsl_ran_gaussian($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 $rho, using the formula
given above.
- gsl_ran_gaussian_tail($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, $sigma = 1.
- gsl_ran_landau($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
$x for the Landau distribution using an
approximation to the formula given above.
- gsl_ran_geometric($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
$k from a geometric distribution with probability
parameter p, using the formula given above.
- gsl_ran_hypergeometric($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 $t, using the formula
given above.
- gsl_ran_gumbel1($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 $b,
using the formula given above.
- gsl_ran_logistic($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 $a, using the formula given above.
- gsl_ran_lognormal($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 $sigma, using
the formula given above.
- gsl_ran_logarithmic($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 $p, using the formula given
above.
- gsl_ran_multinomial($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, $P)
- This function returns the probability for the multinomial distribution
P(counts[1], counts[2], ..., counts[K]) with parameters p[K].
- gsl_ran_multinomial_lnpdf($counts, $P)
- This function returns the logarithm of the probability for the multinomial
distribution P(counts[1], counts[2], ..., counts[K]) with parameters
p[K].
- gsl_ran_negative_binomial($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 $n,
using the formula given above.
- gsl_ran_pascal($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 $n, using the
formula given above.
- gsl_ran_pareto($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, $b)
- This function computes the probability density p(x) at x for a Pareto
distribution with exponent a and scale b, using the formula given
above.
- gsl_ran_poisson($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
$lambda, using the formula given above.
- gsl_ran_rayleigh($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
$a, using the formula given above.
- gsl_ran_tdist($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
$x for a t-distribution with nu degrees of
freedom, using the formula given above.
- gsl_ran_laplace($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
$a, using the formula given above.
- gsl_ran_levy($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). $r is a gsl_rng
structure
- gsl_ran_weibull($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 $exponent,
using the formula given above.
- gsl_ran_dir_2d($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).
- 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_function_here /.
You can also write use Math::GSL::Randist qw/:all/; to use all available functions of the module.
Other tags are also available, 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
official 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.
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;
Jonathan "Duke" Leto <jonathan@leto.net> and Thierry Moisan
<thierry.moisan@gmail.com>
Copyright (C) 2008-2021 Jonathan "Duke" Leto and Thierry Moisan
This program is free software; you can redistribute it and/or
modify it under the same terms as Perl itself.
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