Random Number Distributions

# Title: Random Number Distributions

`GSL::Rng#gaussian`
`GSL::Rng#gaussian(sigma)`
  These return a Gaussian random variate, with mean zero and standard deviation sigma. The argument sigma can be omitted in the case of unit Gaussian distribution, sigma=1.
`GSL::Rng#gaussian_ratio_method`
`GSL::Rng#gaussian_ratio_method(sigma)`
  Use Kinderman-Monahan ratio method
`GSL::Rng#gaussian_tail(a, sigma)`
`GSL::Rng#bivariate_gaussian(sigma_x, sigma_y, rho)`
`GSL::Rng#exponential(mu)`
`GSL::Rng#laplace(a)`
`GSL::Rng#exppow(a, b)`
`GSL::Rng#cauchy(a)`
`GSL::Rng#rayleigh(sigma)`
`GSL::Rng#rayleigh_tail(a, sigma)`
`GSL::Rng#landau()`
`GSL::Rng#levy(c, alpha)`
`GSL::Rng#levy_skew(c, alpha, beta)`
`GSL::Rng#gamma(a, b)`
`GSL::Rng#flat(a, b)`
`GSL::Rng#lognormal(zeta, sigma)`
`GSL::Rng#chisq(nu)`
`GSL::Rng#fdist(nu1, nu2)`
`GSL::Rng#tdist(nu)`
`GSL::Rng#beta(a, b)`
`GSL::Rng#logistic(a)`
`GSL::Rng#pareto(a, b)`

...

and more, see the GSL reference.

`GSL::Rng#shuffle(v, n)`
  This randomly shuffles the order of n objects, stored in the GSL::Vector object v.
`GSL::Rng#choose(v, k)`

  This returns a GSL::Vector object with k objects taken randomly from the GSL::Vector object v.

  The objects are sampled without replacement, thus each object can only appear once in the returned vector. It is required that k be less than or equal to the length of the vector v.

`GSL::Rng#sample(v, k)`
  This method is like the method `choose` but samples k items from the original vector v with replacement, so the same object can appear more than once in the output sequence. There is no requirement that k be less than the length of v.

## 1 Module functions

`GSL::Ran::gaussian_pdf(x, sigma)`
  This function computes the probability density at x for a Gaussian distribution with standard deviation sigma.
`GSL::Ran::gaussian_tail_pdf(x, a, sigma)`
`GSL::Ran::bivariate_gaussian_pdf(x, y, sigma_x, sigma_y, rho)`
`GSL::Ran::exponential_pdf(x, mu)`
`GSL::Ran::laplace_pdf(x, a)`
`GSL::Ran::exppow_pdf(x, a, b)`
`GSL::Ran::cauchy_pdf(x, a)`
`GSL::Ran::rayleigh_pdf(x, sigma)`
`GSL::Ran::rayleigh_tail_pdf(x, a, sigma)`
`GSL::Ran::landau_pdf(x)`
`GSL::Ran::levy_pdf(x, c, alpha)`
`GSL::Ran::levy_skew_pdf(x, c, alpha, beta)`
`GSL::Ran::gamma_pdf(x, a, b)`
`GSL::Ran::flat_pdf(x, a, b)`
`GSL::Ran::lognormal_pdf(x, zeta, sigma)`
`GSL::Ran::chisq_pdf(x, nu)`
`GSL::Ran::fdist_pdf(x, nu1, nu2)`
`GSL::Ran::tdist_pdf(x, nu)`
`GSL::Ran::beta_pdf(x, a, b)`
`GSL::Ran::logistic_pdf(x, a)`
`GSL::Ran::pareto_pdf(x, a, b)`

...

### 1.1 Cumulative Probabilities

These methods are defined as module functions of the modules `GSL` and `GSL::Cdf`, as

`GSL::cdf_gaussian_P(x, sigma = 1)`
`GSL::Cdf::gaussian_P(x, sigma = 1)`
`GSL::cdf_gaussian_Q(x, sigma = 1)`
`GSL::Cdf::gaussian_Q(x, sigma = 1)`

...

and more, see the GSL reference.

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