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= Random Number Distributions

== The Gaussian Distribution
--- GSL::Rng#gaussian(sigma = 1)
--- GSL::Ran::gaussian(rng, sigma = 1)
--- GSL::Rng#ugaussian
--- GSL::Ran::ugaussian
    These return a Gaussian random variate, with mean zero and standard 
    deviation ((|sigma|)). 

--- GSL::Ran::gaussian_pdf(x, sigma = 1)
    Computes the probability density p(x) at ((|x|)) for a Gaussian distribution 
    with standard deviation ((|sigma|)).

--- GSL::Rng#gaussian_ratio_method(sigma = 1)
--- GSL::Ran::gaussian_ratio_method(rng, sigma = 1)
    Use Kinderman-Monahan ratio method.

--- GSL::Cdf::gaussian_P(x, sigma = 1)
--- GSL::Cdf::gaussian_Q(x, sigma = 1)
--- GSL::Cdf::gaussian_Pinv(P, sigma = 1)
--- GSL::Cdf::gaussian_Qinv(Q, sigma = 1)
--- GSL::Cdf::ugaussian_P(x)
--- GSL::Cdf::ugaussian_Q(x)
--- GSL::Cdf::ugaussian_Pinv(P)
--- GSL::Cdf::ugaussian_Qinv(Q)
    These methods compute the cumulative distribution functions P(x), Q(x) 
    and their inverses for the Gaussian distribution with standard 
    deviation ((|sigma|)).

== The Gaussian Tail Distribution
--- GSL::Rng#gaussian_tail(a, sigma = 1)
--- GSL::Ran#gaussian_tail(rng, a, sigma = 1)
--- GSL::Rng#ugaussian_tail(a)
--- GSL::Ran#ugaussian_tail(rng)
    These methods provide 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.

--- GSL::Ran::gaussian_tail_pdf(x, a, sigma = 1)
--- GSL::Ran::ugaussian_tail_pdf(x, a)
    These methods compute the probability density p(x) at ((|x|)) for a Gaussian 
    tail distribution with standard deviation ((|sigma|)) 
    and lower limit ((|a|)).

== The Bivariate Gaussian Distribution
--- GSL::Rng#bivariate_gaussian(sigma_x, sigma_y, rho)
--- GSL::Ran::bivariate_gaussian(rng, sigma_x, sigma_y, rho)
    These methods generate 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.

--- GSL::Ran::bivariate_gaussian_pdf(x, y, sigma_x, sigma_y, rho)
    This method 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|)).

== The Exponential Distribution
--- GSL::Rng#exponential(mu)
--- GSL::Ran::exponential(rng, mu)
    These methods return a random variate from the exponential 
    distribution with mean ((|mu|)).

--- GSL::Ran::exponential_pdf(x, mu)
    This method computes the probability density p(x) at ((|x|)) 
    for an exponential distribution with mean ((|mu|)).

--- GSL::Cdf::exponential_P(x, mu)
--- GSL::Cdf::exponential_Q(x, mu)
--- GSL::Cdf::exponential_Pinv(P, mu)
--- GSL::Cdf::exponential_Qinv(Q, mu)
    These methods compute the cumulative distribution functions P(x), Q(x) 
    and their inverses for the exponential distribution with mean ((|mu|)).

==  The Laplace Distribution
--- GSL::Rng#laplace(a)
--- GSL::Ran::laplace(rng, a)
    These methods return a random variate from the Laplace distribution 
    with width ((|a|)).

--- GSL::Ran::laplace_pdf(x, a)
    This method computes the probability density p(x) at ((|x|)) 
    for a Laplace distribution with width ((|a|)).

--- GSL::Cdf::laplace_P(x, a)
--- GSL::Cdf::laplace_Q(x, a)
--- GSL::Cdf::laplace_Pinv(P, a)
--- GSL::Cdf::laplace_Qinv(Q, a)
    These methods compute the cumulative distribution functions P(x), Q(x) 
    and their inverses for the Laplace distribution with width ((|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|URL:http://www.gnu.org/software/gsl/manual/gsl-ref_19.html#SEC286>)).

==  Shuffling and Sampling
--- GSL::Rng#shuffle(v, n)
    This randomly shuffles the order of ((|n|)) objects, 
    stored in the ((<GSL::Vector|URL:vector.html>)) object ((|v|)). 
--- GSL::Rng#choose(v, k)
    This returns a ((<GSL::Vector|URL:vector.html>)) object with ((|k|)) objects 
    taken randomly from the ((<GSL::Vector|URL:vector.html>)) 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|)).

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