pdf – Probability Distribution Functions

Most of the functions described in the module rnd returns a continues variate over a finite or infinite interval. For this kind of distributions we can define a probability density function, pdf, such that the product p(x) dx gives the probability that the variate x lie between x and x + dx. GSL shell gives you a set of functions to calculate this probability wi the module pdf.

The module pdf offer the same functions of the module rnd with the same names. The only difference is that the pdf function will give, for a given value x the probability density of obtaining this value. So for example to obtain the probability p(x) for a given values of x for a Gaussian distribution and a given value of σ you can call the function:

pdf.gaussian(x, sigma)

Note that the first argument is the value x and you don’t need to pass the random number generator.

So the pdf module provides the equivalent functions of the module rnd to calculate the probability function.

pdf.gaussian(x[, sigma])
See Gaussian distribution.
pdf.exponential(x[, mu])
See Exponential Distribution.
pdf.chisq(x[, nu])
See Chi square Distribution.
pdf.laplace(x[, a])
See Laplace Distribution.
pdf.tdist(x[, nu])
See t- Distribution.
pdf.cauchy(x[, a])
See Cauchy Distribution.
pdf.rayleigh(x[, sigma])
See Rayleigh Distribution.
pdf.fdist(x, nu1, nu2)
See F- Distribution.
pdf.gamma(x, a, b)
See Gamma Distribution.
pdf.beta(x, a, b)
See Beta Distribution.
pdf.gaussian_tail(x, a, sigma)
See Gaussian tail Distribution.
pdf.exppow(x, a, b)
See Exponential Power Distribution.
pdf.lognormal(x, zeta, sigma)
See Lognormal Distribution.
pdf.binomial(x, p, n)
See Binomial Distribution.
pdf.poisson(x[, mu])
See Poisson Distribution.

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