The Beta Distribution¶

gsl_ran_beta(a, b)¶

This function returns a random variate from the beta distribution. The distribution function is,

\[p(x) dx = {\Gamma(a+b) \over \Gamma(a) \Gamma(b)} x^{a-1} (1-x)^{b-1} dx\]

for \(0 \leq x \leq 1\).

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_cdf_beta_P(x, a, b)¶

gsl_cdf_beta_Q(x, a, b)¶

gsl_cdf_beta_Pinv(P, a, b)¶

gsl_cdf_beta_Qinv(Q, a, b)¶: These functions compute the cumulative distribution functions \(P(x), Q(x)\) and their inverses for the beta distribution with parameters a and b.

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The t-distribution

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The Logistic Distribution