## File: The-Beta-Distribution.html

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 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108  GNU Scientific Library – Reference Manual: The Beta Distribution

20.21 The Beta Distribution

Function: double gsl_ran_beta (const gsl_rng * r, double a, double 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 <= x <= 1.

Function: double gsl_ran_beta_pdf (double x, double a, double 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.

Function: double gsl_cdf_beta_P (double x, double a, double b)
Function: double gsl_cdf_beta_Q (double x, double a, double b)
Function: double gsl_cdf_beta_Pinv (double P, double a, double b)
Function: double gsl_cdf_beta_Qinv (double Q, double a, double b)

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