## File: The-Type_002d1-Gumbel-Distribution.html

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 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110  GNU Scientific Library – Reference Manual: The Type-1 Gumbel Distribution

20.26 The Type-1 Gumbel Distribution

Function: double gsl_ran_gumbel1 (const gsl_rng * r, double a, double b)

This function returns a random variate from the Type-1 Gumbel distribution. The Type-1 Gumbel distribution function is,

p(x) dx = a b \exp(-(b \exp(-ax) + ax)) dx

for -\infty < x < \infty.

Function: double gsl_ran_gumbel1_pdf (double x, double a, double b)

This function computes the probability density p(x) at x for a Type-1 Gumbel distribution with parameters a and b, using the formula given above.

Function: double gsl_cdf_gumbel1_P (double x, double a, double b)
Function: double gsl_cdf_gumbel1_Q (double x, double a, double b)
Function: double gsl_cdf_gumbel1_Pinv (double P, double a, double b)
Function: double gsl_cdf_gumbel1_Qinv (double Q, double a, double b)

These functions compute the cumulative distribution functions P(x), Q(x) and their inverses for the Type-1 Gumbel distribution with parameters a and b.