The Type-2 Gumbel Distribution¶

gsl_ran_gumbel2(a, b)¶

This function returns a random variate from the Type-2 Gumbel distribution. The Type-2 Gumbel distribution function is,

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

for \(-\infty < x < \infty\).

gsl_ran_gumbel2_pdf(x, a, b)¶: This function computes the probability density \(p(x)\) at \(x\) for a Type-2 Gumbel distribution with parameters a and b, using the formula given above.

gsl_cdf_gumbel2_P(x, a, b)¶

gsl_cdf_gumbel2_Q(x, a, b)¶

gsl_cdf_gumbel2_Pinv(P, a, b)¶

gsl_cdf_gumbel2_Qinv(Q, a, b)¶: These functions compute the cumulative distribution functions \(P(x), Q(x)\) and their inverses for the Type-2 Gumbel distribution with parameters a and b.

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The Type-1 Gumbel Distribution

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The Poisson Distribution