The Type-1 Gumbel Distribution¶
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gsl_ran_gumbel1(a, 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 \(-\infty < x < \infty\).
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gsl_ran_gumbel1_pdf(x, a, b)¶
This function computes the probability density \(p(x)\) at \(x\) for a Type-1 Gumbel distribution with parameters
aandb, using the formula given above.
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gsl_cdf_gumbel1_P(x, a, b)¶
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gsl_cdf_gumbel1_Q(x, a, b)¶
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gsl_cdf_gumbel1_Pinv(P, a, b)¶
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gsl_cdf_gumbel1_Qinv(Q, a, b)¶
These functions compute the cumulative distribution functions \(P(x), Q(x)\) and their inverses for the Type-1 Gumbel distribution with parameters
aandb.