Type-1 Gumbel distribution

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In probability theory, the Type-1 Gumbel distribution function is

[f(x|a,b)= a b \exp(-(b \exp(-ax) + ax))\,]

for

[-\infty < x < \infty].

The distribution is mainly used in survival analysis (also known as duration analysis or event-history modelling).

Reference

Taken from the [gsl-ref_19.html#SEC309], used under GFDL.

Probability distributions [ view] • [ talk] • [ edit]
Univariate Multivariate
Discrete: Bernoulli • binomial • Boltzmann • compound Poisson • degenerate • degree • Gauss-Kuzmin • geometric • hypergeometric • logarithmic • negative binomial • parabolic fractal • Poisson • Rademacher • Skellam • uniform • Yule-Simon • zeta • Zipf • Zipf-Mandelbrot Ewens • multinomial
Continuous: Beta • Beta prime • Cauchy • chi-square • exponential • exponential power • F • fading • Fisher's z • Fisher-Tippett • Gamma • generalized extreme value • generalized hyperbolic • generalized inverse Gaussian • Hotelling's T-square • hyperbolic secant • hyper-exponential • hypoexponential • inverse chi-square • inverse gaussian • inverse gamma • Kumaraswamy • Landau • Laplace • Lévy • Lévy skew alpha-stable • logistic • log-normal • Maxwell-Boltzmann • Maxwell speed • normal (Gaussian) • Pareto • Pearson • polar • raised cosine • Rayleigh • relativistic Breit-Wigner • Rice • Student's t • triangular • type-1 Gumbel • type-2 Gumbel • uniform • Voigt • von Mises • Weibull • Wigner semicircle Dirichlet • Kent • matrix normal • multivariate normal • von Mises-Fisher • Wigner quasi • Wishart
Miscellaneous: Cantor • conditional • exponential family • infinitely divisible • location-scale family • marginal • maximum entropy • phase-type • posterior • prior • quasi • sampling

	Probability distributions [ view] • [ talk] • [ edit]
Univariate	Multivariate
Discrete:	Bernoulli • binomial • Boltzmann • compound Poisson • degenerate • degree • Gauss-Kuzmin • geometric • hypergeometric • logarithmic • negative binomial • parabolic fractal • Poisson • Rademacher • Skellam • uniform • Yule-Simon • zeta • Zipf • Zipf-Mandelbrot	Ewens • multinomial
Continuous:	Beta • Beta prime • Cauchy • chi-square • exponential • exponential power • F • fading • Fisher's z • Fisher-Tippett • Gamma • generalized extreme value • generalized hyperbolic • generalized inverse Gaussian • Hotelling's T-square • hyperbolic secant • hyper-exponential • hypoexponential • inverse chi-square • inverse gaussian • inverse gamma • Kumaraswamy • Landau • Laplace • Lévy • Lévy skew alpha-stable • logistic • log-normal • Maxwell-Boltzmann • Maxwell speed • normal (Gaussian) • Pareto • Pearson • polar • raised cosine • Rayleigh • relativistic Breit-Wigner • Rice • Student's t • triangular • type-1 Gumbel • type-2 Gumbel • uniform • Voigt • von Mises • Weibull • Wigner semicircle	Dirichlet • Kent • matrix normal • multivariate normal • von Mises-Fisher • Wigner quasi • Wishart
Miscellaneous:	Cantor • conditional • exponential family • infinitely divisible • location-scale family • marginal • maximum entropy • phase-type • posterior • prior • quasi • sampling

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