, Volume 14, Issue 2, pp 417–431 | Cite as

Using the empirical moment generating function in testing for the Weibull and the type I extreme value distributions



We introduce two families of statistics, functionals of the empirical moment generating function process of the logarithmically transformed data, for testing goodness of fit to the two-parameter Weibull distribution or, equivalently, to the type I extreme value model. We show that when affine invariant estimators are used for the parameters of the extreme value distribution, the distributions of these statistics to not depend on the underlying parameters and one of them has a limiting chi-squared distribution. We estimate, via simulations, some finite sample quantiles for the statistics introduced and evaluate their power against a varied set of alternatives.

Key Words

Weibull distribution extreme value distributions goodness of fit testing moment generating function 

AMS subject classification

Primary 62F03 Secondary 60F05 


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Copyright information

© Sociedad Española de Estadistica e Investigacion Operativa 2005

Authors and Affiliations

  1. 1.Instituto Venezolano de Investigaciones CientíficasVenezuela
  2. 2.Dpto. de Estadística e I.O.Universidad de ValladolidSpain
  3. 3.Dpto. de Cómputo Científico y EstadísticaUniversidad Simón BolívarVenezuela

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