Abstract

MONTOYA, JOSÉ A.; FIGUEROA, GUDELIA  and  PUK\V SI\V C, NU\V SA. Profile Likelihood Estimation of the Vulnerability P(X\textgreater v) and the Mixing Proportion p Parameters in the Gumbel Mixture Model. Rev.Colomb.Estad. [online]. 2013, vol.36, n.2, pp.193-208. ISSN 0120-1751.

This paper concerns to the problem of making inferences about the vulnerability θ=P(X\textgreater v) and the mixing proportion p parameters, when the random variable X is distributed as a mixture of two Gumbel distributions and v is a known fixed value. A profile likelihood approach is proposed for the estimation of these parameters. This approach is a powerful though simple method for separately estimating a parameter of interest in the presence of unknown nuisance parameters. Inferences about θ, p or \left(θ,p\right) are given in terms of profile likelihood regions and can be easily obtained on a computer. This methodology is illustrated through a real problem where the main purpose is to model the size of non-metallic inclusions in steel.

Keywords : Invariance principle; Likelihood approach; Likelihood region; Mixture of distributions.

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