## Abstract

This paper concerns to the problem of making inferences about the vulnerability θ = P(X > 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 (θ, p) 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.

Translated title of the contribution | estimación de verosimilitud perfil de los parámetros de vulnerabilidad P(X > v) y proporción de mezcla p en el modelo gumbel de mezclas |
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Original language | English |

Pages (from-to) | 193-208 |

Number of pages | 16 |

Journal | Revista Colombiana de Estadistica |

Volume | 36 |

Issue number | 2 |

State | Published - Dec 2013 |

## Keywords

- Invariance principle
- Likelihood approach
- Likelihood region
- Mixture of distributions