Estimation of P(X <= Y ) for a Bivariate Weibull Distribution
ABSTRACT Nous étudions ici l'estimation de R=P(X<Y), quand X et Y sont des variables aleatoires qui suivent la loi bivariate Weibull et X est censurée à Y. On obtient la loi marginale pour les données observées et on en tire MLE,UMVUE,MME de R. Ainsi on obtient les estimateurs de Bayes sur la fonction SEL. On a effectué une simulation de Monte-Carlo pour comparer ces estimateurs.
Article: A multivariate Weibull distribution[Show abstract] [Hide abstract]
ABSTRACT: We introduce a new multivariate Weibull (MVW) distribution with many interesting properties. We obtain the maximum likelihood estimate (MLE) of the parameters and their asymptotic multivariate normal (AMVN) distribution in MVW model. We propose large sample studentized tests for testing multivariate exponentiality and also tests for independence and identical marginals of the components.
Article: Approximate Bayesian methods[Show abstract] [Hide abstract]
ABSTRACT: This paper develops asymptotic expensions for the ratios of integrals that occur in Bayesian analysis: for example, the posterior mean. The first term omitted is 0(n-2) and it is shown how the term 0(n-1) can be of importanceTrabajos de Estadistica y de Investigacion Operativa 01/1980; DOI:10.1007/BF02888353
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ABSTRACT: A number of multivariate exponential distributions are known, but they have not been obtained by methods that shed light on their applicability. This paper presents some meaningful derivations of a multivariate exponential distribution that serves to indicate conditions under which the distribution is appropriate. Two of these derivations are based on “shock models,” and one is based on the requirement that residual life is independent of age. It is significant that the derivations all lead to the same distribution.For this distribution, the moment generating function is obtained, comparison is made with the case of independence, the distribution of the minimum is discussed, and various other properties are investigated. A multivariate Weibull distribution is obtained through a change of variables.Journal of the American Statistical Association 03/1967; 62(317):30-44. DOI:10.1080/01621459.1967.10482885 · 2.11 Impact Factor