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Article: Approximate Bayesian methods
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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(n2) and it is shown how the term 0(n1) can be of importanceTrabajos de Estadistica y de Investigacion Operativa 01/1980;  [show abstract] [hide abstract]
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  J AMER STATIST ASSN. 01/1967; 62(317):3044.  [show abstract] [hide abstract]
ABSTRACT: Probability (P) of equipment failure consequent upon stress exceeding builtin strength has been estimated assuming a bivariate normal stressstrength distribution. The UMVUE of P when parameters other than the means are known has been derived. An alternative estimator based on maximum likelihood estimates has been proposed in the case when all the five parameters are unknown. Asymptotic variances of both these estimators have been worked out. Some relevant numerical computations have also been reported.Microelectronics Reliability 25(4):699–702. · 1.14 Impact Factor
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