A two-stage sequential allocation scheme for estimating the product of the means of several independent populations under the squared error loss is proposed. The scheme specifies how a total of M observations can be allocated to the various populations in an optimal fashion, and yields, asymptotically as M -t m, a Bayes risk that is smaller than the risk obtained under the balanced design.
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The induction of one or more parameter(s) in parent distributions opened new doors for flexible modeling in modern distribution theory. Among well-established generalized (G) classes for flexible modeling, the exponentiated-G, Marshall-Olkin-G and odd log-logistic-G families offer induction of one additional parameter while the beta-G and Kumaraswamy-G classes offer two extra shape parameters. The Marshall-Olkin-odd-loglogistic-G (MOOLL-G) family serves as an alternative to the beta-G and Kumaraswamy-G classes. A new motivation for the MOOLL-G family for competing risk scenarios, some useful properties, and parameter estimation are addressed. The new log-MOOLL-Weibull regression is useful for analysis of real life data. The accuracy of the estimates and the residuals is addressed via Monte Carlo simulations. The presented models outperform some other well-known models.
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