iosr-Jm   Volume-13 ~ Issue-3 ~ May-June 2017

Abstract: The present theory of consistent estimators of the parameters of statistical structures of homogeneous Gaussian fields can be used, for example, in the reliability predication of different engineering designs. In the paper there are discussed Gaussian homogeneous fields statistical structuresE S i I i , , ,  in Banach space of measures. We prove necessary and sufficient conditions for existence of such estimators.

Keywords: Consistent estimators, orthogonal, weakly separable, strongly separable statistical structures. Classification 62HO5, 62H12

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Abstract: The exponential distribution is perhaps the most widely applied statistical distribution in reliability. Anew continuous bivariate distribution called the bivariate beta-exponential distribution (BBE) that extends the bivariate exponential distribution are proposed. We introduce a new bivariate beta-exponential distributions (BBE) based on some types of copulas. Parametric and semiparametric methods are used to estimate the parameters of the models. Finally, Simulation is studied to illustrate methods of inference discussed and examine the satisfactory performance of the proposed distributions.

Keywords: Beta exponential distribution, beta G distribution, bivariate beta exponential distributions; Maximum likelihood method; copula;

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