Multivariate Marshall and Olkin Exponential Minification Process

Abstract

A stationary bivariate minification process with bivariate Marshall-Olkin exponential distribution that was earlier studied by Miroslav et al [15]is in this paper extended to multivariate minification process with multivariate Marshall and Olkin exponential distribution as its stationary marginal distribution. The innovation and the joint distributions of random vectors (X_n ⁽¹⁾,  X_n ⁽²⁾ ,..., X_n ^(k)) and (X ⁽¹⁾ _n-j, (X⁽²⁾ _n-j,..., X^(k) _n-j),  j >0, are presented. The autocovariance and the autocorrelation matrices are developed. Lastly, the unknown parameters are estimated and their asymptotic properties are also investigated in this research work.

Keywords: Ergodic; Estimation; Minification process; Multivariate Marshall and Olkin Exponential Distribution; uniformly mixing.