This paper proposed the exact distribution of Cook's distance used to evaluate the influential observations in multiple linear regression analysis. The authors adopted the relationship proposed by Weisberg (1980), Belsey et al. (1980) and showed the derived density function of the cook's distance in terms of the series expression form. Moreover, the first two moments of the distribution are derived and the authors computed the critical points of Cook's distance at 5 % and 1 % significance level for different sample sizes based on no.of predictors. Finally, the numerical example shows the identification of the influential observations and the results extracted from the proposed approach is more scientific, systematic and it's exactness outperforms the traditional rule of thumb approach.

This paper introduces the bivariate extension of the amoroso distribution and its density function is expressed in terms of hyper-geometric function. The standard amoroso distribution, cumulative distribution functions, conditional distributions, and its moments are also derived. The Product moments, Co-variance, correlations, and Shannon’s differential entropy are also shown. Moreover, the generating functions such as moment, Cumulant, Characteristic functions are expressed in Fox-wright function, and the Survival, hazard, and Cumulative hazard functions are also computed. The special cases of the bivariate amoroso distribution are also discussed and nearly 780 bivariate mixtures of distributions can be derived. Finally, the two-dimensional probability surfaces are visualized for the selected special cases and we also showed the estimation of parameters by the method of maximum likelihood approach, and the constrained maximum likelihood approach is also computed by using Non-linear Programming with a numerical application

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