Exact distribution of Cook's distance and identiﬁcation of inﬂuential observations

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.

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