Comparing the Fisher information matrix in record values and random observations for the general class of exponentiated distributions

Abstract

In this paper, the Fisher information matrix (FIM) contained in n record values is considered for the two parameter distributions belong to the exponentiated and inverse exponentiated class of distributions. The problem of existence and uniqueness of the maximum likelihood estimates of the parameters for these families are also considered based on record values. The explicit expressions for the elements of the FIM contained in record values as well as in independent and identically (iid) observations are obtained. The Fisher information (FI) matrices are compared by using the relative efficiency, the total information and the total variance. A simulation study is carried out to compare the FI matrices. A real data analysis has also been performed for illustrative purposes.