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.
Highlights
Suppose X is absolutely continuous with cumulative density function(cdf) F(x; θ ) and probability density function f (x; θ ), where θ is a vector parameter (θ1, ..., θm)
The Fisher information (FI) for only one unknown parameter distributions or families were considered based on records and compared with the corresponding FI contained in iid observations
We have derived explicit expressions of the Fisher information matrix (FIM) for the two parameter exponentiated class of distributions based on record values as well as on iid observations
Summary
Suppose X is absolutely continuous with cumulative density function(cdf) F(x; θ ) and probability density function (pdf) f (x; θ ), where θ is a vector parameter (θ1, ..., θm). Some recent contributions on the topic can be found in the papers by Gupta and Kundu [12, 13], Alshunnar et al [5], Raqab [22] and Ahmad et al [1] In these papers, two different measures, the trace of the FIM and the sum of the asymptotic variances of the MLEs of the parameters are generally used to discriminate the interested distributions. We establish the existence and uniqueness of the MLEs based on lower record values in
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