Generalized exponential records: existence of maximum likelihood estimates and its comparison with transforming based estimates
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In this paper, and based on records of a sequence of iid random variables from the generalized exponential distribution, we consider the problem of the existence of the maximum likelihood estimates of the shape and scale parameters. Existence and uniqueness of the MLE’s are proved. Different transforming based estimates and confidence intervals of these parameters are then derived. The performances of the so obtained estimates and confidence intervals are compared through an extensive numerical simulation study. Analysis of a real data set has also been presented for illustrative purposes.
KeywordsRecord statistics Generalized exponential distribution Maximum likelihood estimate Pivotal quantity Confidence interval Uniform distribution Exponential distribution
Mathematics Subject Classification62G30 62E15 62F10
The authors are grateful to the associate editor and referees for their helpful comments and suggestions.