Affiliations: Department of Statistics, Central University of Haryana, Mahendergarh, India
Correspondence:
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Corresponding author: Devendra Kumar, Department of Statistics, Central University of Haryana, Mahendergarh, India. E-mail: [email protected].
Abstract: In this paper, we have considered the exponentiated Pareto type I distribution. Various structural properties of the exponentiated Pareto type I distribution (such as quantile function, moments, incomplete moments, conditional moments, mean deviation about mean and median, stochastic ordering, Bonferroni and Lorenz curves, Renyi entropy and order statistics) are derived. We establish explicit expressions and recurrence relations for single and product moments of record values from exponentiated Pareto type I distribution. These recurrence relations enable computations of the means, variances and covariances of all record values for all sample sizes in a simple and effcient manner. By using these relations, we tabulate the first four moments and variances of record values. The maximum likelihood estimators of the unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non-linear equations only. The asymptotic confidence intervals for the parameters are also obtained based on asymptotic variance covariance matrix. An application of the model to a real data sets is presented and compared with the fit attained by some other well-known two and three parameters distributions.
Keywords: Sample, record values, recurrence relations, exponentiated Pareto type I distribution, characterization2000 MS Classification: 60E05, 62F10
