Extended exponential distribution based on order statistics |
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Authors: | Devendra Kumar Sanku Dey Saralees Nadarajah |
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Institution: | 1. Department of Statistics, Amity University, Noida, India;2. Department of Statistics, St. Anthony College, Shillong, India;3. School of Mathematics, University of Manchester, Manchester, UK |
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Abstract: | The extended exponential distribution due to Nadarajah and Haghighi (2011 Nadarajah, S., Haghighi, F. (2011). An extension of the exponential distribution. Statistics 45:543–558.Taylor &; Francis Online], Web of Science ®] , Google Scholar]) is an alternative to and always provides better fits than the gamma, Weibull, and the exponentiated exponential distributions whenever the data contain zero values. We establish recurrence relations for the single and product moments of order statistics from the extended exponential distribution. These recurrence relations enable computation of the means, variances, and covariances of all order statistics for all sample sizes in a simple and efficient manner. By using these relations, we tabulate the means, variances, and covariances of order statistics and derive best linear unbiased estimates of the extended exponential distribution. Finally, a data application is provided. |
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Keywords: | Extended exponential distribution order statistics recurrence relations single and product moments |
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