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Inferences for generalized exponential distribution based on record statistics. (English) Zbl 0992.62013

Summary: We consider the three parameter generalized exponential distribution. Exact expressions for single and product moments of record statistics are derived. These expressions are written in terms of Riemann zeta and polygamma functions. Recurrence relations for single and product moments of record statistics are also obtained. These relations can be used to obtain the higher order moments from those of the lower order. The means, variances and covariances of the record statistics are computed for various values of the shape parameter and for some record statistics. These values are used to compute the coefficients of the best linear unbiased estimators of the location and scale parameters. The variances of these estimators are also presented. The predictors of the future record statistics are also discussed.

MSC:

62E15 Exact distribution theory in statistics
62G32 Statistics of extreme values; tail inference
62M20 Inference from stochastic processes and prediction
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