Estimation for Two-Parameter Generalized Exponential Distribution Based on Records Kang, Suk Bok; Seo, Jung In; Kim, Yongku;
This paper derives maximum likelihood estimators (MLEs) and some approximate MLEs (AMLEs) of unknown parameters of the generalized exponential distribution when data are lower record values. We derive approximate Bayes estimators through importance sampling and obtain corresponding Bayes predictive intervals for unknown parameters for lower record values from the generalized exponential distribution. For illustrative purposes, we examine the validity of the proposed estimation method by using real and simulated data.
Generalized exponential distribution;approximate maximum likelihood estimator;record values;
Ahmadi, J. and Balakrishnan, N. (2011). Distribution-free prediction intervals for order statistics based on record coverage, Journal of the Korean Statistical Society, 40, 181-192.
Ahsanullah, M. (1995). Record Statistics, Nova Science Publishers, New York
Asgharzadeh, A. (2009). Approximate MLE for the scaled generalized exponential distribution under progressive type-II censoring, Journal of the Korean Statistical Society, 38, 223-229.
Balakrishnan, N., Ahsanullah, M. and Chan, P. S. (1992). Relations for single and product moments of record values from Gumbel distribution, Statistical and Probability Letters, 15, 223-227.
Gupta, R. D. and Kundu, D. (1999). Generalized exponential distribution, Australian, New Zealand Journal of Statistics, 41, 173-188.
Jaheen, Z. F. (2006). Empirical Bayes inference for generalized exponential distribution based on records, Communications in Statistics-Theory and Methods, 33, 1851-1861.
Kang, S. B., Cho, Y. S. and Han, J. T. (2009). Estimation for the half logistic distribution based on double hybrid censored samples, Communications of the Korean Statistical Society, 16, 1055-1066.
Kang, S. B. and Seo, J. I. (2011). Estimation in an exponentiated half logistic distribution under progressively type-II censoring, Communications of the Korean Statistical Society, 18, 657-666.
Kundu, D. and Pradhan, B. (2009). Estimating the parameters of the generalized exponential distri- bution in presence of hybrid censoring, Communications in Statistic-Theory and Methods, 38, 2030-2041.
Nichols, M. D. and Padgett, W. J. (2006). A bootstrap control chart for Weibull percentiles, Quality and Reliability Engineering International, 22, 141-151.
Raqab, M. Z. (2002). Inferences for generalized exponential distribution based on record statistics, Journal of Statistical Planning and Inference, 104, 339-350.
Soliman, A. A., Abd Ellah, A. H. and Sultan, K. S. (2006). Comparison of estimates using record statistics fromWeibull model: Bayesian and non-Bayesian approaches, Computational Statistics & Data Analysis, 51, 2065-2077.