Generalized exponential distribution: Existing results and some recent developments

Journal of Statistical Planning and Inference

Volumn 137, Issue 11, 2007, Pages 3537-3547

  Gupta, Rameshwar D ^a   Kundu, Debasis ^b  

^a UNIVERSITY OF NEW BRUNSWICK   (Canada)

^b INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

Author keywords

Bayes estimator; Density function; Fisher information; Hazard function; Maximum likelihood estimator; Order statistics; Stress Strength model

Indexed keywords

EID: 34447510876     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2007.03.030     Document Type: Article

References (33)

1. Ahuja J.C., and Nash S.W. The generalized Gompertz-Verhulst family of distributions. Sankhya, Ser. A 29 (1967) 141-156
2. Chandler K.N. The distribution and frequency of records. J. Roy. Statist. Soc. Ser. B 14 (1952) 220-228
3. Cox, D.R., 1961. Tests of separate families of hypotheses. In: Proceedings of the Fourth Berkeley Symposium in Mathematical Statistics and Probability, University of California Press, California, pp. 105-123.
4. Efron B., and Johnstone I. Fisher information in terms of the hazard rate. Ann. Statist. 18 (1990) 38-62
5. Galton F. Natural Inheritance (1889), MacMillan, London
6. Gompertz B. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philos. Trans. Roy. Soc. London 115 (1825) 513-585
7. Gupta R.D., and Kundu D. Generalized exponential distributions. Austral. New Zealand J. Statist. 41 (1999) 173-188
8. Gupta R.D., and Kundu D. Exponentiated exponential family; an alternative to gamma and Weibull. Biometrical J. 43 (2001) 117-130
9. Gupta R.D., and Kundu D. Generalized exponential distributions: different methods of estimation. J. Statist. Comput. Simulation 69 (2001) 315-338
10. Gupta R.D., and Kundu D. Generalized exponential distributions: statistical inferences. J. Statist. Theory Appl. 1 (2002) 101-118
11. Gupta R.D., and Kundu D. Discriminating between the Weibull and the GE distributions. Comput. Statist. Data Anal. 43 (2003) 179-196
12. Gupta R.D., and Kundu D. Closeness of gamma and generalized exponential distribution. Comm. Statist.-Theory Methods 32 4 (2003) 705-721
13. Gupta R.D., and Kundu D. Discriminating between gamma and generalized exponential distributions. J. Statist. Comput. Simulation 74 2 (2004) 107-121
14. Gupta R.D., and Kundu D. Comparison of the Fisher information between the Weibull and generalized exponential distribution. J. Statist. Plann. Inference 136 (2006) 3130-3144
15. Gupta R.C., Gupta P.L., and Gupta R.D. Modeling failure time data by Lehmann alternatives. Comm. Statist.-Theory and Methods 27 (1998) 887-904
16. Gupta R.D., Gupta R.C., and Sankaran P.G. Some characterization results based on the (reversed) hazard rate function. Comm. Statist.-Theory Methods 33 12 (2004) 3009-3031
17. Hosking J.R.M. L-moment: analysis and estimation of distributions using linear combinations of order statistics. J. Roy. Statist. Soc. Ser. B 52 1 (1990) 105-124
18. Kotz S., Lumelskii Y., and Pensky M. The Stress-Strength Model and its Generalizations-Theory and Applications (2003), World Scientific, New York
19. Kundu D., and Gupta R.D. Estimation of P (Y < X) for generalized exponential distribution. Metrika 61 (2005) 291-308
20. Kundu, D., Gupta, R.D., 2007. Bayesian estimation for the generalized exponential distribution, Comput. Statist. Data Anal., submitted for publication.
21. Kundu D., Gupta R.D., and Manglick A. Discriminating between the log-normal and generalized exponential distribution. J. Statist. Plann. Inference 127 (2005) 213-227
22. Kundu D., Gupta R.D., and Manglick A. A convenient way of generating normal random variables using generalized exponential distribution. J. Modern Appl. Statist. Methods 5 (2006) 266-272
23. Lindley D.V. Approximate Bayesian method. Trabajos Estadist. 31 (1980) 223-237
24. MacGillivray H.L. Skewness and asymmetry: measures and orderings. Ann. Statist. 14 (1986) 994-1011
25. Mudholkar G.S., and Srivastava D.K. Exponentiated Weibull family for analyzing bathtub failure data. IEEE Trans. Reliability 42 (1993) 299-302
26. Nanda A.K., and Gupta R.D. Some properties of reversed hazard function. Statist. Methods 3 (2001) 108-124
27. Nassar M.M., and Eissa F.L. Bayesian estimation for the exponentiated Weibull model. Comm. Statist.-Theory and Methods 33 (2004) 2343-2362
28. Raqab M.Z. Inferences for generalized exponential distribution based on record statistics. J. Statist. Plann. Inference 104 (2002) 339-350
29. Raqab M.Z., and Ahsanullah M. Estimation of the location and scale parameters of generalized exponential distribution based on order statistics. J. Statist. Comput. Simulation 69 (2001) 109-124
30. Verhulst, P.F., 1838. Notice sur la loi la population suit dans son accroissement. Correspondence mathematique et physique, publiee L. A. J. Quetelet, vol. 10, pp. 113-121.
31. Verhulst, P.F., 1845. Recherches mathematiques sur la loi-d'-accroissement de la population. Nouvelles Memoires de l'Academie Royale des Sciencs et Belles-Lettres de Bruxelles [i.e. Memoires, Series 2], vol. 18, 38pp.
32. Verhulst, P.F., 1847. Deuxieme memoire sur la loi d'accroissement de la population. Memoires de l'Academie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique, Series 2, vol. 20, 32pp.
33. Zheng G. Fisher information matrix in type-II censored data from exponentiated exponential family. Biometrical J. 44 (2002) 353-357