Generalized exponential distribution: Existing results and some recent developments. (English) Zbl 1119.62011
Summary: G. S. Mudholkar and D. K. Srivastava [Exponentiated Weibull family for analyzing bathtub failure data. IEEE Trans. Reliab. 42, No. 2, 299-302 (1993)] introduced the three-parameter exponentiated Weibull distribution. The two-parameter exponentiated exponential or generalized exponential distribution is a particular member of the exponentiated Weibull distribution. The generalized exponential distribution has a right skewed unimodal density function and monotone hazard function similar to the density functions and hazard functions of the gamma and Weibull distributions. It is observed that it can be used quite effectively to analyze lifetime data in place of gamma, Weibull and log-normal distributions. The genesis of this model, several properties, different estimation procedures and their properties, estimation of the stress-strength parameter, and closeness of this distribution to some of the well-known distribution functions are discussed in this article.
MSC:
| 62E15 | Exact distribution theory in statistics |
| 62N02 | Estimation in survival analysis and censored data |
| 62F15 | Bayesian inference |
| 62F10 | Point estimation |
| 62E20 | Asymptotic distribution theory in statistics |
Keywords:
Bayes estimator; Density function; Fisher information; Hazard function; Maximum likelihood estimator; Order statistics; Stress-Strength modelCitations:
Zbl 0800.62609Software:
LMOMENTSReferences:
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