On an extension of the exponential-geometric distribution. (English) Zbl 1075.62008

Adamidis, Konstantinos; Dimitrakopoulou, Theodora; Loukas, Sotirios

Stat. Probab. Lett. 73, No. 3, 259-269 (2005).

Summary: Various statistical properties and reliability aspects of a two-parameter distribution with decreasing and increasing failure rate are explored; the model includes the exponential-geometric distribution [A. W. Marshall and I. Olkin, Biometrika 84, No. 3, 641–652 (1997; Zbl 0888.62012); K. Adamidis and S. Loukas, Stat. Probab. Lett. 39, 35–42 (1998; Zbl 0908.62096)]] as a special case. Characterizations are given and the estimation of parameters is studied by the method of maximum likelihood. An EM algorithm [A. P. Dempster et al., J. R. Stat. Soc. B. 39, 1–38 (1977; Zbl 0364.62022)] is proposed for computing the estimates, and expressions for their asymptotic variances and covariances are derived. Numerical examples based on real data are included.

MSC:

62E10	Characterization and structure theory of statistical distributions
62N05	Reliability and life testing
62N02	Estimation in survival analysis and censored data
65C60	Computational problems in statistics (MSC2010)
62F10	Point estimation

Keywords:

Characterization; Compounding; EM Algorithm; Exponential distribution; Exponential-geometric distribution; Failure rate; Geometric distribution; Lifetime distributions; Maximum likelihood estimation; Mean residual lifetime; Modified extreme value distribution

References:

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