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