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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.

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
Full Text: DOI
[1] Adamidis, K.; Loukas, S., A lifetime distribution with decreasing failure rate, Statist. probab. lett., 39, 35-42, (1998) · Zbl 0908.62096
[2] Barlow, R.E., Cambo, R., 1975. Total time on test processes and applications to failure data analysis. Reliability and Fault Tree Analysis, Society for Industrial and Applied Mathematics, Philadelphia, pp. 451-481.
[3] Barlow, R.E.; Proschan, F., Statistical theory of reliability and life-testing probability models, (1975), Holt, Reinhart and Winston Inc. New York · Zbl 0379.62080
[4] Chang, M.N.; Rao, P.V., Improved estimation of survival functions in the new-better-than-used class, Technometrics, 35, 192-203, (1993) · Zbl 0775.62265
[5] Dempster, A.P.; Laird, N.M.; Rubin, D.B., Maximum likelihood from incomplete data via the EM algorithm (with discussion), J. R. statist. soc. B, 39, 1-38, (1977) · Zbl 0364.62022
[6] Erdelyi, A.; Magnus, W.; Oberhettinger, F.; Tricomi, F.G., Higher transcendental functions, (1953), McGraw-Hill Book Company Inc. New York · Zbl 0052.29502
[7] Marshall, A.W.; Olkin, I., A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika, 84, 641-652, (1997) · Zbl 0888.62012
[8] McLachlan, C.J.; Krishnan, T., The EM algorithm and extensions, (1997), Wiley New York · Zbl 0882.62012
[9] Meng, X.-L.; Rubin, D.B., Maximum likelihood estimation via the ECM algorithm: a general framework, Biometrika, 80, 267-278, (1993) · Zbl 0778.62022
[10] Quesenberry, C.P.; Kent, J., Selecting among probability distributions used in reliability, Technometrics, 24, 59-65, (1982)
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