A new lifetime distribution. (English) Zbl 1162.62309

Summary: A new two-parameter distribution with decreasing failure rate is introduced. Various properties of the introduced distribution are discussed. The EM algorithm is used to determine the maximum likelihood estimates and the asymptotic variances and covariance of these estimates are obtained. Simulation studies are performed in order to assess the accuracy of the approximation of the variances and covariance of the maximum likelihood estimates and investigate the convergence of the proposed EM scheme. Illustrative examples based on real data are also given.


62E10 Characterization and structure theory of statistical distributions
62N05 Reliability and life testing
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[1] Adamidis, K., An EM algorithm for estimating negative binomial parameters, Austral. New Zealand J. statist., 41, 2, 213-221, (1999) · Zbl 0962.62013
[2] Adamidis, K.; Loukas, S., A life time distribution with decreasing failure rate, Statist. probab. lett., 39, 35-42, (1998) · Zbl 0908.62096
[3] Adamidis, K.; Dimitrakopoulou, T.; Loukas, S., On an extension of the exponential – geometric distribution, Statist. probab. lett., 73, 259-269, (2005) · Zbl 1075.62008
[4] Barlow, R.E.; Marshall, A.W., Bounds for distributions with monotone hazard rate I and II, Ann. math. statist., 35, 1234-1274, (1964) · Zbl 0245.60012
[5] Barlow, R.E.; Marshall, A.W., Tables of bounds for distributions with monotone hazard rate, J. amer. statist. assoc., 60, 872-890, (1965)
[6] Barlow, R.E.; Marshall, A.W.; Proschan, F., Properties of probability distributions with monotone hazard rate, Ann. math. statist., 34, 375-389, (1963) · Zbl 0249.60006
[7] Cox, D.R.; Lewis, P.A.W., The statistical analysis of series of events, (1978), Chapman & Hall London
[8] Cozzolino, J.M., Probabilistic models of decreasing failure rate processes, Naval res. logist. quart., 15, 361-374, (1968) · Zbl 0164.20503
[9] Dahiya, R.C.; Gurland, J., Goodness of fit tests for the gamma and exponential distributions, Technometrics, 14, 791-801, (1972) · Zbl 0239.62021
[10] Dempster, A.P.; Laird, N.M.; Rubin, D.B., Maximum likelihood from incomplete data via the EM algorithm (with discussion), J. roy. statist. soc. ser. B, 39, 1-38, (1977) · Zbl 0364.62022
[11] Gleser, L.J., The gamma distribution as a mixture of exponential distributions, Amer. statist., 43, 115-117, (1989)
[12] Gurland, J.; Sethuraman, J., Reversal of increasing failure rates when pooling failure data, Technometrics, 36, 416-418, (1994) · Zbl 0825.62722
[13] Karlis, D., An EM algorithm for multivariate Poisson distribution and related models, J. appl. statist., 30 1, 63-77, (2003) · Zbl 1121.62408
[14] Little, R.J.A.; Rubin, D.B., Incomplete data, ()
[15] Lomax, K.S., Business failures: another example of the analysis of failure data, J. amer. statist. assoc., 49, 847-852, (1954) · Zbl 0056.13702
[16] Marshall, A.W.; Proschan, F., Maximum likelihood estimates for distributions with monotone failure rate, Ann. math. statist., 36, 69-77, (1965) · Zbl 0128.38506
[17] McLachlan, G.J.; Krishnan, T., The EM algorithm and extension, (1997), Wiley New York
[18] McNolty, F.; Doyle, J.; Hansen, E., Properties of the mixed exponential failure process, Technometrics, 22, 555-565, (1980) · Zbl 0448.62076
[19] Nassar, M.M., Two properties of mixtures of exponential distributions, IEEE trans. raliab., 37, 4, 383-385, (1988) · Zbl 0662.62010
[20] Ng, H.K.T.; Chan, P.S.; Balakrishnan, N., Estimation of parameters from progressively censored data using EM algorithm, Comput. statist. data anal., 39, 371-386, (2002) · Zbl 0993.62085
[21] Proschan, F., Theoretical explanation of observed decreasing failure rate, Technometrics, 5, 375-383, (1963)
[22] Saunders, S.C.; Myhre, J.M., Maximum likelihood estimation for two-parameter decreasing hazard rate distributions using censored data, J. amer. statist. assoc., 78, 664-673, (1983) · Zbl 0528.62085
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