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A lifetime distribution with decreasing failure rate. (English) Zbl 0908.62096
Summary: A two-parameter distribution with decreasing failure rate is introduced. Various properties are discussed and the estimation of parameters is studied by the method of maximum likelihood. The estimates are attained by the EM algorithm and expressions for their asymptotic variances and covariances are obtained. Numerical examples based on real data are presented.

##### MSC:
 62N05 Reliability and life testing 62F10 Point estimation 62E10 Characterization and structure theory of statistical distributions
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##### References:
 [1] Barlow, R.E.; Marshall, A.W.; Proschan, F., Properties of probability distributions with monotone hazard rate, Ann. of math. statist., 34, 375-389, (1963) · Zbl 0249.60006 [2] 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 [3] Barlow, R.E.; Marshall, A.W., Tables of bounds for distributions with monotone hazard rate, J. amer. statist. assoc., 60, 872-890, (1965) [4] Cox, D.R.; Lewis, P.A.W., The statistical analysis of series of events, (1978), Chapman & Hall London · Zbl 0148.14005 [5] Cozzolino, J.M., Probabilistic models of decreasing failure rate processes, Naval res. logist. quart., 15, 361-374, (1968) · Zbl 0164.20503 [6] Dahiya, R.C.; Gurland, J., Goodness of fit tests for the gamma and exponential distributions, Technometrics, 14, 791-801, (1972) · Zbl 0239.62021 [7] 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 [8] Erdelyi, A.; Magnus, W.; Oberhettinger, F.; Tricomi, F.G., Higher transcendental functions, (1953), McGraw-Hill New York · Zbl 0052.29502 [9] Gleser, L.J., The gamma distribution as a mixture of exponential distributions, Amer. statist., 43, 115-117, (1989) [10] Gurland, J.; Sethuraman, J., Reversal of increasing failure rates when pooling failure data, Technometrics, 36, 416-418, (1994) · Zbl 0825.62722 [11] Lomax, K.S., Business failures: another example of the analysis of failure data, J. amer. statist. assoc., 49, 847-852, (1954) · Zbl 0056.13702 [12] Louis, T.A., Finding the observed information when using the EM algorithm, J. roy. statist. soc. ser. B, 44, 226-233, (1982) · Zbl 0488.62018 [13] Marshall, A.W.; Proschan, F., Maximum likelihood estimates for distributions with monotone failure rate, Ann. math. statist, 36, 69-77, (1965) · Zbl 0128.38506 [14] McNolty, F.; Doyle, J.; Hansen, E., Properties of the mixed exponential failure process, Technometrics, 22, 555-565, (1980) · Zbl 0448.62076 [15] Meilijson, I., A fast improvement to the EM algorithm on its own terms, J. roy. statist. soc. ser. B, 51, 127-138, (1989) · Zbl 0674.65118 [16] Patil, G.P.; Boswell, M.T.; Joshi, S.W.; Ratnaparkhi, M.V., () [17] Proschan, F., Theoretical explanation of observed decreasing failure rate, Technometrics, 5, 375-383, (1963) [18] 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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