A two-parameter lifetime distribution with decreasing failure rate

In this paper, a new two-parameter lifetime distribution with decreasing failure rate is introduced. Various properties of the proposed distribution are discussed. The estimation of the parameters attained by the EM algorithm and their asymptotic variances and covariances are obtained. In order to assess the accuracy of the approximation of variances and covariances of the maximum likelihood estimators, simulation studies are performed and experimental results are illustrated based on real data sets.

[1]  M. M. Nassar,et al.  Two properties of mixtures of exponential distributions , 1988 .

[2]  J. Sethuraman,et al.  Shorter Communication: Reversal of Increasing Failure Rates When Pooling Failure Data , 1994 .

[3]  F. Proschan,et al.  Importance of System Components and Fault Tree Events. , 1975 .

[4]  J. Sethuraman,et al.  Reversal of Increasing Failure Rates When Pooling Failure Data , 1994 .

[5]  Leonard Lewin,et al.  Polylogarithms and Associated Functions , 1981 .

[6]  Mojtaba Ganjali,et al.  On some lifetime distributions with decreasing failure rate , 2009, Comput. Stat. Data Anal..

[7]  R. E. Barlow,et al.  Total time on test processes and applications to failure data , 1975 .

[8]  F. McNolty,et al.  Properties of the Mixed Exponential Failure Process , 1980 .

[9]  P. V. Rao,et al.  Improved Estimation of Survival Functions in the New-Better-Than-Used Class , 1993 .

[10]  Sam C. Saunders,et al.  Maximum Likelihood Estimation for Two-Parameter Decreasing Hazard Rate Distributions Using Censored Data , 1983 .

[11]  Konstantinos Adamidis.  Theory & Methods: An EM algorithm for estimating negative binomial parameters , 1999 .

[12]  Frank Proschan.  Theoretical Explanation of Observed Decreasing Failure Rate , 2000, Technometrics.

[13]  S. Loukas,et al.  On an extension of the exponential-geometric distribution , 2005 .

[14]  A. W. Marshall,et al.  Bounds for Distributions with Monotone Hazard Rate, II , 1964 .

[15]  Frank Proschan,et al.  Maximum Likelihood Estimation for Distributions with Monotone Failure Rate , 1965 .

[16]  Frank Proschan,et al.  Theoretical Explanation of Observed Decreasing Failure Rate , 2000, Technometrics.

[17]  J. Cozzolino.  Probabilistic models of decreasing failure rate processes , 1968 .

[18]  A. W. Marshall,et al.  Tables of Bounds for Distributions with Monotone Hazard Rate , 1965 .

[19]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[20]  Leon Jay Gleser,et al.  The Gamma Distribution as a Mixture of Exponential Distributions , 1989 .

[21]  K. Lomax.  Business Failures: Another Example of the Analysis of Failure Data , 1954 .

[22]  Coskun Kus,et al.  A new lifetime distribution , 2007, Comput. Stat. Data Anal..

[23]  C. Quesenberry,et al.  Selecting Among Probability Distributions Used in Reliability , 1982 .

[24]  J. Gurland,et al.  Goodness of Fit Tests for the Gamma and Exponential Distributions , 1972 .

[25]  S. Loukas,et al.  A lifetime distribution with decreasing failure rate , 1998 .

[26]  G. McLachlan,et al.  The EM algorithm and extensions , 1996 .

[27]  A. W. Marshall,et al.  Properties of Probability Distributions with Monotone Hazard Rate , 1963 .

[28]  Narayanaswamy Balakrishnan,et al.  Estimation of parameters from progressively censored data using EM algorithm , 2002 .