A new lifetime distribution

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.

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

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

[3]  D. Karlis An EM algorithm for multivariate Poisson distribution and related models , 2003 .

[4]  David R. Cox,et al.  The statistical analysis of series of events , 1966 .

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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