The logistic–exponential survival distribution

For various parameter combinations, the logistic-exponential survival distribution belongs to four common classes of survival distributions: increasing failure rate, decreasing failure rate, bathtub-shaped failure rate, and upside-down bathtub-shaped failure rate. Graphical comparison of this new distribution with other common survival distributions is seen in a plot of the skewness versus the coefficient of variation. The distribution can be used as a survival model or as a device to determine the distribution class from which a particular data set is drawn. As the three-parameter version is less mathematically tractable, our major results concern the two-parameter version. Boundaries for the maximum likelihood estimators of the parameters are derived in this article. Also, a fixed-point method to find the maximum likelihood estimators for complete and censored data sets has been developed. The two-parameter and the three-parameter versions of the logistic-exponential distribution are applied to two real-life data sets. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 55: 252-264, 2008

[1]  L. Leemis,et al.  Minimum Kolmogorov–Smirnov test statistic parameter estimates , 2006 .

[2]  Deo Kumar Srivastava,et al.  The exponentiated Weibull family: a reanalysis of the bus-motor-failure data , 1995 .

[3]  Pandu R. Tadikamalla,et al.  Systems of frequency curves generated by transformations of logistic variables , 1982 .

[4]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[5]  M. Crowder.  Classical Competing Risks , 2001 .

[6]  U. Hjorth.  A Reliability Distribution With Increasing, Decreasing, Constant and Bathtub-Shaped Failure Rates , 1980 .

[7]  Andrew G. Glen,et al.  The Arctangent Survival Distribution , 1997 .

[8]  B. Everitt,et al.  Finite Mixture Distributions , 1981 .

[9]  K. C. Burns.  Motion sickness incidence: distribution of time to first emesis and comparison of some complex motion conditions. , 1984, Aviation, space, and environmental medicine.

[10]  Melania Pintilie,et al.  Competing Risks: A Practical Perspective , 2006 .

[11]  I. W. Burr.  Cumulative Frequency Functions , 1942 .

[12]  Martin Crowder,et al.  Statistical Analysis of Reliability Data , 1991 .

[13]  J. Bert Keats,et al.  Statistical Methods for Reliability Data , 1999 .

[14]  W. Nelson.  Statistical Methods for Reliability Data , 1998 .

[15]  J. Lieblein,et al.  Statistical Investigation of the Fatigue Life of Deep-Groove Ball Bearings , 1956 .

[16]  W. R. Buckland.  Theory of Competing Risks , 1978 .

[17]  Sigmund J. Amster,et al.  Report: Statistical methods for reliability improvement , 1986, AT&T Technical Journal.

[18]  D. Cox,et al.  Analysis of Survival Data. , 1986 .

[19]  Geoffrey J. McLachlan,et al.  Finite Mixture Models , 2019, Annual Review of Statistics and Its Application.

[20]  C. Caroni,et al.  The Correct “Ball Bearings” Data , 2002, Lifetime data analysis.

[21]  H. A. David.  The theory of competing risks , 1980 .