Journal of Statistical Theory and Practice

, Volume 9, Issue 1, pp 122–133 | Cite as

A Generalization of the Exponential-Logarithmic Distribution

  • Vasileios Pappas
  • Konstantinos AdamidisEmail author
  • Sotirios Loukas


A three-parameter lifetime distribution with increasing, decreasing, and unimodal failure rates is presented as a generalization of the exponential-logarithmic distribution introduced by Tahmasbi and Rezaei (2008). Various statistical properties and reliability aspects are explored and the estimation of parameters is studied, using the standard maximum likelihood procedures with complete data; the estimation is discussed briefly when some observations are randomly right-censored. Simulation results and applications of the model to real data are included.


Decreasing failure rate Entropy Exponential-logarithmic distribution Increasing failure rate Maximum likelihood estimation Mean residual lifetime Random censoring Unimodal failure rate 

AMS Subject Classification

60E99 62N05 


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  1. Adamidis, K., and S. Loukas. 1998. A lifetime distribution with decreasing failure rate, Stat. Probability Lett., 39, 35–42.MathSciNetCrossRefGoogle Scholar
  2. Cox, D. R. and Oakes, D. 1984. Analysis of survival data. New York, NY: Chapman and Hall.Google Scholar
  3. Glaser, R. E. 1980. Bathtub and related failure rate characterizations. J. Am. Stat. Assoc., 75, 667–672.MathSciNetCrossRefGoogle Scholar
  4. Kuş, C. 2007. A new lifetime distribution. Comput. Stat. Data Anal., 51, 4497–4509.MathSciNetCrossRefGoogle Scholar
  5. Lai, C. D., and M. Xie. 2006. Stochastic ageing and dependence for reliability. New York, NY: Springer.zbMATHGoogle Scholar
  6. Lawless, J. F. 2003. Statistical models and methods for lifetime data. New York, NY: Wiley.zbMATHGoogle Scholar
  7. Marshall, A. W., and I. Olkin. 2007. Life distributions. New York, NY: Springer.zbMATHGoogle Scholar
  8. Proschan, F. 1963. Theoretical explanation of observed decreasing failure rate. Technometrics, 5, 375–383.CrossRefGoogle Scholar
  9. R Development Core Team. 2011. A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Google Scholar
  10. Self, S. G., and K.-L. Liang. 1987. Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. J. Am. Stat. Assoc., 82, 605–610.MathSciNetCrossRefGoogle Scholar
  11. Tahmasbi, R., and S. Rezaei. 2008. A two-parameter lifetime distribution with decreasing failure rate. Comput. Stat. Data Anal., 52, 3889–3901.MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2015

Authors and Affiliations

  • Vasileios Pappas
    • 1
  • Konstantinos Adamidis
    • 2
    Email author
  • Sotirios Loukas
    • 1
  1. 1.Department of MathematicsUniversity of IoanninaIoanninaGreece
  2. 2.Department of Business Administration of Food & Agricultural EnterprisesUniversity of PatrasAgrinioGreece

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