Logarithm Transformed Fr´echet Distribution : Properties and Estimation


  • Sanku Dey St. Anthony’s College, Shillong-793001, Meghalaya
  • Mazen Nassar Zagazig University, Egypt
  • Devendra Kumar Central University of Haryana
  • Fahad Alaboud King Abdulaziz University, Jeddah




In this paper, a new three-parameter distribution called the Alpha Logarithm Transformed Fr\'{e}chet (ALTF) distribution is introduced which offers a more flexible distribution for modeling lifetime data. Various properties of the proposed distribution, including explicit expressions for the quantiles, moments, incomplete moments, conditional moments, moment generating function R\'{e}nyi and $\delta$-entropies, stochastic ordering, stress-strength reliability and order statistics are derived. The new distribution can have decreasing, reversed J-shaped and upside-down bathtub failure rate functions depending on its parameter values. The maximum likelihood method is used to estimate the distribution parameters. A simulation study is conducted to evaluate the performance of the maximum likelihood estimates. Finally, the proposed extended model is applied on real data sets and the results are given which illustrate the superior performance of the ALTF distribution compared to some other well-known distributions.

Author Biography

Devendra Kumar, Central University of Haryana




How to Cite

Dey, S., Nassar, M., Kumar, D., & Alaboud, F. (2018). Logarithm Transformed Fr´echet Distribution : Properties and Estimation. Austrian Journal of Statistics, 48(1), 70-93. https://doi.org/10.17713/ajs.v48i1.634



Special Issue on Lifetime Data Modelling (closed)