Logarithm Transformed Fr´echet Distribution : Properties and Estimation

Austrian Journal of Statistics

article

Sanku Dey¹  Mazen Nassar²  Devendra Kumar³  Fahad Alaboud⁴ 

[1] Department of Statistics St. Anthony’s College;Department of StatisticsFaculty of Commerce Zagazig University;Department of Statistics Central University of Haryana;Department of Statistics Faculty of Science, King Abdulaziz University

关键词: logarithm transformed distribution;    hazard rate function;    maximum likelihood estimation;    asymptotic variance-covariance matrix.;   

DOI  :  10.17713/ajs.v48i1.634

学科分类：医学（综合）

来源: Austrian Statistical Society

【 摘 要 】

In this paper, a new three-parameter distribution called the Alpha LogarithmTransformed Fr´echet (ALTF) distribution is introduced which offers a more flexibledistribution 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´enyi and δ-entropies, stochasticordering, stress-strength reliability and order statistics are derived. The new distribution can have decreasing, reversed J-shaped and upside-down bathtub failurerate functions depending on its parameter values. The maximum likelihood methodis used to estimate the distribution parameters. A simulation study is conductedto evaluate the performance of the maximum likelihood estimates. Finally, the proposed extended model is applied on real data sets and the results are given whichillustrate the superior performance of the ALTF distribution compared to some otherwell-known distributions.

【 授权许可】

CC BY