Alpha logarithm transformed fréchetdistribution: Properties and estimation
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Date
2019
Journal Title
Journal ISSN
Volume Title
Publisher
Austrian Journal of Statistics
Abstract
In this paper, a new three-parameter distribution called the Alpha Logarithm
Transformed Fr echet (ALTF) distribution is introduced which o ers a more
exible
distribution for modeling lifetime data. Various properties of the proposed distribu-
tion, including explicit expressions for the quantiles, moments, incomplete moments,
conditional moments, moment generating function R enyi and -entropies, stochastic
ordering, stress-strength reliability and order statistics are derived. The new dis-
tribution 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 pro-
posed 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.
Description
Keywords
logarithm transformed distribution, hazard rate function, maximum likeli- hood estimation, asymptotic variance-covariance matrix.