# A New Lifetime Distribution with Decreasing and Upside-Down Bathtub-Shaped Hazard Rate Function

## DOI:

https://doi.org/10.6092/issn.1973-2201/8442## Keywords:

Lomax distribution, Hazard rate function, Maximum likelihood estimation, Survival function## Abstract

We introduce a new lifetime distribution, called the alpha-power transformed Lomax (APTL) distribution which generalizes the Lomax distribution to provide better fits than the Lomax distribution and some of its known generalizations. Various properties of the proposed distribution, including explicit expressions for the quantiles, mode, moments, conditional moments, mean residual lifetime, stochastic ordering, Bonferroni and Lorenz curve, stress-strength reliability and order statistics are derived. The new distribution can have a decreasing and upside-down bathtub failure rate function depending on its parameters. The maximum likelihood estimators of the three unknown parameters of APTL are obtained. A simulation study is carried out to examine the performances of the maximum likelihood estimates in terms of their mean squared error using simulated samples. Finally, the potentiality of the distribution is analyzed by means of two real data sets. For the real data sets, this distribution is found to be superior in its ability to sufficiently model both the data sets as compared to the Lomax (L) distribution, exponentiated-Lomax (EL) distribution, gamma-Lomax (GL) distribution, beta-Lomax (BL) distribution and Kumaraswamy-Lomax (KuL) distribution.

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*Statistica*,

*79*(4), 399–426. https://doi.org/10.6092/issn.1973-2201/8442

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