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

Statistica

Devendra Kumar¹  Mazen Nassar²  Ayman Alzaatreh³  Sanku Dey⁴  Muhammad Hussain Tahir⁵ 

[1] Central University of Haryana;King Abdulaziz University;Nazarbayev University;St. Anthony's College;The Islamia University of Bahawalpur;

关键词: lomax distribution;    hazard rate function;    maximum likelihood estimation;    survival function;   

DOI  :  10.6092/issn.1973-2201/8442

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown