The U family of distributions: Properties and applications

Authors

  • Farrukh Jamal The Islamia University of Bahawalpur
  • Christophe Chesneau Université de Caen
  • Abdus Saboor Kohat University of Science and Technology
  • Muhammad Aslam King Abdulaziz University
  • Muhammad H. Tahir The Islamia University of Bahawalpur
  • Wali Khan Mashwani Kohat University of Sciences and Technology

DOI:

https://doi.org/10.1515/ms-2022-0015

Keywords:

Weibull distribution, general family of distributions, moments; simulation, data analysis

Abstract

In this article, we develop a new general family of distributions aimed at unifying some well-established lifetime distributions and offering new work perspectives. A special family member based on the so-called modified Weibull distribution is highlighted and studied. It differs from the competition with a very flexible hazard rate function exhibiting increasing, decreasing, constant, upside- down bathtub and bathtub shapes. This panel of shapes remains rare and particularly desirable for modeling purposes. We provide the main mathematical properties of the special distribution, such as a tractable infinite series expansion of the probability density function, moments of several kinds (raw, incomplete, probability weighted ...) with discussions on the skewness and kurtosis. The stochastic ordering structure and stress-strength parameter are also considered, as well as the basics of the order statistics. Then, an emphasis is put on the inferential features of the related model. In particular, the estimation of the model parameters is employed by the maximum likelihood method, with a simulation study to confirm the suitability of the approach. Three practical data sets are then analyzed. It is observed that the proposed model gives better fits than other well-known lifetime models derived from the Weibull model.

Author Biographies

Farrukh Jamal, The Islamia University of Bahawalpur

Department of Statistics
The Islamia University of Bahawalpur
Punjab 63100
PAKISTAN

Christophe Chesneau, Université de Caen

Université de Caen,
LMNO, Campus II, Science 3,
Caen 14032
FRANCE

Abdus Saboor, Kohat University of Science and Technology

Department of Mathematics
Kohat University of Science and Technology
Kohat
PAKISTAN

Muhammad Aslam, King Abdulaziz University

Department of Statistics
Faculty of Science
King Abdulaziz University
Jeddah
SAUDI ARABIA

Muhammad H. Tahir, The Islamia University of Bahawalpur

Department of Statistics
The Islamia University of Bahawalpur
Punjab 63100
PAKISTAN

Wali Khan Mashwani, Kohat University of Sciences and Technology

Institute of Numerical Sciences
Kohat University of Sciences and Technology
KPK
PAKISTAN

Published

2022-02-16

Issue

Section

Articles - Other topics