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