A new generalized family of distributions: Properties and applications

Sajid Mehboob Zaidi; Mashail M. AL Sobhi; M. El-Morshedy; Ahmed Z. Afify; Sajid Mehboob Zaidi; Mashail M. AL Sobhi; M. El-Morshedy; Ahmed Z. Afify

doi:10.3934/math.2021028

AIMS Mathematics

2021, Volume 6, Issue 1: 456-476. doi: 10.3934/math.2021028

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Research article

A new generalized family of distributions: Properties and applications

1.
Department of Statistics, Govt. Postgraduate College B. R. Bahawalpur, Bahawalpur 63100, Pakistan
2.
Mathematics Department, Umm-Al-Qura University, Makkah, Saudi Arabia
3.
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
4.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
5.
Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt

Received: 12 August 2020 Accepted: 09 October 2020 Published: 19 October 2020
MSC : 60E05, 62F10

We come up with a new class called log-logistic tan generalized family which provides sub-models with left skewed, symmetrical, right skewed, unimodal, bimodal and reversed-J densities, and increasing, decreasing, modified bathtub, bathtub, unimodal, reversed-J shaped, and J-shaped hazard rates. Some of its sub-models are provided along with some general structural properties. The parameter estimation has been conducted via maximum likelihood. Moreover, the estimators behavior are assessed using various simulation results. The capability of the log-logistic tan-Weibull model is proved using two real-life data sets. It provides higher quality fit than competing Weibull extensions, among others.
- bathtub failure rates,
- maximum likelihood estimation,
- order statistics,
- simulation,
- Weibull distribution
Citation: Sajid Mehboob Zaidi, Mashail M. AL Sobhi, M. El-Morshedy, Ahmed Z. Afify. A new generalized family of distributions: Properties and applications[J]. AIMS Mathematics, 2021, 6(1): 456-476. doi: 10.3934/math.2021028

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Abstract

We come up with a new class called log-logistic tan generalized family which provides sub-models with left skewed, symmetrical, right skewed, unimodal, bimodal and reversed-J densities, and increasing, decreasing, modified bathtub, bathtub, unimodal, reversed-J shaped, and J-shaped hazard rates. Some of its sub-models are provided along with some general structural properties. The parameter estimation has been conducted via maximum likelihood. Moreover, the estimators behavior are assessed using various simulation results. The capability of the log-logistic tan-Weibull model is proved using two real-life data sets. It provides higher quality fit than competing Weibull extensions, among others.

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