The unit generalized log Burr XII distribution: properties and application

Fiaz Ahmad Bhatti; Azeem Ali; G. G. Hamedani; Mustafa Ç. Korkmaz; Munir Ahmad; Fiaz Ahmad Bhatti; Azeem Ali; G. G. Hamedani; Mustafa Ç. Korkmaz; Munir Ahmad

doi:10.3934/math.2021592

AIMS Mathematics

2021, Volume 6, Issue 9: 10222-10252. doi: 10.3934/math.2021592

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Research article

The unit generalized log Burr XII distribution: properties and application

1.
National College of Business Administration and Economics, Lahore Pakistan
2.
University of Veterinary and Animal Sciences, Lahore, Pakistan
3.
Marquette University, Milwaukee, WI 53201-1881, USA
4.
Artvin Çoruh University, Department of Measurement and Evaluation, Artvin, Turkey

Received: 31 December 2020 Accepted: 16 June 2021 Published: 12 July 2021
MSC : 60E05, 62E15, 62F10

In this paper, a three-parameter bounded unit distribution with a flexible hazard rate called the unit generalized log Burr XII (UGLBXII) distribution is derived. To show the importance of the proposed distribution, we establish some of its mathematical properties such as random number generator, ordinary moments, generalized TL moments, conditional moments, reliability and uncertainty measures. We characterize the UGLBXII distribution via innovative techniques. We also present the bivariate‐ and multivariate‐type distributions via Morgenstern (Mor) family and via Clayton family. Six estimation methods such as the maximum likelihood, maximum product spacings, least squares, weighted least squares, Cramer-von Mises and Anderson-Darling methods are adopted to estimate its unknown parameters. We perform simulation studies on the basis of the graphical results to see the performance of the above estimators. Two real data sets are considered to prove the empirical superiority of the proposed model.
- generalized TL moments,
- maximum likelihood estimation,
- Pearson differential equation
Citation: Fiaz Ahmad Bhatti, Azeem Ali, G. G. Hamedani, Mustafa Ç. Korkmaz, Munir Ahmad. The unit generalized log Burr XII distribution: properties and application[J]. AIMS Mathematics, 2021, 6(9): 10222-10252. doi: 10.3934/math.2021592

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Abstract

In this paper, a three-parameter bounded unit distribution with a flexible hazard rate called the unit generalized log Burr XII (UGLBXII) distribution is derived. To show the importance of the proposed distribution, we establish some of its mathematical properties such as random number generator, ordinary moments, generalized TL moments, conditional moments, reliability and uncertainty measures. We characterize the UGLBXII distribution via innovative techniques. We also present the bivariate‐ and multivariate‐type distributions via Morgenstern (Mor) family and via Clayton family. Six estimation methods such as the maximum likelihood, maximum product spacings, least squares, weighted least squares, Cramer-von Mises and Anderson-Darling methods are adopted to estimate its unknown parameters. We perform simulation studies on the basis of the graphical results to see the performance of the above estimators. Two real data sets are considered to prove the empirical superiority of the proposed model.

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