A weighted Topp-Leone G family of distributions: properties, applications for modelling reliability data and different method of estimation

Hashempour‎, Majid

doi:10.15672/hujms.795721

Hacettepe Journal of Mathematics and Statistics

2022

DOI: 10.15672/hujms.795721

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A weighted Topp-Leone G family of distributions: properties, applications for modelling reliability data and different method of estimation

Majid Hashempour‎

Abstract: ‎Based on the Topp-Leone distribution‎, ‎we propose a new family of continuous‎ ‎distributions with one shape parameter called the weighted Topp-Leone family (WTL-G)‎. ‎We study some basic properties including quantile function‎, ‎asymptotic‎, ‎mixture for cdf and pdf‎, ‎various entropies and order statistics‎ .‎Then we study Lindley case as special case with more details‎. ‎The maximum likelihood estimates of parameters are compared with various methods of estimations by conducting a simulation study‎. ‎F… Show more

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2023

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Cited by 2 publications

References 33 publications

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Bayesian and Non-Bayesian Estimation for a New Extension of Power Topp–Leone Distribution under Ranked Set Sampling with Applications

Alotaibi

Al-Moisheer

Elbatal

et al. 2023

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In this article, we intend to introduce and study a new two-parameter distribution as a new extension of the power Topp–Leone (PTL) distribution called the Kavya–Manoharan PTL (KMPTL) distribution. Several mathematical and statistical features of the KMPTL distribution, such as the quantile function, moments, generating function, and incomplete moments, are calculated. Some measures of entropy are investigated. The cumulative residual Rényi entropy (CRRE) is calculated. To estimate the parameters of the KMPTL distribution, both maximum likelihood and Bayesian estimation methods are used under simple random sample (SRS) and ranked set sampling (RSS). The simulation study was performed to be able to verify the model parameters of the KMPTL distribution using SRS and RSS to demonstrate that RSS is more efficient than SRS. We demonstrated that the KMPTL distribution has more flexibility than the PTL distribution and the other nine competitive statistical distributions: PTL, unit-Gompertz, unit-Lindley, Topp–Leone, unit generalized log Burr XII, unit exponential Pareto, Kumaraswamy, beta, Marshall-Olkin Kumaraswamy distributions employing two real-world datasets.

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Bayesian and Non-Bayesian Estimation for a New Extension of Power Topp–Leone Distribution under Ranked Set Sampling with Applications

Alotaibi

Al-Moisheer

Elbatal

et al. 2023

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A novel weighted family of probability distributions with applications to world natural gas, oil, and gold reserves

Hassan,

Alsadat,

Chesneau

et al. 2023

MBE

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<abstract><p>Recent innovations have focused on the creation of new families that extend well-known distributions while providing a huge amount of practical flexibility for data modeling. Weighted distributions offer an effective approach for addressing model building and data interpretation problems. The main objective of this work is to provide a novel family based on a weighted generator called the length-biased truncated Lomax-generated (LBTLo-G) family. Discussions are held about the characteristics of the LBTLo-G family, including expressions for the probability density function, moments, and incomplete moments. In addition, different measures of uncertainty are determined. We provide four new sub-distributions and investigated their functionalities. Subsequently, a statistical analysis is given. The LBTLo-G family's parameter estimation is carried out using the maximum likelihood technique on the basis of full and censored samples. Simulation research is conducted to determine the parameters of the LBTLo Weibull (LBTLoW) distribution. Four genuine data sets are considered to illustrate the fitting behavior of the LBTLoW distribution. In each case, the application outcomes demonstrate that the LBTLoW distribution can, in fact, fit the data more accurately than other rival distributions.</p></abstract>

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A weighted Topp-Leone G family of distributions: properties, applications for modelling reliability data and different method of estimation

Cited by 2 publications

References 33 publications

Bayesian and Non-Bayesian Estimation for a New Extension of Power Topp–Leone Distribution under Ranked Set Sampling with Applications

Bayesian and Non-Bayesian Estimation for a New Extension of Power Topp–Leone Distribution under Ranked Set Sampling with Applications

A novel weighted family of probability distributions with applications to world natural gas, oil, and gold reserves

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