Inverted Length-Biased Exponential Model: Statistical Inference and Modeling

This research article proposes a new probability distribution, referred to as the inverted length-biased exponential distribution. The hazard rate function (HZRF) and density function (PDF) in the new distribution allow additional flexibility as well as some desired features. It provides a more flex...

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Autor principal:	Waleed Almutiry
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/2b9670163bb94390a6d7c6f5295b2638
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spelling	oai:doaj.org-article:2b9670163bb94390a6d7c6f5295b26382021-11-08T02:36:44ZInverted Length-Biased Exponential Model: Statistical Inference and Modeling2314-478510.1155/2021/1980480https://doaj.org/article/2b9670163bb94390a6d7c6f5295b26382021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/1980480https://doaj.org/toc/2314-4785This research article proposes a new probability distribution, referred to as the inverted length-biased exponential distribution. The hazard rate function (HZRF) and density function (PDF) in the new distribution allow additional flexibility as well as some desired features. It provides a more flexible approach that may be used to represent many forms of real-world data. The quantile function (QuF), moments (MOs), moment generating function (MOGF), mean residual lifespan (MRLS), mean inactivity time (MINT), and probability weighted moments (PRWMOs) are among the mathematical and statistical features of the inverted length-biased exponential distribution. In the case of complete and type II censored samples (TIICS), the maximum likelihood (MLL) strategy can be used to estimate the model parameters. An asymptotic confidence interval (COI) of parameter is constructed at two confidence levels. We perform simulation study to examine the accuracy of estimates depending upon some statistical measures. Simulation results show that there is great agreement between theoretical and empirical studies. We demonstrate the new model’s relevance and adaptability by modeling three lifespan datasets. The proposed model is a better fit than the half logistic inverse Rayleigh (HLOIR), type II Topp–Leone inverse Rayleigh (TIITOLIR), and transmuted inverse Rayleigh (TRIR) distributions. We anticipate that the expanded distribution will attract a broader range of applications in a variety of fields of research.Waleed AlmutiryHindawi LimitedarticleMathematicsQA1-939ENJournal of Mathematics, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Waleed Almutiry Inverted Length-Biased Exponential Model: Statistical Inference and Modeling
description	This research article proposes a new probability distribution, referred to as the inverted length-biased exponential distribution. The hazard rate function (HZRF) and density function (PDF) in the new distribution allow additional flexibility as well as some desired features. It provides a more flexible approach that may be used to represent many forms of real-world data. The quantile function (QuF), moments (MOs), moment generating function (MOGF), mean residual lifespan (MRLS), mean inactivity time (MINT), and probability weighted moments (PRWMOs) are among the mathematical and statistical features of the inverted length-biased exponential distribution. In the case of complete and type II censored samples (TIICS), the maximum likelihood (MLL) strategy can be used to estimate the model parameters. An asymptotic confidence interval (COI) of parameter is constructed at two confidence levels. We perform simulation study to examine the accuracy of estimates depending upon some statistical measures. Simulation results show that there is great agreement between theoretical and empirical studies. We demonstrate the new model’s relevance and adaptability by modeling three lifespan datasets. The proposed model is a better fit than the half logistic inverse Rayleigh (HLOIR), type II Topp–Leone inverse Rayleigh (TIITOLIR), and transmuted inverse Rayleigh (TRIR) distributions. We anticipate that the expanded distribution will attract a broader range of applications in a variety of fields of research.
format	article
author	Waleed Almutiry
author_facet	Waleed Almutiry
author_sort	Waleed Almutiry
title	Inverted Length-Biased Exponential Model: Statistical Inference and Modeling
title_short	Inverted Length-Biased Exponential Model: Statistical Inference and Modeling
title_full	Inverted Length-Biased Exponential Model: Statistical Inference and Modeling
title_fullStr	Inverted Length-Biased Exponential Model: Statistical Inference and Modeling
title_full_unstemmed	Inverted Length-Biased Exponential Model: Statistical Inference and Modeling
title_sort	inverted length-biased exponential model: statistical inference and modeling
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/2b9670163bb94390a6d7c6f5295b2638
work_keys_str_mv	AT waleedalmutiry invertedlengthbiasedexponentialmodelstatisticalinferenceandmodeling
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Inverted Length-Biased Exponential Model: Statistical Inference and Modeling

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