On the Beta Exponential Pareto Distribution

Aryal, Gokarna

doi:10.19139/soic-2310-5070-437

Cited by 2 publications

(2 citation statements)

References 19 publications

(28 reference statements)

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“…The convolution of exponential and Pareto distributions by [18] produced the Exponential Pareto (EP) distribution which [19,20,21,22,23,24] further generalized and studied with diverse applications using different approaches. [25] proposed Transmuted Topp-Leone extended Frechet distribution for modeling extreme value of dataset with some application.…”

Section: Introductionmentioning

confidence: 99%

Modeling Extreme Stochastic Variations using the Maximum Order Statistics of Convoluted Distributions

Adeyemi

Adeleke

Akarawak

2023

J. Nig. Soc. Phys. Sci.

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Modeling extreme stochastic phenomena associated with catastrophic temperatures, heat waves, earthquakes and destructive floods is an aspect of proactive mitigation of risk. Hydrologists, reliability engineers, meteorologist and researchers among other stakeholders are faced with the challenges of providing adequate model for fitting real life datasets from the extreme natural hazardous occurrences in our environment. Convoluted distributions (CD) and generalized extreme value (GEV) distribution for r- largest order statistics (r-LOS) have been some of the prominent existing techniques for modeling the extreme events. This study explored the properties of order statistics from the convoluted distribution as alternative procedure for analyzing the extreme maximum with the aim of obtaining superior modeling fit compared to some other existing techniques. The new procedure called MAXOS-G employed the potential properties of the Maximum Order Statistics (MAXOS) and the flexibilities of convoluted distributions where G is taken to beWeibull-Exponential Pareto (WEP) and the New Kumaraswamy-Weibull (NKwei) distributions. The maximum order statistics of the WEP distribution (MAXOS-WEP) and NKwei distribution (MAXOS-NKwei) was derived and applied to three datasets consisting of annual maximum flood discharges, annual maximum precipitation and annual maximum one-day rainfall. Some properties of the MAXOS-WEP was investigated including the moment, mean, variance, skewness, and kurtosis. Characterization of WEP distribution by the L-moment of maximum order statistics was presented and coefficient of L-variation, L-skewness and L-kurtosis were derived. The results from the application to three datasets using R-software justified the importance of this new procedure for modeling the maximum events. The MAXOS-NKwei and MAXOS-WEP models provide superior goodness-of-fit to the datasets than the WEP and NKwei distributions and better than some previously proposed convoluted distributions for modeling the datasets.

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Section: Introductionmentioning

confidence: 99%

Modeling Extreme Stochastic Variations using the Maximum Order Statistics of Convoluted Distributions

Adeyemi

Adeleke

Akarawak

2023

J. Nig. Soc. Phys. Sci.

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“…𝛽 ,k,𝜃 are the parameters of the distribution The EP distribution has further gained extensive studies with applications from Luguterah and Nasiru (2015) , using the quadratic rank transmutation map (QRTM) to develop the Transmuted Exponential Pareto (TEP) distribution, the beta-G framework was used by Aryal (2019) and later by Rashwan and Kamel (2020) for the construction of Beta Exponential Pareto (BEP) model. Kumaraswamy Exponential Pareto (KEP) distribution was introduced by Elbatal and Aryal (2017) using the Kum-G technique and most recently, the Gompertz-G technique was explored for developing the Gompertz Exponential Pareto distribution by (Adeyemi et al, 2021) .…”

Section: Introductionmentioning

confidence: 99%

Extension of Exponential Pareto Distribution with the Order Statistics: Some Properties and Application to Lifetime Dataset

Adeyemi

Adeleke

Akarawak

2023

Sci. Technol. Indones

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The Exponential Pareto (EP) model has been extended by applied and theoretical statisticians for wider applications and new knowledge using different techniques but the Weibull-X technique has not been considered. This article proposed a new extension of the EP model called the Weibull-Exponential Pareto (WEP) distribution to provide better modeling that fits real-life datasets and to explore the statistical theory of order statistics from the proposed distribution. Statistical properties investigated include the Shannon and Renyi entropies; the moments and moment generating function. Distribution of order statistics and the moment of order statistics were derived including the mean and variance of order statistics. WEP distribution has unimodal, decreasing, and increasing failure rates; and it can be negatively or positively skewed and approximately symmetric with the potential for fitting platykurtic, mesokurtic, and leptokurtic lifetime data. The parameters of the distribution were estimated using the method of maximum likelihood estimation (MLE), which was examined for consistency through a simulation study. The performance of the proposed distribution was investigated by application to flood peaks exceedances and some lifetime datasets from engineering. The results from data analysis using the R-software revealed that the WEP distribution has the potential to provide a superior model that fits the three data sets better than some notable existing distributions and previous extensions of the EP model in the literature. The statistical property of order statistics extended in the study established some important results that characterized some notable lifetime distributions in the literature.

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On the Beta Exponential Pareto Distribution

Cited by 2 publications

References 19 publications

Modeling Extreme Stochastic Variations using the Maximum Order Statistics of Convoluted Distributions

Modeling Extreme Stochastic Variations using the Maximum Order Statistics of Convoluted Distributions

Extension of Exponential Pareto Distribution with the Order Statistics: Some Properties and Application to Lifetime Dataset

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