Order Statistics Properties of the Two Parameter Lomax Distribution

Dar, Javid Gani; Al-Hossain, Abdullah Y.

doi:10.18187/pjsor.v11i2.980

Cited by 5 publications

(2 citation statements)

References 19 publications

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“…The study of r − out − o f − n system of size n identical components characterized with independent life-lengths requires the statistical tools of order statistics; when r = 1 and r = n; it is called the parallel and series system respectively which is the maximum X (n:n) and minimum X (1:n) order statistics called the extreme order statistics. The extreme order statistics of two parameter Lomax distribution was studied by [35].…”

Section: Order Statisticsmentioning

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: Order Statisticsmentioning

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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“…For improved form of these results, Samuel and Thomas [3], Arnold et al [1], and Ali and Khan [4] have reviewed many recurrence relations and identities for the moments of order statistics arising from several specific continuous distributions such as normal, Cauchy, logistic, gamma and exponential. Very recently, Dar and Abdullah [5] have studied the sampling distribution of order statistics of the two parametric Lomax distribution and derived the exact analytical expressions of entropy, residual entropy and past residual entropy for order statistics of Lomax distribution.…”

Section: Introductionmentioning

confidence: 99%

Order Statistics of Inverse Pareto Distribution

Mustafa

Ijaz²,

Jamal³

2022

Computational Journal of Mathematical and Statistical Sciences

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In this paper we study the distribution of order statistics of the inverse Pareto distribution. We consider the single and product moment of order statistics from inverse Pareto distribution. Also, we establish some recurrence relation for single moments of order statistics. The exact analytical expressions of entropy, residual entropy and past residual entropy for order statistics of inverse Pareto distribution is derived.

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On order statistics from Laplace-type distributions

Aly

2020

Statistics & Probability Letters

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Order Statistics Properties of the Two Parameter Lomax Distribution

Cited by 5 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

Order Statistics of Inverse Pareto Distribution

On order statistics from Laplace-type distributions

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