Generalized Pareto Distribution Based on Generalized Order Statistics and Associated Inference

Malik, Mansoor Rashid; Kumar, Devendra

doi:10.21307/stattrans-2019-024

Cited by 3 publications

(1 citation statement)

References 18 publications

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“…Reference [16] estimated the parameters of the generalized Pareto distribution based on GOS using ML, bootstrap, and Bayesian under the LSE and LINEX loss functions. Reference [17] studied the properties, recurrence relations of moments, and ML estimate of the parameters for the generalized Pareto distribution based on the GOS.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Estimation of the Stress-Strength Reliability Based on Generalized Order Statistics for Pareto Distribution

Ezmareh,

Yari

2023

Journal of Probability and Statistics

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The aim of this paper is to obtain a Bayesian estimator of stress-strength reliability based on generalized order statistics for Pareto distribution. The dependence of the Pareto distribution support on the parameter complicates the calculations. Hence, in literature, one of the parameters is assumed to be known. In this paper, for the first time, two parameters of Pareto distribution are considered unknown. In computing the Bayesian confidence interval for reliability based on generalized order statistics, the posterior distribution has a complex form that cannot be sampled by conventional methods. To solve this problem, we propose an acceptance-rejection algorithm to generate a sample of the posterior distribution. We also propose a particular case of this model and obtain the classical and Bayesian estimators for this particular case. In this case, to obtain the Bayesian estimator of stress-strength reliability, we propose a variable change method. Then, these confidence intervals are compared by simulation. Finally, a practical example of this study is provided.

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Section: Introductionmentioning

confidence: 99%

Bayesian Estimation of the Stress-Strength Reliability Based on Generalized Order Statistics for Pareto Distribution

Ezmareh,

Yari

2023

Journal of Probability and Statistics

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Statistical inference of the inverted exponentiated Lomax distribution using generalized order statistics with application to COVID-19

Nassr,

Hassan,

Almetwally

et al. 2023

AIP Advances

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In this study, the parameters of the inverted exponentiated Lomax distribution via generalized order statistics are assessed using Bayesian and maximum likelihood approaches. The maximum likelihood estimators along with approximate confidence intervals are calculated. Under the squared error loss function, the Bayesian estimator, percentile bootstrap, and bootstrap-t credible periods are produced. Furthermore, the proposed estimators are dedicated to schemes such as type-II censored ordinary order statistics joint density function. A numerical simulation is used to assess the behavior and sensitivity of the estimates for various sample sizes. From the posterior distributions, the Metropolis–Hastings technique is used to generate Markov chain Monte Carlo samples. We utilize this technique to examine a current dataset of interest: daily cases of COVID-19 instances detected in Saudi Arabia from May 31 to October 28, 2020 (inclusive). In the future, the proposed methodology could be useful for analyzing data on COVID-19 instances in other countries for comparative studies.

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Sufficient statistics for the Pareto distribution parameter

Pulkin

Tatarintsev

2021

Rossijskij tehnologičeskij žurnal

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The task of estimating the parameters of the Pareto distribution, first of all, of an indicator of this distribution for a given sample, is relevant. This article establishes that for this estimate, it is sufficient to know the product of the sample elements. It is proved that this product is a sufficient statistic for the Pareto distribution parameter. On the basis of the maximum likelihood method the distribution degree indicator is estimated. It is proved that this estimate is biased, and a formula eliminating the bias is justified. For the product of the sample elements considered as a random variable the distribution function and probability density are found; mathematical expectation, higher moments, and differential entropy are calculated. The corresponding graphs are built. In addition, it is noted that any function of this product is a sufficient statistic, in particular, the geometric mean. For the geometric mean also considered as a random variable, the distribution function, probability density, and the mathematical expectation are found; the higher moments, and the differential entropy are also calculated, and the corresponding graphs are plotted. In addition, it is proved that the geometric mean of the sample is a more convenient sufficient statistic from a practical point of view than the product of the sample elements. Also, on the basis of the Rao–Blackwell–Kolmogorov theorem, effective estimates of the Pareto distribution parameter are constructed. In conclusion, as an example, the technique developed here is applied to the exponential distribution. In this case, both the sum and the arithmetic mean of the sample can be used as sufficient statistics.

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Generalized Pareto Distribution Based on Generalized Order Statistics and Associated Inference

Cited by 3 publications

References 18 publications

Bayesian Estimation of the Stress-Strength Reliability Based on Generalized Order Statistics for Pareto Distribution

Bayesian Estimation of the Stress-Strength Reliability Based on Generalized Order Statistics for Pareto Distribution

Statistical inference of the inverted exponentiated Lomax distribution using generalized order statistics with application to COVID-19

Sufficient statistics for the Pareto distribution parameter

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