scholarly journals Inferences for Generalized Pareto Distribution Based on Progressive First-Failure Censoring Scheme

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Rashad M. El-Sagheer ◽  
Taghreed M. Jawa ◽  
Neveen Sayed-Ahmed
Keyword(s):  
Pareto Distribution ◽  
Confidence Region ◽  
Generalized Pareto Distribution ◽  
Simulated Data ◽  
Maximum Likelihood Estimates ◽  
Unknown Parameters ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Failure Data ◽  
Generalized Pareto

In this article, we consider estimation of the parameters of a generalized Pareto distribution and some lifetime indices such as those relating to reliability and hazard rate functions when the failure data are progressive first-failure censored. Both classical and Bayesian techniques are obtained. In the Bayesian framework, the point estimations of unknown parameters under both symmetric and asymmetric loss functions are discussed, after having been estimated using the conjugate gamma and discrete priors for the shape and scale parameters, respectively. In addition, both exact and approximate confidence intervals as well as the exact confidence region for the estimators are constructed. A practical example using a simulated data set is analyzed. Finally, the performance of Bayes estimates is compared with that of maximum likelihood estimates through a Monte Carlo simulation study.

scholarly journals The Gamma Generalized Pareto Distribution with Applications in Survival Analysis

2017 ◽  
Vol 6 (3) ◽  
pp. 141 ◽  
Author(s):  
Thiago A. N. De Andrade ◽  
Luz Milena Zea Fernandez ◽  
Frank Gomes-Silva ◽  
Gauss M. Cordeiro
Keyword(s):  
Monte Carlo Simulation ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Real Data ◽  
Model Parameters ◽  
Monte Carlo Simulation Study ◽  
Lorenz Curves ◽  
Generalized Pareto ◽  
Mathematical Properties ◽  
Pareto Model

We study a three-parameter model named the gamma generalized Pareto distribution. This distribution extends the generalized Pareto model, which has many applications in areas such as insurance, reliability, finance and many others. We derive some of its characterizations and mathematical properties including explicit expressions for the density and quantile functions, ordinary and incomplete moments, mean deviations, Bonferroni and Lorenz curves, generating function, R\'enyi entropy and order statistics. We discuss the estimation of the model parameters by maximum likelihood. A small Monte Carlo simulation study and two applications to real data are presented. We hope that this distribution may be useful for modeling survival and reliability data.

Bayesian Survival Analysis for Generalized Pareto Distribution Under Progressively Type II Censored Data

2019 ◽  
Vol 27 (01) ◽  
pp. 2050001
Author(s):  
Shaowei Li ◽  
Wenhao Gui
Keyword(s):  
Pareto Distribution ◽  
Survival Function ◽  
Information Matrix ◽  
Generalized Pareto Distribution ◽  
Delta Method ◽  
Point Estimate ◽  
Type Ii ◽  
Nonparametric Bootstrap ◽  
Monte Carlo Simulation Study ◽  
Generalized Pareto

In this paper, based on the progressively type II censoring data of generalized Pareto distribution, we consider the maximum likelihood estimation and asymptotic interval estimations of survival function and hazard function by using the Fisher information matrix and delta method. Also, we present a nonparametric Bootstrap-p method to generate the bootstrap samples and derive confidence interval estimation. In addition, we propose the Bayes estimator of Adaptive Rejection Metropolis Sampling algorithm to derive the point estimate and credible intervals. Finally, Monte Carlo simulation study is carried out to compare the performances of the three proposed methods based on different data schemes. An illustrative example is presented.

scholarly journals Bayesian and Non-Bayesian Inference for the Generalized Pareto Distribution Based on Progressive Type II Censored Sample

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 319 ◽  
Author(s):  
Xuehua Hu ◽  
Wenhao Gui
Keyword(s):  
Confidence Intervals ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Delta Method ◽  
Type Ii ◽  
Unknown Parameters ◽  
Hazard Functions ◽  
Generalized Pareto ◽  
Censored Sample ◽  
Type Ii Censored Sample

In this paper, first we consider the maximum likelihood estimators for two unknown parameters, reliability and hazard functions of the generalized Pareto distribution under progressively Type II censored sample. Next, we discuss the asymptotic confidence intervals for two unknown parameters, reliability and hazard functions by using the delta method. Then, based on the bootstrap algorithm, we obtain another two pairs of approximate confidence intervals. Furthermore, by applying the Markov Chain Monte Carlo techniques, we derive the Bayesian estimates of the two unknown parameters, reliability and hazard functions under various balanced loss functions and the corresponding confidence intervals. A simulation study was conducted to compare the performances of the proposed estimators. A real dataset analysis was carried out to illustrate the proposed methods.

scholarly journals Estimation of the upper cutoff parameter for the tapered Pareto distribution

2001 ◽  
Vol 38 (A) ◽  
pp. 158-175 ◽  
Author(s):  
Y. Y. Kagan ◽  
F. Schoenberg
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Maximum Likelihood Estimates ◽  
Cutoff Parameter ◽  
Generalized Pareto ◽  
Tapered Pareto Distribution ◽  
Tapered Pareto

The tapered (or generalized) Pareto distribution, also called the modified Gutenberg-Richter law, has been used to model the sizes of earthquakes. Unfortunately, maximum likelihood estimates of the cutoff parameter are substantially biased. Alternative estimates for the cutoff parameter are presented, and their properties discussed.

scholarly journals Climate change in a Point-Over-Threshold model: an example on ocean-wave-storm hazard in NE Spain

2010 ◽  
Vol 26 ◽  
pp. 113-117 ◽  
Author(s):  
R. Tolosana-Delgado ◽  
M. I. Ortego ◽  
J. J. Egozcue ◽  
A. Sánchez-Arcilla
Keyword(s):  
Climate Change ◽  
Pareto Distribution ◽  
Threshold Model ◽  
Generalized Pareto Distribution ◽  
Ocean Wave ◽  
Data Set ◽  
Climate Conditions ◽  
Generalized Pareto ◽  
Distribution Parameters ◽  
Ne Spain

Abstract. A reparametrization of the Generalized Pareto Distribution is here proposed. It is suitable to parsimoniously check trend assumptions within a Point-Over-Threshold model of hazardous events. This is based on considerations about the scale of both the excesses of the event magnitudes and the distribution parameters. The usefulness of this approach is illustrated with a data set from two buoys, where hypotheses about the homogeneity of climate conditions and lack of trends are assessed.

scholarly journals Pareto Distribution under Hybrid Censoring: Some Estimation

2021 ◽  
Vol 19 (1) ◽  
pp. 2-17
Author(s):  
Gyan Prakash
Keyword(s):  
Pareto Distribution ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Unknown Parameters ◽  
Data Set ◽  
Hybrid Censoring ◽  
Pareto Model

In the present study, the Pareto model is considered as the model from which observations are to be estimated using a Bayesian approach. Properties of the Bayes estimators for the unknown parameters have studied by using different asymmetric loss functions on hybrid censoring pattern and their risks have compared. The properties of maximum likelihood estimation and approximate confidence length have also been investigated under hybrid censoring. The performances of the procedures are illustrated based on simulated data obtained under the Metropolis-Hastings algorithm and a real data set.

scholarly journals On the Properties of the New Generalized Pareto Distribution and Its Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Najma Salahuddin ◽  
Alamgir Khalil ◽  
Wali Khan Mashwani ◽  
Sharifah Alrajhi ◽  
Sanaa Al-Marzouki ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Mean Squared Error ◽  
Generalized Pareto Distribution ◽  
Real Data ◽  
Parametric Estimation ◽  
Maximum Likelihood Estimates ◽  
Suggested Model ◽  
Practical Applications ◽  
Generalized Pareto

In this paper, a new generalization of the Generalized Pareto distribution is proposed using the generator suggested in [1], named as Khalil Extended Generalized Pareto (KEGP) distribution. Various shapes of the suggested model and important mathematical properties are investigated that includes moments, quantile function, moment-generating function, measures of entropy, and order statistics. Parametric estimation of the model is discussed using the technique of maximum likelihood. A simulation study is performed for the assessment of the maximum likelihood estimates in terms of their bias and mean squared error using simulated sample estimates. The practical applications are illustrated via two real data sets from survival and reliability theory. The suggested model provided better fits than the other considered models.

scholarly journals Estimation of the upper cutoff parameter for the tapered Pareto distribution

2001 ◽  
Vol 38 (A) ◽  
pp. 158-175 ◽  
Author(s):  
Y. Y. Kagan ◽  
F. Schoenberg
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Maximum Likelihood Estimates ◽  
Cutoff Parameter ◽  
Generalized Pareto ◽  
Tapered Pareto Distribution ◽  
Tapered Pareto

The tapered (or generalized) Pareto distribution, also called the modified Gutenberg-Richter law, has been used to model the sizes of earthquakes. Unfortunately, maximum likelihood estimates of the cutoff parameter are substantially biased. Alternative estimates for the cutoff parameter are presented, and their properties discussed.

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