The beta generalized Pareto distribution with application to lifetime data

2011 ◽  
Vol 81 (11) ◽  
pp. 2414-2430 ◽  
Author(s):  
Eisa Mahmoudi
Keyword(s):  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Lifetime Data ◽  
Generalized Pareto

Inference on P(Y

2020 ◽  
Vol 72 (2) ◽  
pp. 89-110
Author(s):  
Manoj Chacko ◽  
Shiny Mathew
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Maximum Likelihood Estimators ◽  
Record Values ◽  
Asymptotic Distributions ◽  
Bayes Estimators ◽  
Generalized Pareto ◽  
Pareto Distributions ◽  
Generalized Pareto Distributions

In this article, the estimation of [Formula: see text] is considered when [Formula: see text] and [Formula: see text] are two independent generalized Pareto distributions. The maximum likelihood estimators and Bayes estimators of [Formula: see text] are obtained based on record values. The Asymptotic distributions are also obtained together with the corresponding confidence interval of [Formula: see text]. AMS 2000 subject classification: 90B25

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.

scholarly journals A multiple threshold method for fitting the generalized Pareto distribution and a simple representation of the rainfall process

2010 ◽  
Vol 7 (4) ◽  
pp. 4957-4994 ◽  
Author(s):  
R. Deidda
Keyword(s):  
Time Series ◽  
Distribution Function ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Daily Rainfall ◽  
Rainfall Time Series ◽  
Threshold Method ◽  
Generalized Pareto ◽  
Multiple Threshold ◽  
Optimum Threshold

Abstract. Previous studies indicate the generalized Pareto distribution (GPD) as a suitable distribution function to reliably describe the exceedances of daily rainfall records above a proper optimum threshold, which should be selected as small as possible to retain the largest sample while assuring an acceptable fitting. Such an optimum threshold may differ from site to site, affecting consequently not only the GPD scale parameter, but also the probability of threshold exceedance. Thus a first objective of this paper is to derive some expressions to parameterize a simple threshold-invariant three-parameter distribution function which is able to describe zero and non zero values of rainfall time series by assuring a perfect overlapping with the GPD fitted on the exceedances of any threshold larger than the optimum one. Since the proposed distribution does not depend on the local thresholds adopted for fitting the GPD, it will only reflect the on-site climatic signature and thus appears particularly suitable for hydrological applications and regional analyses. A second objective is to develop and test the Multiple Threshold Method (MTM) to infer the parameters of interest on the exceedances of a wide range of thresholds using again the concept of parameters threshold-invariance. We show the ability of the MTM in fitting historical daily rainfall time series recorded with different resolutions. Finally, we prove the supremacy of the MTM fit against the standard single threshold fit, often adopted for partial duration series, by evaluating and comparing the performances on Monte Carlo samples drawn by GPDs with different shape and scale parameters and different discretizations.

scholarly journals Spatial distribution of extreme precipitation in the Tibetan Plateau and effects of external forcing factors based on Generalized Pareto distribution

2020 ◽  
Author(s):  
Jiajia Gao ◽  
Jun Du ◽  
Xiaoqing Huang
Keyword(s):  
Spatial Distribution ◽  
Extreme Precipitation ◽  
Pareto Distribution ◽  
Daily Precipitation ◽  
Generalized Pareto Distribution ◽  
The Tibetan Plateau ◽  
External Forcing ◽  
Maximum Rainfall ◽  
Flood Season ◽  
Generalized Pareto

Abstract The daily precipitation data of the years 1955–2017 from May to September were retrieved; then a Generalized Pareto Distribution (GPD) and maximum likelihood methods were adopted to understand trends and calculate the reappearance period of heavy precipitation in the Tibetan Plateau (TP). The daily precipitation values at 22 stations in the TP were found to conform to the model, and theoretical and measured frequencies were consistent. According to the spatial distribution of the maximum precipitation value, the extreme values of Shigatse and Lhasa showed large fluctuations, and the probability of record-breaking precipitation events was low. In the western part of Nagqu, the probability of extreme precipitation was relatively low, and that of record-breaking precipitation was relatively high. The peak values of extreme precipitation in the flood season in the TP generally exhibited a decreasing trend from southeast to northwest, and the extreme value of the flood season that reappeared in the southeast region was approximatelytwice that of the northwest region. The maximum rainfall in most areas will exceed 20 mm in the next 5–10 years, and the maximum rainfall in Shigatse will reach 52.7 mm. After 15 years of recurrence in various regions, the peak rainfall in the flood season has become low. Most of the regions in the model have different responses to ENSO and Indian Ocean monsoon indices with external forcing factors.

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