• Title/Summary/Keyword: Generalized Pareto Distribution

Search Result 38, Processing Time 0.074 seconds

RECURRENCE RELATIONS FOR QUOTIENT MOMENTS OF GENERALIZED PARETO DISTRIBUTION BASED ON GENERALIZED ORDER STATISTICS AND CHARACTERIZATION

  • Kumar, Devendra
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.27 no.3
    • /
    • pp.347-361
    • /
    • 2014
  • Generalized Pareto distribution play an important role in reliability, extreme value theory, and other branches of applied probability and statistics. This family of distribution includes exponential distribution, Pareto or Lomax distribution. In this paper, we established exact expressions and recurrence relations satised by the quotient moments of generalized order statistics for a generalized Pareto distribution. Further the results for quotient moments of order statistics and records are deduced from the relations obtained and a theorem for characterizing this distribution is presented.

ON RELATIONS FOR QUOTIENT MOMENTS OF THE GENERALIZED PARETO DISTRIBUTION BASED ON RECORD VALUES AND A CHARACTERIZATION

  • Kumar, Devendra
    • Journal of applied mathematics & informatics
    • /
    • v.31 no.3_4
    • /
    • pp.327-336
    • /
    • 2013
  • Generalized Pareto distributions play an important role in re-liability, extreme value theory, and other branches of applied probability and statistics. This family of distribution includes exponential distribution, Pareto distribution, and Power distribution. In this paper we establish some recurrences relations satisfied by the quotient moments of the upper record values from the generalized Pareto distribution. Further a char-acterization of this distribution based on recurrence relations of quotient moments of record values is presented.

Noninformative priors for the scale parameter in the generalized Pareto distribution

  • Kang, Sang Gil
    • Journal of the Korean Data and Information Science Society
    • /
    • v.24 no.6
    • /
    • pp.1521-1529
    • /
    • 2013
  • In this paper, we develop noninformative priors for the generalized Pareto distribution when the scale parameter is of interest. We developed the rst order and the second order matching priors. We revealed that the second order matching prior does not exist. It turns out that the reference prior and Jeffrey's prior do not satisfy a first order matching criterion, and Jeffreys' prior, the reference prior and the matching prior are different. Some simulation study is performed and a real example is given.

Noninformative priors for the shape parameter in the generalized Pareto distribution

  • Kang, Sang Gil;Kim, Dal Ho;Lee, Woo Dong
    • Journal of the Korean Data and Information Science Society
    • /
    • v.24 no.1
    • /
    • pp.171-178
    • /
    • 2013
  • In this paper, we develop noninformative priors for the generalized Pareto distribution when the parameter of interest is the shape parameter. We developed the first order and the second order matching priors.We revealed that the second order matching prior does not exist. It turns out that the reference prior satisfies a first order matching criterion, but Jeffrey's prior is not a first order matching prior. Some simulation study is performed and a real example is given.

The Likelihood for a Two-Dimensional Poisson Exceedance Point Process Model

  • Yun, Seok-Hoon
    • Communications for Statistical Applications and Methods
    • /
    • v.15 no.5
    • /
    • pp.793-798
    • /
    • 2008
  • Extreme value inference deals with fitting the generalized extreme value distribution model and the generalized Pareto distribution model, which are recently combined to give a single model, namely a two-dimensional non-homogeneous Poisson exceedance point process model. In this paper, we extend the two-dimensional non-homogeneous Poisson process model to include non-stationary effect or dependence on covariates and then derive the likelihood for the extended model.

A COMPARATIVE EVALUATION OF THE ESTIMATORS OF THE 2-PARAMETER GENERALIZED PARETO DISTRIBUTION

  • Singh, V.P.;Ahmad, M.;Sherif, M.M.
    • Water Engineering Research
    • /
    • v.4 no.3
    • /
    • pp.155-173
    • /
    • 2003
  • Parameters and quantiles of the 2-parameter generalized Pareto distribution were estimated using the methods of regular moments, modified moments, probability weighted moments, linear moments, maximum likelihood, and entropy for Monte Carlo-generated samples. The performance of these seven estimators was statistically compared, with the objective of identifying the most robust estimator. It was found that in general the methods of probability-weighted moments and L-moments performed better than the methods of maximum likelihood estimation, moments and entropy, especially for smaller values of the coefficient of variation and probability of exceedance.

  • PDF

An Alternative Study of the Determination of the Threshold for the Generalized Pareto Distribution (일반화 파레토 분포에서 임계치 결정에 대한 대안적 연구)

  • Yoon, Jeong-Yoen;Cho, Jae-Beom;Jun, Byoung-Cheol
    • The Korean Journal of Applied Statistics
    • /
    • v.24 no.5
    • /
    • pp.931-939
    • /
    • 2011
  • In practice, thresholds are determined by the two subjective assessment methods in a generalized pareto distribution of mean extreme function(MEF-graph) or Hill-graph. To remedy the problem of subjectiveness of these methods, we propose an alternative method to determine the threshold based on the robust statistics. We compared the MEF-graph, Hill-graph and our method through VaRs on the Korean stock market data from January 5, 1987 to August 3, 2009. As a result, the VaR based on the proposed method is not much different from the existing methods, and the standard deviation of VaR for our method was the smallest. The results show that our method can be a promising alternative to determine thresholds of the generalized pareto distributions.

Non-Gaussian analysis methods for planing craft motion

  • Somayajula, Abhilash;Falzarano, Jeffrey M.
    • Ocean Systems Engineering
    • /
    • v.4 no.4
    • /
    • pp.293-308
    • /
    • 2014
  • Unlike the traditional displacement type vessels, the high speed planing crafts are supported by the lift forces which are highly non-linear. This non-linear phenomenon causes their motions in an irregular seaway to be non-Gaussian. In general, it may not be possible to express the probability distribution of such processes by an analytical formula. Also the process might not be stationary or ergodic in which case the statistical behavior of the motion to be constantly changing with time. Therefore the extreme values of such a process can no longer be calculated using the analytical formulae applicable to Gaussian processes. Since closed form analytical solutions do not exist, recourse is taken to fitting a distribution to the data and estimating the statistical properties of the process from this fitted probability distribution. The peaks over threshold analysis and fitting of the Generalized Pareto Distribution are explored in this paper as an alternative to Weibull, Generalized Gamma and Rayleigh distributions in predicting the short term extreme value of a random process.

Comparison of Methods of Selecting the Threshold of Partial Duration Series for GPD Model (GPD 모형 산정을 위한 부분시계열 자료의 임계값 산정방법 비교)

  • Um, Myoung-Jin;Cho, Won-Cheol;Heo, Jun-Haeng
    • Journal of Korea Water Resources Association
    • /
    • v.41 no.5
    • /
    • pp.527-544
    • /
    • 2008
  • Generalized Pareto distribution (GPD) is frequently applied in hydrologic extreme value analysis. The main objective of statistics of extremes is the prediction of rare events, and the primary problem has been the estimation of the threshold and the exceedances which were difficult without an accurate method of calculation. In this paper, to obtain the threshold or the exceedances, four methods were considered. For this comparison a GPD model was used to estimate parameters and quantiles for the seven durations (1, 2, 3, 6, 12, 18 and 24 hours) and the ten return periods (2, 3, 5, 10, 20, 30, 50, 70, 80 and 100 years). The parameters and quantiles of the three-parameter generalized Pareto distribution were estimated with three methods (MOM, ML and PWM). To estimate the degree of fit, three methods (K-S, CVM and A-D test) were performed and the relative root mean squared error (RRMSE) was calculated for a Monte Carlo generated sample. Then the performance of these methods were compared with the objective of identifying the best method from their number.