Parameter estimations for 2-parameter Pareto distribution by pome

The principle of maximum entropy (POME) was employed to derive a new method of parameter estimation for the 2-parameter Pareto distribution. Monte Carlo simulated data were used to evaluate this method and compare it with the methods of moments (MOM), probability weighted moments (PWM), and maximum likelihood estimation (MLE). The parameter estimates yielded by POME were either superior or comparable for small sample sizes when bias and RMSE were used as the criteria, and were either comparable or adequate for large sample sizes.

[1]  J. V. Witter,et al.  Testing exponentiality against generalised Pareto distribution , 1985 .

[2]  H. Joe.  Estimation of quantiles of the maximum of N observations , 1987 .

[3]  M. Tribus.  Rational descriptions, decisions, and designs , 1969 .

[4]  Anthony C. Davison,et al.  Modelling Excesses over High Thresholds, with an Application , 1984 .

[5]  A statistical model for contamination due to long-range atmospheric transport of radionuclides , 1985 .

[6]  A. Otten,et al.  The first and the second e of the extreme value distribution, EV1 , 1991 .

[7]  Richard L. Smith.  Estimating tails of probability distributions , 1987 .

[8]  Jennifer H. Barrett.  An extreme value analysis of the flow of Burbage Brook , 1992 .

[9]  R. Quandt,et al.  Old and new methods of estimation and the pareto distribution , 1966 .

[10]  M. A. J. Van Montfort,et al.  The generalized Pareto distribution applied to rainfall depths. , 1986 .

[11]  Richard L. Smith.  Threshold Methods for Sample Extremes , 1984 .

[12]  Quan J. Wang,et al.  The POT model described by the generalized Pareto distribution with Poisson arrival rate , 1991 .

[13]  S. Saksena,et al.  Best unbiased estimators for the parameters of a two-parameter Pareto distribution , 1984 .

[14]  J. Hosking,et al.  Parameter and quantile estimation for the generalized pareto distribution , 1987 .

[15]  Richard L. Smith,et al.  Models for exceedances over high thresholds , 1990 .

[16]  J. Smith,et al.  Estimating the upper tail of flood frequency distributions , 1987 .

[17]  Henrik Madsen,et al.  Prediction in partial duration series with generalized pareto‐distributed exceedances , 1992 .

[18]  W. DuMouchel.  Estimating the Stable Index $\alpha$ in Order to Measure Tail Thickness: A Critique , 1983 .

[19]  W. L. Cook,et al.  Estimation of Pareto Parameters by Numerical Methods , 1981 .

[20]  I. Good,et al.  The Maximum Entropy Formalism. , 1979 .

[21]  J. Pickands.  Statistical Inference Using Extreme Order Statistics , 1975 .