Using jackknife to correct bias of MLE for the truncated Pareto distribution

2018 ◽  
Vol 48 (6) ◽  
pp. 1706-1713
Author(s):  
Fen Jiang ◽  
Jin Zhang
Keyword(s):  
Pareto Distribution ◽  
Truncated Pareto

scholarly journals On the truncated Pareto distribution with applications

Open Physics ◽  
2008 ◽  
Vol 6 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Lorenzo Zaninetti ◽  
Mario Ferraro
Keyword(s):  
Statistical Analysis ◽  
Probability Distribution ◽  
Pareto Distribution ◽  
Physical Mechanism ◽  
Pareto Tails ◽  
The Masses ◽  
Truncated Pareto

AbstractThe Pareto probability distribution is widely applied in different fields such us finance, physics, hydrology, geology and astronomy. This note deals with an application of the Pareto distribution to astrophysics and more precisely to the statistical analysis of masses of stars and of diameters of asteroids. In particular a comparison between the usual Pareto distribution and its truncated version is presented. Finally, a possible physical mechanism that produces Pareto tails for the distribution of the masses of stars is presented.

scholarly journals A Weighted Estimation for Risk Model

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Mei Ling Huang ◽  
Ke Zhao
Keyword(s):  
Pareto Distribution ◽  
Risk Model ◽  
Estimation Method ◽  
Risk Models ◽  
Semiparametric Method ◽  
The Usa ◽  
Heavy Tailed ◽  
Truncated Pareto ◽  
Weighted Estimation ◽  
Infinite Moments

We propose a weighted estimation method for risk models. Two examples of natural disasters are studied: hurricane loss in the USA and forest fire loss in Canada. Risk data is often fitted by a heavy-tailed distribution, for example, a Pareto distribution, which has many applications in economics, actuarial science, survival analysis, networks, and other stochastic models. There is a difficulty in the inference of the Pareto distribution which has infinite moments in the heavy-tailed case. Firstly this paper applies the truncated Pareto distribution to overcome this difficulty. Secondly, we propose a weighted semiparametric method to estimate the truncated Pareto distribution. The idea of the new method is to place less weight on the extreme data values. This paper gives an exact efficiency function, L1-optimal weights and L2-optimal weights of the new estimator. Monte Carlo simulation results confirm the theoretical conclusions. The two above mentioned examples are analyzed by using the proposed method. This paper shows that the new estimation method is more efficient by mean square error relative to several existing methods and fits risk data well.

Fitting the Truncated Pareto Distribution to Loss Distributions

1988 ◽  
Vol 31 ◽  
pp. 151-158 ◽  
Author(s):  
Albert V. Boyd
Keyword(s):  
Method Of Moments ◽  
Pareto Distribution ◽  
Newton Iteration ◽  
Maximum Likelihood Estimates ◽  
Simple Random Sample ◽  
Unknown Parameters ◽  
The Mean ◽  
Convergence Problems ◽  
Image Position ◽  
Truncated Pareto

Hogg and Klugman use the truncated Pareto distribution with probability density functionwhere δ≥0 is specified and α > 0 and λ > 0 are unknown parameters, to describe insurance claims. This is fitted first of all by the method of moments, using the estimatorsand where is the mean of a simple random sample, and the (biased) varianceThe authors then suggest, on pp. 113–16, that these estimates be used as starting values in a Newton iteration to get the maximum likelihood estimates of the parameters, but this technique can fail as a result of convergence problems. The object of this note is to show that this has led Hogg and Klugman to underestimate seriously the area in the tail of a fitted loss distribution, and to discuss a method of circumventing this difficulty.

A truncated Pareto distribution

2006 ◽  
Vol 30 (1) ◽  
pp. 1-4 ◽  
Author(s):  
M. Masoom Ali ◽  
Saralees Nadarajah
Keyword(s):  
Pareto Distribution ◽  
Truncated Pareto

Parameter Estimation for the Truncated Pareto Distribution

2006 ◽  
Vol 101 (473) ◽  
pp. 270-277 ◽  
Author(s):  
Inmaculada B Aban ◽  
Mark M Meerschaert ◽  
Anna K Panorska
Keyword(s):  
Parameter Estimation ◽  
Pareto Distribution ◽  
Truncated Pareto

scholarly journals A discrete truncated Pareto distribution

2015 ◽  
Vol 26 ◽  
pp. 135-150 ◽  
Author(s):  
Tomasz J. Kozubowski ◽  
Anna K. Panorska ◽  
Matthew L. Forister
Keyword(s):  
Pareto Distribution ◽  
Truncated Pareto

Assessment of the Initial, Promising, and Predicted Geologic and Recoverable Oil Resources of the West Siberian Petroleum Province and Their Structure

2021 ◽  
Vol 62 (5) ◽  
pp. 576-588
Author(s):  
A.E. Kontorovich ◽  
V.R. Livshits ◽  
L.M. Burshtein ◽  
A.R. Kurchikov
Keyword(s):  
Economic Efficiency ◽  
Simulation Modeling ◽  
Pareto Distribution ◽  
Oil Fields ◽  
Shale Oil ◽  
The West ◽  
Unconventional Resources ◽  
Oil Resources ◽  
Total Oil ◽  
Truncated Pareto

Abstract —The structure of the initial and predicted oil resources of the West Siberian petroleum province is quantitatively assessed. The assessment is based on the law of mass distribution of hydrocarbon accumulations, i.e., the truncated Pareto distribution and simulation modeling of the general set of oil fields. This approach makes it possible to estimate the amount of oil and the total oil resources concentrated in intervals of any size, in particular, in intervals of small and fine fields, in order to determine the economic efficiency of their development. The considered estimates do not apply to unconventional resources, such as the shale oil of the Bazhenov Formation.

scholarly journals A Cluster Truncated Pareto Distribution and Its Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Mei Ling Huang ◽  
Vincenzo Coia ◽  
Percy Brill
Keyword(s):  
Real World ◽  
Goodness Of Fit ◽  
Pareto Distribution ◽  
Estimation Method ◽  
Estimation Methods ◽  
Real World Data ◽  
Goodness Of Fit Tests ◽  
Heavy Tailed Distribution ◽  
Heavy Tailed ◽  
Truncated Pareto

The Pareto distribution is a heavy-tailed distribution with many applications in the real world. The tail of the distribution is important, but the threshold of the distribution is difficult to determine in some situations. In this paper we consider two real-world examples with heavy-tailed observations, which leads us to propose a mixture truncated Pareto distribution (MTPD) and study its properties. We construct a cluster truncated Pareto distribution (CTPD) by using a two-point slope technique to estimate the MTPD from a random sample. We apply the MTPD and CTPD to the two examples and compare the proposed method with existing estimation methods. The results of log-log plots and goodness-of-fit tests show that the MTPD and the cluster estimation method produce very good fitting distributions with real-world data.

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