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.

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.

The Changing Size Distribution of California's North Coast Wineries

2014 ◽  
Vol 9 (1) ◽  
pp. 51-61 ◽  
Author(s):  
Don Cyr ◽  
Joseph Kushner ◽  
Tomson Ogwang
Keyword(s):  
Size Distribution ◽  
Small Firms ◽  
Goodness Of Fit ◽  
Nonparametric Density Estimation ◽  
Wine Industry ◽  
Estimation Methods ◽  
North Coast ◽  
Size Distribution Of Firms ◽  
Goodness Of Fit Tests ◽  
Kernel Density Estimates

AbstractIn this paper, we use three different goodness-of-fit tests for log-normality in conjunction with kernel nonparametric density estimation methods to examine both the size distribution of California North Coast wineries over time and by age. Our kernel density estimates indicate that the size distribution of wineries has changed from positively skewed to bimodal. These results are inconsistent with those in other industries, but are consistent with recent empirical research in the wine industry, which finds that smaller firms are comprising a larger component of market share. In terms of the distribution of firm size by age, our results indicate that as wineries age, the size distribution of firms becomes less skewed and more bimodal, which is also inconsistent with the research on other industries which finds that as firms age, the size distribution becomes more normal. Our results indicate that unlike other industries, where entry is very difficult, small firms can enter the wine industry and survive. (JEL Classifications: L11, L22, L25)

scholarly journals Goodness-of-fit tests for Pareto distribution based on a characterization and their asymptotics

Statistics ◽  
2014 ◽  
Vol 49 (5) ◽  
pp. 1026-1041 ◽  
Author(s):  
Marko Obradović ◽  
Milan Jovanović ◽  
Bojana Milošević
Keyword(s):  
Goodness Of Fit ◽  
Pareto Distribution ◽  
Goodness Of Fit Tests

scholarly journals comparison of methods for the estimation of Weibull distribution parameters

2014 ◽  
Vol 11 (1) ◽  
Author(s):  
Felix Nwobi ◽  
Chukwudi Ugomma
Keyword(s):  
Weibull Distribution ◽  
Stock Prices ◽  
Goodness Of Fit ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Goodness Of Fit Tests ◽  
Distribution Parameters ◽  
Kolmogorov Smirnov ◽  
The Mean ◽  
Maximum Likelihood Estimation Method

In this paper we study the different methods for estimation of the parameters of the Weibull distribution. These methods are compared in terms of their fits using the mean square error (MSE) and the Kolmogorov-Smirnov (KS) criteria to select the best method. Goodness-of-fit tests show that the Weibull distribution is a good fit to the squared returns series of weekly stock prices of Cornerstone Insurance PLC. Results show that the mean rank (MR) is the best method among the methods in the graphical and analytical procedures. Numerical simulation studies carried out show that the maximum likelihood estimation method (MLE) significantly outperformed other methods.

scholarly journals Selecting the best probability distribution for at-site flood frequency analysis; a study of Torne River

2019 ◽  
Vol 1 (12) ◽  
Author(s):  
Mahmood Ul Hassan ◽  
Omar Hayat ◽  
Zahra Noreen
Keyword(s):  
Probability Distribution ◽  
Frequency Analysis ◽  
Goodness Of Fit ◽  
Direct Method ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Goodness Of Fit Tests ◽  
Pearson Type

AbstractAt-site flood frequency analysis is a direct method of estimation of flood frequency at a particular site. The appropriate selection of probability distribution and a parameter estimation method are important for at-site flood frequency analysis. Generalized extreme value, three-parameter log-normal, generalized logistic, Pearson type-III and Gumbel distributions have been considered to describe the annual maximum steam flow at five gauging sites of Torne River in Sweden. To estimate the parameters of distributions, maximum likelihood estimation and L-moments methods are used. The performance of these distributions is assessed based on goodness-of-fit tests and accuracy measures. At most sites, the best-fitted distributions are with LM estimation method. Finally, the most suitable distribution at each site is used to predict the maximum flood magnitude for different return periods.

Modélisation des erreurs pour le système de prévision PRÉVIS

2004 ◽  
Vol 31 (5) ◽  
pp. 892-897 ◽  
Author(s):  
Mario Lefebvre
Keyword(s):  
Statistical Models ◽  
Goodness Of Fit ◽  
Pareto Distribution ◽  
Laplace Distribution ◽  
Critical Threshold ◽  
Gaussian Distributions ◽  
Goodness Of Fit Tests ◽  
Generalized Pareto ◽  
Forecasting System

This paper examines models for the errors in forecasts of river and (or) watershed flows produced by the PREVIS forecasting system, which is used by Alcan, among other companies. We analyzed the following statistical models: generalized Pareto, Laplace, and Gaussian distributions, depending on the flow value forecasted by PREVIS. These models enable us to quantify the precision of the forecasts produced by PREVIS, as well as the risk of seeing the flow exceed a certain critical threshold, given the forecasted flow.Key words: modeling, Laplace distribution, Pareto distribution, goodness-of-fit tests, critical threshold.

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