scholarly journals A Doubling Method for the Generalized Lambda Distribution

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Todd C. Headrick ◽  
Mohan D. Pant
Keyword(s):  
Monte Carlo ◽  
Pearson Correlation ◽  
Relative Bias ◽  
Simulation Studies ◽  
Generalized Lambda Distribution ◽  
New Family ◽  
Heavy Tailed Distributions ◽  
Moment Estimates ◽  
Doubling Method ◽  
Heavy Tailed

This paper introduces a new family of generalized lambda distributions (GLDs) based on a method of doubling symmetric GLDs. The focus of the development is in the context of L-moments and L-correlation theory. As such, included is the development of a procedure for specifying double GLDs with controlled degrees of L-skew, L-kurtosis, and L-correlations. The procedure can be applied in a variety of settings such as modeling events and Monte Carlo or simulation studies. Further, it is demonstrated that estimates of L-skew, L-kurtosis, and L-correlation are substantially superior to conventional product-moment estimates of skew, kurtosis, and Pearson correlation in terms of both relative bias and efficiency when heavy tailed distributions are of concern.

scholarly journals Characterizing Tukey and -Distributions through -Moments and the -Correlation

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Todd C. Headrick ◽  
Mohan D. Pant
Keyword(s):  
Monte Carlo ◽  
Risk Analysis ◽  
Extreme Events ◽  
Pearson Correlation ◽  
Simulation Studies ◽  
Nonnormal Distributions ◽  
Heavy Tailed Distributions ◽  
Moment Estimates ◽  
Asymmetric Distributions ◽  
Heavy Tailed

This paper introduces the Tukey family of symmetric and asymmetric -distributions in the contexts of univariate -moments and the -correlation. Included is the development of a procedure for specifying nonnormal distributions with controlled degrees of -skew, -kurtosis, and -correlations. The procedure can be applied in a variety of settings such as modeling events (e.g., risk analysis, extreme events) and Monte Carlo or simulation studies. Further, it is demonstrated that estimates of -skew, -kurtosis, and -correlation are substantially superior to conventional product-moment estimates of skew, kurtosis, and Pearson correlation in terms of both relative bias and efficiency when heavy-tailed distributions are of concern.

scholarly journals A Method for Simulating Nonnormal Distributions with Specified L-Skew, L-Kurtosis, and L-Correlation

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Todd C. Headrick ◽  
Mohan D. Pant
Keyword(s):  
Monte Carlo ◽  
Pearson Correlation ◽  
Theoretical Development ◽  
Nonnormal Distributions ◽  
Heavy Tailed Distributions ◽  
Moment Estimates ◽  
Monte Carlo Studies ◽  
Asymmetric Distributions ◽  
Heavy Tailed ◽  
Primary Focus

This paper introduces two families of distributions referred to as the symmetric κ and asymmetric - distributions. The families are based on transformations of standard logistic pseudo-random deviates. The primary focus of the theoretical development is in the contexts of L-moments and the L-correlation. Also included is the development of a method for specifying distributions with controlled degrees of L-skew, L-kurtosis, and L-correlation. The method can be applied in a variety of settings such as Monte Carlo studies, simulation, or modeling events. It is also demonstrated that estimates of L-skew, L-kurtosis, and L-correlation are superior to conventional product-moment estimates of skew, kurtosis, and Pearson correlation in terms of both relative bias and efficiency when moderate-to-heavy-tailed distributions are of concern.

scholarly journals A Logistic -Moment-Based Analog for the Tukey -, , , and - System of Distributions

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Todd C. Headrick ◽  
Mohan D. Pant
Keyword(s):  
Monte Carlo ◽  
Standard Error ◽  
Relative Bias ◽  
Relative Standard Error ◽  
Moment Estimators ◽  
Heavy Tailed Distributions ◽  
Relative Standard ◽  
Standard Normal ◽  
Heavy Tailed

This paper introduces a standard logistic L-moment-based system of distributions. The proposed system is an analog to the standard normal conventional moment-based Tukey g-h, g, h, and h-h system of distributions. The system also consists of four classes of distributions and is referred to as (i) asymmetric -, (ii) log-logistic , (iii) symmetric , and (iv) asymmetric -. The system can be used in a variety of settings such as simulation or modeling events—most notably when heavy-tailed distributions are of interest. A procedure is also described for simulating -, , , and - distributions with specified L-moments and L-correlations. The Monte Carlo results presented in this study indicate that estimates of L-skew, L-kurtosis, and L-correlation associated with the -, , , and - distributions are substantially superior to their corresponding conventional product-moment estimators in terms of relative bias and relative standard error.

scholarly journals Moment-Based Density Approximation Techniques as Applied to Heavy-tailed Distributions

2019 ◽  
Vol 8 (3) ◽  
pp. 1
Author(s):  
John Sang Jin Kang ◽  
Serge B. Provost ◽  
Jiandong Ren
Keyword(s):  
Density Estimation ◽  
Density Functions ◽  
Density Approximation ◽  
Simulation Studies ◽  
Esscher Transform ◽  
Approximation Techniques ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Made In

Several advances are made in connection with the approximation and estimation of heavy-tailed distributions. It is first explained that on initially applying the Esscher transform to heavy-tailed density functions such as the Pareto, Studentt and Cauchy, said densities can be approximated by employing a certain moment-based methodology. Alternatively, density approximants can be obtained by appropriately truncating such distributions or mapping them onto finite supports. These techniques are then extended to the context of density estimation, their validity being demonstrated by means of simulation studies. As well, illustrative actuarial examples are presented.

scholarly journals Bayesian Estimation of Random Parameter Models of Responses with Normal and Skew-t Distibutions Evidence from Monte Carlo Simulation

2018 ◽  
Vol 24 (1) ◽  
pp. 27-50
Author(s):  
Mohammad Masjkur ◽  
Henk Folmer
Keyword(s):  
Monte Carlo ◽  
Dose Response ◽  
Random Parameter ◽  
Response Models ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Response Modeling ◽  
T Distribution ◽  
Valuation Criteria ◽  
Skew Normal

Random parameter models have been found to outperform xed pa-rameter models to estimate dose-response relationships with independent errors. Amajor restriction, however, is that the responses are assumed to be normally andsymmetrically distributed. The purpose of this paper is to analyze Bayesian infer-ence of random parameter response models in the case of independent responseswith normal and skewed, heavy-tailed distributions by way of Monte Carlo simu-lation. Three types of Bayesian estimators are considered: one applying a normal,symmetrical prior distribution, a second applying a Skew-normal prior and, a thirdapplying a Skew-t-distribution. We use the relative bias (RelBias) and Root MeanSquared Error (RMSE) as valuation criteria. We consider the commonly applied lin-ear Quadratic and the nonlinear Spillman-Mitscherlich dose-response models. Onesimulation examines the performance of the estimators in the case of independent,normally and symmetrically distributed responses; the other in the case of indepen-dent responses following a heavy-tailed, Skew-t-distribution. The main nding isthat the estimator based on the Skew-t prior outperforms the alternative estima-tors applying the normal and Skew-normal prior for skewed, heavy-tailed data. Fornormal data, the Skew-t prior performs approximately equally well as the Skew-normal and the normal prior. Furthermore, it is more ecient than its alternatives.Overall, the Skew-t prior seems to be preferable to the normal and Skew-normal fordose-response modeling.

scholarly journals A Method for Simulating Burr Type III and Type XII Distributions through -Moments and -Correlations

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Mohan D. Pant ◽  
Todd C. Headrick
Keyword(s):  
Relative Efficiency ◽  
Simulation Studies ◽  
Distribution Fitting ◽  
Fracture Roughness ◽  
Nonnormal Distributions ◽  
Type Iii ◽  
Burr Distributions ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Pearson Correlations

This paper derives the Burr Type III and Type XII family of distributions in the contexts of univariate -moments and the -correlations. Included is the development of a procedure for specifying nonnormal distributions with controlled degrees of -skew, -kurtosis, and -correlations. The procedure can be applied in a variety of settings such as statistical modeling (e.g., forestry, fracture roughness, life testing, operational risk, etc.) and Monte Carlo or simulation studies. Numerical examples are provided to demonstrate that -moment-based Burr distributions are superior to their conventional moment-based analogs in terms of estimation and distribution fitting. Evaluation of the proposed procedure also demonstrates that the estimates of -skew, -kurtosis, and -correlation are substantially superior to their conventional product moment-based counterparts of skew, kurtosis, and Pearson correlations in terms of relative bias and relative efficiency—most notably when heavy-tailed distributions are of concern.

scholarly journals Modelling Insurance Losses with a New Family of Heavy-Tailed Distributions

2020 ◽  
Vol 66 (1) ◽  
pp. 537-550
Author(s):  
Muhammad Arif ◽  
Dost Muhammad Khan ◽  
Saima Khan Khosa ◽  
Muhammad Aamir ◽  
Adnan Aslam ◽  
...  
Keyword(s):  
New Family ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed
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