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Full-Text Articles in Statistical Methodology
An L-Moment Based Characterization Of The Family Of Dagum Distributions, Mohan D. Pant, Todd C. Headrick
An L-Moment Based Characterization Of The Family Of Dagum Distributions, Mohan D. Pant, Todd C. Headrick
Mohan Dev Pant
This paper introduces a method for simulating univariate and multivariate Dagum distributions through the method of L-moments and L-correlation. A method is developed for characterizing non-normal Dagum distributions with controlled degrees of L-skew, L-kurtosis, and L-correlations. The procedure can be applied in a variety of contexts such as statistical modeling (e.g., income distribution, personal wealth distributions, etc.) and Monte Carlo or simulation studies. Numerical examples are provided to demonstrate that -moment-based Dagum distributions are superior to their conventional moment-based analogs in terms of estimation and distribution fitting. Evaluation of the proposed method also demonstrates that the estimates of L-skew, L-kurtosis, …
A Method For Simulating Burr Type Iii And Type Xii Distributions Through L-Moments And L-Correlations, Mohan D. Pant, Todd C. Headrick
A Method For Simulating Burr Type Iii And Type Xii Distributions Through L-Moments And L-Correlations, Mohan D. Pant, Todd C. Headrick
Mohan Dev Pant
This paper derives the Burr Type III and Type XII family of distributions in the contexts of univariate L-moments and the L-correlations. Included is the development of a procedure for specifying nonnormal distributions with controlled degrees of L-skew, L-kurtosis, and L-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 L-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 …
A Doubling Technique For The Power Method Transformations, Mohan D. Pant, Todd C. Headrick
A Doubling Technique For The Power Method Transformations, Mohan D. Pant, Todd C. Headrick
Mohan Dev Pant
Power method polynomials are used for simulating non-normal distributions with specified product moments or L-moments. The power method is capable of producing distributions with extreme values of skew (L-skew) and kurtosis (L-kurtosis). However, these distributions can be extremely peaked and thus not representative of real-world data. To obviate this problem, two families of distributions are introduced based on a doubling technique with symmetric standard normal and logistic power method distributions. The primary focus of the methodology is in the context of L-moment theory. As such, L-moment based systems of equations are derived for simulating univariate and multivariate non-normal distributions with …
An L-Moment-Based Analog For The Schmeiser-Deutsch Class Of Distributions, Todd C. Headrick, Mohan D. Pant
An L-Moment-Based Analog For The Schmeiser-Deutsch Class Of Distributions, Todd C. Headrick, Mohan D. Pant
Mohan Dev Pant
This paper characterizes the conventional moment-based Schmeiser-Deutsch (S-D) class of distributions through the method of L-moments. The system can be used in a variety of settings such as simulation or modeling various processes. A procedure is also described for simulating S-D distributions with specified L-moments and L-correlations. The Monte Carlo results presented in this study indicate that the estimates of L-skew, L-kurtosis, and L-correlation associated with the S-D class of distributions are substantially superior to their corresponding conventional product-moment estimators in terms of relative bias—most notably when sample sizes are small.
A Logistic L-Moment-Based Analog For The Tukey G-H, G, H, And H-H System Of Distributions, Todd C. Headrick, Mohan D. Pant
A Logistic L-Moment-Based Analog For The Tukey G-H, G, H, And H-H System Of Distributions, Todd C. Headrick, Mohan D. Pant
Mohan Dev Pant
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 γ-κ, (ii) log-logistic γ, (iii) symmetric κ, and (iv) asymmetric κL-κR. 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 γ-κ, γ, κ, and κL-κR distributions with specified L-moments and L-correlations. The …
A Method For Simulating Nonnormal Distributions With Specified L-Skew, L-Kurtosis, And L-Correlation, Todd C. Headrick, Mohan D. Pant
A Method For Simulating Nonnormal Distributions With Specified L-Skew, L-Kurtosis, And L-Correlation, Todd C. Headrick, Mohan D. Pant
Mohan Dev Pant
This paper introduces two families of distributions referred to as the symmetric κ and asymmetric κL-κR 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 …
Simulating Non-Normal Distributions With Specified L-Moments And L-Correlations, Todd C. Headrick, Mohan D. Pant
Simulating Non-Normal Distributions With Specified L-Moments And L-Correlations, Todd C. Headrick, Mohan D. Pant
Mohan Dev Pant
This paper derives a procedure for simulating continuous non-normal distributions with specified L-moments and L-correlations in the context of power method polynomials of order three. It is demonstrated that the proposed procedure has computational advantages over the traditional product-moment procedure in terms of solving for intermediate correlations. Simulation results also demonstrate that the proposed L-moment-based procedure is an attractive alternative to the traditional procedure when distributions with more severe departures from normality are considered. Specifically, estimates of L-skew and L-kurtosis are superior to the conventional estimates of skew and kurtosis in terms of both relative bias and relative standard error. …
On The Order Statistics Of Standard Normal-Based Power Method Distributions, Todd C. Headrick, Mohan D. Pant
On The Order Statistics Of Standard Normal-Based Power Method Distributions, Todd C. Headrick, Mohan D. Pant
Mohan Dev Pant
This paper derives a procedure for determining the expectations of order statistics associated with the standard normal distribution (Z) and its powers of order three and five (Z^3 and Z^5). The procedure is demonstrated for sample sizes of n ≤ 9. It is shown that Z^3 and Z^5 have expectations of order statistics that are functions of the expectations for Z and can be expressed in terms of explicit elementary functions for sample sizes of n ≤ 5. For sample sizes of n = 6, 7 the expectations of the order statistics for Z, Z^3, and Z^5 only require a …
A Doubling Method For The Generalized Lambda Distribution, Todd C. Headrick, Mohan D. Pant
A Doubling Method For The Generalized Lambda Distribution, Todd C. Headrick, Mohan D. Pant
Mohan Dev Pant
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 …
Characterizing Tukey H And Hh-Distributions Through L-Moments And The L-Correlation, Todd C. Headrick, Mohan D. Pant
Characterizing Tukey H And Hh-Distributions Through L-Moments And The L-Correlation, Todd C. Headrick, Mohan D. Pant
Mohan Dev Pant
This paper introduces the Tukey family of symmetric h and asymmetric hh-distributions in the contexts of univariate L-moments and the L-correlation. Included is the development of a procedure for specifying nonnormal distributions 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 (e.g., risk analysis, extreme 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 …
On Simulating Univariate And Multivariate Burr Type Iii And Type Xii Distributions, Todd C. Headrick, Mohan D. Pant, Yanyan Sheng
On Simulating Univariate And Multivariate Burr Type Iii And Type Xii Distributions, Todd C. Headrick, Mohan D. Pant, Yanyan Sheng
Mohan Dev Pant
This paper describes a method for simulating univariate and multivariate Burr Type III and Type XII distributions with specified correlation matrices. The methodology is based on the derivation of the parametric forms of a pdf and cdf for this family of distributions. The paper shows how shape parameters can be computed for specified values of skew and kurtosis. It is also demonstrated how to compute percentage points and other measures of central tendency such as the mode, median, and trimmed mean. Examples are provided to demonstrate how this Burr family can be used in the context of distribution fitting using …