Zaven A. Karian

The extended generalized lambda distribution system for fitting distributions to data: history, completion of theory, tables, applications, the “final word” on moment fits

The generalized lambda distribution, GLD(λ1, λ2 λ3, λ4), is a four-parameter family that has been used for fitting distributions to a wide variety of data sets. The analysis of the λ3 and λ4 values that actually yield valid distributions has (until now) been incomplete. Moreover, because of computational problems and theoretical shortcomings, the moment space over which the GLD can be applied has been limited. This paper completes the analysis of the λ3 and λ4 values that are associated with valid distributions, improves previous computational methods to reduce errors associated with fitting data, expands the parameter space over which the GLD can be used, and uses a four-parameter generalized beta distribution to cover the portion of the parameter space where the GLD is not applicable. In short, the paper extends the GLD to an EGLD system that can be used for fitting distributions to data sets that that are cited in the literature as actually occurring in practice. Examples of use of the proposed system ...

Fitting the generalized lambda distribution to data: a method based on percentiles

The generalized lambda distribution, GLD(λ1:,λ2:,λ3:,λ4), is a four‐parameter family that has been used for fitting distributions to a wide variety of data sets. In almost all cases the method of moments has been used to determine the parameters of the GLD that fits a given data set, negating the possibility of applying those members of the GLD family that do not possess the first four moments and yet may provide superior fits to the data. This paper develops a method for fitting a GLD distribution to data that is based on percentiles rather than moments. This approach makes a larger portion of the GLD family accessible for data fitting and eases some of the computational difficulties encountered in the method of moments. Examples of the use of the proposed system are included.

The extended generalized lambda distribution (EGLD) system for fitting distributions to data with moments, II: tables

SYNOPTIC ABSTRACTThe Generalized Lambda Distribution, GLD(λ1, λ2, λ3, λ4), is a four-parameter family that has been used for fitting distributions to a variety of data sets. This paper deals with the extension of the GLD to a system, designated by EGLD, that can be used for fitting distributions to data sets that are cited in the literature as actually occurring in practice. The EGLD can achieve all possible (mean, variance, skewness, kurtosis) vectors; the GLD could not do this. Previous computational methods for determining λ1, λ2, λ3, λ4 of the GLD have been improved and expanded and more refined tables are provided for finding λ1, λ2, λ3, λ4. New tables for EGLD fits that are beyond the capability of the GLD are also provided.This research paper was supported by NATO Research Grant No. CRG 931030.

Fitting the generalized lambda distribution (GLD) system by a method of percentiles, II: tables

SYNOPTIC ABSTRACTThe Generalized Lambda Distribution, GLD(λ1, λ2, λ3, λ4), is a four-parameter family that has been used for fitting distributions to data sets. With rare exceptions, the method of moments has been used for estimating the GLD parameters, making it impossible to fit a GLD distribution whose first four moments do not exist. This paper deals with the use of an estimation method that is based on percentiles. To provide practitioners ready access to this method, extensive tables are provided to facilitate parameter estimation.This research paper was supported by NATO Research Grant No. CRG 931030 and a Robert C. Good Fellowship from Denison University.

The Role of Statistics in IS/IT: Practical Gains from Mined Data

Data mining has, in the past, tended to use simplistic statistical methods (or even none at all). In this paper we show by example how cutting edge (but easy to use and comprehend) statistical methods can yield substantial gains in data mining. The role of statistics in IS/IT (information systems and information technology) in general can be substantial, yielding more nearly optimal performance of problems at the emerging frontiers in all their aspects.

Computational Issues in Fitting Statistical Distributions to Data

SYNOPTIC ABSTRACT In fitting statistical distributions to data the practitioner almost always needs to compute the parameters of a family of distributions. Such computations are frequently difficult to implement and may require considerable effort and computation time. This paper discusses the computing difficulties that can arise in fitting statistical distributions to data and illustrates these problems through examples that use the Weibull distribution, the generalized lambda distribution, and the Johnson system of distributions. In all cases fits are obtained by the method of moments using either the Maple computing environment or the R statistical system.

The Completeness and Uniqueness of Johnson's System in Skewness–Kurtosis Space

Abstract In empirical research, there exist great difficulties in applying results based on assumption of a normal distribution because often data do not come from a normal distribution. For given data, the Johnson system, originally presented by Johnson, provides a possible distribution by covering every possible combination of skewness and kurtosis completely and uniquely. In this paper, we prove the uniqueness and completeness of the Johnson system in its skewness–kurtosis space.

GPSS for Microcomputers: A Software Review of GPSS/PC

SYNOPTIC ABSTRACTSince its introduction in the early 1960s, the GPSS (General Purpose Simulation System) Computer simulation language has become a major vehicle for the implementation of discrete event Computer simulations. The availability of quality language processors, the suitability of GPSS for discrete event modeling applications, and the presence of well-written references (e.g., Bobillier Kahan and Probst (1976) and Schriber (1974)) have all contributed to the popularity of GPSS among analysts involved with discrete event simulations. GPSS dialects have been available on almost all mainframes, such as IBM 360/370s and PDP-20s, and many minicomputers, such as VAX-11 and Prime systems, for some time. GPSS/PC (Minuteman Software (1984a)), the subject of this review, extends the scope of this powerful tool to the IBM-PC and IBM-PC compatible microcomputers under MS-DOS 1.1 or MS-DOS 2.0 operating Systems.

A central Ohio consortium for retraining in computer science

A Consortium of eight Central Ohio colleges and universities is described. The purpose of the Consortium is to provide opportunities for faculty at the participating institutions to be retrained in the field of computer science. These faculty will then be able to return to their home institutions to develop and teach computer science curricula. The program provides flexibility of scheduling the retraining, in terms of the time of year and nature of the retraining undertaken by the individual participants.

Fitting Statistical Distributions to Data in Hurricane Modeling

Fitting probability distributions to hurricane related data is an essential ac tivity in hurricane planning, designing structures, and catastrophe modeling applications. The recent devastating hurricane seasons and the resultant debates over design cr it ria and computer models using analyses based on these fits motivate a closer examinat ion of this issue. The primary objective in this paper is to describe the background and applicati ons of historical hurricane data fitting, the operational aspects of which have dictat e adjustments to the standard methodology. The emphasis here is on the interaction between data quality and dynamics, the need for rapid but stable assessments of that data, and statistical fitting methodologies. Validation and applications are discusse d, along with an analysis of the return periods of damage in the New Orleans area.