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

Karian, Zaven A.; Dudewicz, Edward J.

doi:10.1080/03610919908813579

Cited by 49 publications

(26 citation statements)

References 11 publications

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“…This leads to the matching quantiles estimation (MQE) for the purpose of matching a target distribution. To the best of our knowledge, MQE has not been used in this particular context, though the idea of matching quantiles has been explored in other contexts; see, for example, Karian and Dudewicz (1999), Small and McLeish (1994), and Dominicy and Veredas (2013). Furthermore, our inference procedure is different from those in the aforementioned papers due to the different nature of our problem.…”

Section: Introductionmentioning

confidence: 84%

Matching a Distribution by Matching Quantiles Estimation

Sgouropoulos

Yao

Yastremiz

2015

Journal of the American Statistical Association

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Motivated by the problem of selecting representative portfolios for backtesting counterparty credit risks, we propose a matching quantiles estimation (MQE) method for matching a target distribution by that of a linear combination of a set of random variables. An iterative procedure based on the ordinary least-squares estimation (OLS) is proposed to compute MQE. MQE can be easily modified by adding a LASSO penalty term if a sparse representation is desired, or by restricting the matching within certain range of quantiles to match a part of the target distribution. The convergence of the algorithm and the asymptotic properties of the estimation, both with or without LASSO, are established. A measure and an associated statistical test are proposed to assess the goodness-of-match. The finite sample properties are illustrated by simulation. An application in selecting a counterparty representative portfolio with a real dataset is reported. The proposed MQE also finds applications in portfolio tracking, which demonstrates the usefulness of combining MQE with LASSO.

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Section: Introductionmentioning

confidence: 84%

Matching a Distribution by Matching Quantiles Estimation

Sgouropoulos

Yao

Yastremiz

2015

Journal of the American Statistical Association

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“…Figura 2: Aproximación de la distribución normal estándar y Weibull a través de la DLG El método propuesto en Karian & Dudewicz (1999), busca ajustar una DLG a un conjunto de datos, encontrando el valor de los cuatro parámetros λ 1 , λ 2 , λ 3 , λ 4 mediante un método que iguala cuatro estadísticas muestrales a sus cuatro contrapartes para la DLG, resolviendo para los valores λ 1 , λ 2 , λ 3 , λ 4 y esperando que el resultado genere una distribución DLG válida.…”

Section: Ajuste De La Dlg Mediante El Método De Percentilesunclassified

“…Figura 9: Aproximación de la N (0, 1) a partir de la DLG Para este tipo de aproximaciones los autores del método Karian & Dudewicz (1999) definen una forma de evaluar el error en el ajuste.…”

Section: Implementación Del Método De Percentilesunclassified

“…El método de Momentos Karian et al (1996), el método de L-momentos Karvanen & Nuutinen (2008), el método de Maxima Verosimilitud Steve (2007), entre otros, son métodos que buscan estimar los cuatro parámetros de los cuales depende la DLG. El método en el que aquí nos centramos corresponde al Método de Percentiles presentado por Karian & Dudewicz (1999) y obtenido por los autores a partir de verificar algunas restricciones que tiene el método de momentos.…”

Section: Introductionunclassified

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Estimación de parámetros de la distribución Lambda generalizada a partir del método de percentiles

Caita

Mayorga

2012

RevComEst

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ResumenLa Distribución Lambda Generalizada es una distribución de cuatro parámetros definida mediante su función percentíl. Su forma funcional permite modelar diversos conjuntos de datos además de una amplia gama de distribuciones. Para ello se requiere de la estimación de sus cuatro parámetros a través de diferentes métodos entre los que se tienen: método de momentos, método de mínimos cuadrados, método de máxima verosimilitud, entre otros. En este documento se pretende hacer una descripción del método de estimación de la distribución de interés, denominado método de percentiles. Se ilustra además su aplicación, ajustando esta distribución a un conjunto de datos además de aproximar una distribución teórica particular.Palabras clave: Ajuste de datos, aproximación de distribuciones, distribución Lambda Generalizada, estimación de parámetros, método de percentiles. AbstractThe Generalized Lambda Distribution (GLD) is a four-parameter distribution defined by a percentile function. Its functional form allows to model different data sets and a wide range of distributions. The four parameters estimation may be carried out through different methods such as: moments method, least squares method, maximum likelihood method, among others. This paper wants to describe the method for estimating the distribution of interest, called the Method of Percentiles. An illustration is shown, fitting the distribution to data sets well approximate to a particular theoretical distribution.

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“…The various methods for estimation of the optimal values for the parameter vector in the literature include, among others (1) moment-matching approach by Ramberg & Schmeister (1974) and Ramberg et al (1979), (2) percentile-based approach by Karian & Dudewicz (1999), (3) histogram-based approach by Su (2005), (4) goodness-of-fit approach by Owen (1988), (5) maximum likelihood (ML) and maximum spacing approaches by Cheng & Amin (1983) and Ranneby (1984) and (6) least squares (LS)-approach (see Karvanen & Nuutinen, 2008;Öztürk & Dale, 1982Öztürk & Dale, , 1985. Su (2007a) discussed two general approaches to fitting generalised lambda distributions to data; using the discretised method and maximum likelihood estimation (or an approach that aims to provide a definite fit to the data set such as maximising the goodness of fit) with his own authored GLDEX package in R (R Core Team, 2016).…”

Section: Generalised Lambda Distribution (Gld)mentioning

confidence: 99%

Generalised Lambda Distributions by Method of Moments and Maximum Likelihood using the JSE-ASI Returns

Owusu

Korkpoe

2017

AJFA

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The four-parameter generalised lambda distribution provides the flexibility required to describe the key moments of any distribution as compared with the normal distribution which characterises the distribution with only two moments. As markets have increasingly become nervous, the inadequacies of the normal distribution in capturing correctly the tail events and describing fully the entire distribution of market returns have been laid bare. The focus of this paper is to compare the generalised method of moments (GMM) and maximum likelihood essential estimates (MLE) methods as subsets of the GLD for a better fit of JSE All Share Index returns data. We have demonstrated that the appropriate method of the GLD to completely describe the measures of central tendency and dispersion by additionally capturing the risk dimensions of skewness and kurtosis of the return distribution is the Generalised Method of Moments (GMM) with the Kolmogorov-Smirnoff Distance good-of-fit statistics and the quantile-quantile graph. These measures are very important to any investor in the equity markets.

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

Cited by 49 publications

References 11 publications

Matching a Distribution by Matching Quantiles Estimation

Matching a Distribution by Matching Quantiles Estimation

Estimación de parámetros de la distribución Lambda generalizada a partir del método de percentiles

Generalised Lambda Distributions by Method of Moments and Maximum Likelihood using the JSE-ASI Returns

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