Published
2012-08-21

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

Parameter estimation in the generalized Lambda distribution by using the percentile method

DOI: https://doi.org/10.15332/s2027-3355.2012.0001.04
Luis Alejandro Másmela Caita
Docente. Universidad Distrital Francisco José de Caldas.
Héctor Fabián Rodríguez Mayorga
Estudiante. Universidad Distrital Francisco José de Caldas.
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Abstract (en)

The 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.

Keywords (en): Ajuste de datos, aproximación de distribuciones, distribución Lambda Generalizada, estimación de parámetros, método de percentiles.

Abstract (es)

La 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.
Keywords (es): Ajuste de datos, aproximación de distribuciones, distribución Lambda Generalizada, estimación de parámetros, método de percentiles.

References

Johnson, N. L. & Kotz, S. (1970), Distribution in Statistics: Continuous Univariate Distributions, New York: John Wiley.

Karian, Z. & Dudewicz, E. (1999), ‘Fitting the generalized lambda distribution to data: a method based on percentiles’, Communications in Statistics - Simulation and Computation, 28, 793 – 819.

Karian, Z. & Dudewicz, E. (2011), Handbook of Fitting Statistical Distributions with R, Boca Rato´n: CRC Press.

Karian, Z., Dudewicz, E. & Mcdonald, P. (1996), ‘The extended generalized lambda distribution (egld) system for fitting distributions to data with moments, ii:tables’, The American Journal of Mathematical and Management Sciences 16, 271–332.

Karvanen, J. & Nuutinen, A. (2008), ‘Characterizing the generalized lambda dis- tribution by l-moments’, Computational Statistics & Data Analysis 52, 1971– 1983.

Ramberg, J. S., Tadikamalla, P. R., Dudewicz, E. J. & Mykytka, E. F. (1979), ‘A probability distribution and its uses in fitting data’, Technometrics 21, 201 – 214.

Steve, S. (2007), ‘Numerical maximum log likelihood estimation fot generalized lambda distribution’, Computational Statistics and Data Analysis 51, 3983 – 3998.

Tukey, J. (1960), The practical relation between the common transformation of percentages of counts and of amounts, Technical Report 36, Princeton University.

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How to Cite

Másmela Caita, L. A., & Rodríguez Mayorga, H. F. (2012). Parameter estimation in the generalized Lambda distribution by using the percentile method. Comunicaciones En Estadística, 5(1), 81-95. https://doi.org/10.15332/s2027-3355.2012.0001.04

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