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Revista Colombiana de Estadística

Print version ISSN 0120-1751

Rev.Colomb.Estad. vol.38 no.2 Bogotá July/Dec. 2015

https://doi.org/10.15446/rce.v38n2.51663 

http://dx.doi.org/10.15446/rce.v38n2.51663

Parameter Estimation of Power Function Distribution with TL-moments

Estimación de parámetros de distribuciones de funciones de potencia con momentos TL

MIRZA NAVEED-SHAHZAD1, ZAHID ASGHAR2, FARRUKH SHEHZAD3, MUBEEN SHAHZADI4

1University of Gujrat, Department of Statistics, Gujrat, Pakistan. Lecturer. Email: nvd.shzd@uog.edu.com
2Quaid-i-Azam University, Department of Statistics, Islamabad, Pakistan. Assistant Professor. Email: zahid.g@gmail.com
3COMSATS Institute of Information Technology, Department of Statistics, Lahore, Pakistan. Assistant Professor. Email: fshehzad.stat@gmail.com
4University of Gujrat, Department of Statistics, Gujrat, Pakistan. School Teacher. Email: mbn.shzdi@gmail.com


Abstract

Accurate estimation of parameters of a probability distribution is of immense importance in statistics. Biased and imprecise estimation of parameters can lead to erroneous results. Our focus is to estimate the parameter of Power function distribution accurately because this density is now widely used for modelling various types of data. In this study, L-moments, TL-moments, LL-moments and LH-moments of power function distribution are derived. In addition, the coefficient of variation, skewness and kurtosis are obtained by method of moments, L-moments and TL-moments. Parameters of the density are estimated using linear moments and compared with method of moments and MLE on the basis of bias, root mean square error and coefficients through simulation study. L-moments proved to be superior for the parameter estimation and this conclusion is equally true for different parametric values and sample size.

Key words: Moments, Monte Carlo Simulation, Order Statistics, Parameter estimation, Power function distribution.


Resumen

La distribución de función de potencias es ampliamente usada. Dada su importancia, es necesario estimar sus parámetros de manera precisa. En este artículo, los momentos TL de la distribución de función de potencias son derivados así como sus casos especiales tales como los momentos L, LL y LH. Los coeficientes de variación, sesgo y curtosis son obtenidos a partir de los momentos L y TL. Los parámetros desconocidos son estimados y los momentos lineales son comparados con el método de momentos y estimadores máximo verosímiles en la base del sesgo, raíz del error cuadrático medio a través de un estudio de simulación. Los momentos L permiten obtener estimaciones más precisas y esta conclusión es verdad para diferentes valores paramétricos y tamaño de muestra.

Palabras clave: distribución de función de potencias, estadísticas de orden, estimación de parámetros, momentos, simulación de Monte Carlo.


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[Recibido en marzo de 2014. Aceptado en noviembre de 2014]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv38n2a01,
    AUTHOR  = {Naveed-Shahzad, Mirza and Asghar, Zahid and Shehzad, Farrukh and Shahzadi, Mubeen},
    TITLE   = {{Parameter Estimation of Power Function Distribution with TL-moments}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2015},
    volume  = {38},
    number  = {2},
    pages   = {321-334}
}