Parameter Estimation of Power Function Distribution with TL-moments

• MIRZA NAVEED-SHAHZAD ^[1] ; ZAHID ASGHAR ^[2] ; FARRUKH SHEHZAD ^[3] ; MUBEEN SHAHZADI ^[1]
  1. [1] University of Gujrat

     University of Gujrat

     Pakistán

     
  2. [2] Quaid-i-Azam University

     Quaid-i-Azam University

     Pakistán

     
  3. [3] COMSATS Institute of Information Technology

     COMSATS Institute of Information Technology

     Pakistán

     

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• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 38, Nº. 2, 2015, págs. 321-334
• Idioma: inglés
• DOI: 10.15446/rce.v38n2.51663
• Títulos paralelos:
  • Estimación de parámetros de distribuciones de funciones de potencia con momentos TL
• Enlaces
  • Texto completo
• Resumen
  • español

    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.

  • English

    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.

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