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Revista Colombiana de Estadística
versão impressa ISSN 0120-1751
Rev.Colomb.Estad. vol.37 no.1 Bogotá jan./jun. 2014
https://doi.org/10.15446/rce.v37n1.44369
http://dx.doi.org/10.15446/rce.v37n1.44369
1King Abdulaziz University, Department of Statistics, Jeddah, Saudi Arabia. Professor. Email: bmalzahrani@kau.edu.sa
2King Abdulaziz University, Department of Statistics, Jeddah, Saudi Arabia. Ph.D student. Email: hsagor123@gmail.com
In this paper we propose a new three-parameter lifetime distribution with upside-down bathtub shaped failure rate. The distribution is a compound distribution of the zero-truncated Poisson and the Lomax distributions (PLD). The density function, shape of the hazard rate function, a general expansion for moments, the density of the rth order statistic, and the mean and median deviations of the PLD are derived and studied in detail. The maximum likelihood estimators of the unknown parameters are obtained. The asymptotic confidence intervals for the parameters are also obtained based on asymptotic variance-covariance matrix. Finally, a real data set is analyzed to show the potential of the new proposed distribution.
Key words: Asymptotic variance-covariance matrix, Compounding, Lifetime distributions, Lomax distribution, Poisson distribution, Maximum likelihood estimation.
En este artículo se propone una nueva distribución de sobrevida de tres parámetros con tasa fallo en forma de bañera. La distribución es una mezcla de la Poisson truncada y la distribución Lomax. La función de densidad, la función de riesgo, una expansión general de los momentos, la densidad del r-ésimo estadístico de orden, y la media así como su desviación estándar son derivadas y estudiadas en detalle. Los estimadores de máximo verosímiles de los parámetros desconocidos son obtenidos. Los intervalos de confianza asintóticas se obtienen según la matriz de varianzas y covarianzas asintótica. Finalmente, un conjunto de datos reales es analizado para construir el potencial de la nueva distribución propuesta.
Palabras clave: mezclas, distribuciones de sobrevida, distribució n Lomax, distribución Poisson, estomación máximo-verosímil.
Texto completo disponible en PDF
References
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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv37n1a15,
AUTHOR = {Al-Zahrani, Bander and Sagor, Hanaa},
TITLE = {{The Poisson-Lomax Distribution}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2014},
volume = {37},
number = {1},
pages = {225-245}
}