Transmuted Singh-Maddala Distribution: A new Flexible and Upside-Down Bathtub Shaped Hazard Function Distribution

• MIRZA NAVEED SHAHZAD ^[1] ; FATON MEROVCI ^[3] ; ZAHID ASGHAR ^[2]
  1. [1] University of Gujrat

     University of Gujrat

     Pakistán

     
  2. [2] Quaid-i-Azam University

     Quaid-i-Azam University

     Pakistán

     
  3. [3] University of Prishtina ''Hasan Prishtina''

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• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 40, Nº. 1, 2017, págs. 1-27
• Idioma: inglés
• DOI: 10.15446/rce.v40n1.50085
• Títulos paralelos:
  • Distribución Singh-Maddala transmutada: una nueva distribución, flexible y con forma de bañera invertida para la función de riesgo
• Enlaces
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• Resumen
  • español

    La distribución Singh-Maddala es muy popular para analizar datos de ingresos, gastos, actuariales, ambientales y de confiabilidad. Para mejorar su alcance y aplicación se propone su extensión a la distribución de cuatro parámetros Singh-Maddala transmutada. Esta es más flexible en la modelación de diversos conjuntos de datos. Sus propiedades básicas, las funciones de confiabilidad y riesgos son estudiadas. La función de riesgo es decrecientes o tiene forma de bañera invertida. Como se requiere en varios estudios de sobrevivencia se exploran sus estadísticas de orden y los momentos TL, con sus casos especiales L, TL, LL y LH. Se emplea máxima verosimilitud para la estimación de los cuatro parámetros. Datos reales son usados para ilustrar la utilidad y potencialidad del modelo propuesto. Los resultados indican que la distribución propuesta ajusta mejor que la original.

  • English

    The Singh-Maddala distribution is very popular to analyze the data on income, expenditure, actuarial, environmental, and reliability related studies. To enhance its scope and application, we propose four parameters transmuted Singh-Maddala distribution, in this study. The proposed distribution is relatively more flexible than the parent distribution to model a variety of data sets. Its basic statistical properties, reliability function, and behaviors of the hazard function are derived. The hazard function showed the decreasing and an upside-down bathtub shape that is required in various survival analysis. The order statistics and generalized TL-moments with their special cases such as L-, TL-, LL-, and LH-moments are also explored. Furthermore, the maximum likelihood estimation is used to estimate the unknown parameters of the transmuted Singh-Maddala distribution. The real data sets are considered to illustrate the utility and potential of the proposed model. The results indicate that the transmuted Singh-Maddala distribution models the datasets better than its parent distribution.

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