¹University of Gujrat, Department of Statistics, Gujrat, Pakistan. PhD. Email: nvd.shzd@uog.edu.pk
²University of Prishtina ''Hasan Prishtina'', Pristina, Republic of Kosovo. PhD. Email: fmerovci@yahoo.com
³Quaid-i-Azam University, Department of Statistics, Islamabad, Pakistan. PhD. Email: g.zahid@gmail.com

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.

Key words: Moments, Parameter Estimation, Transmuted Singh-Maddala Distribution, TL-Moments, Upsidedown Bathtub Shaped Hazard Rate.

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.

Palabras clave: distribución Singh-Maddala transmuetada, función de riesgo invertida, momentos, momentos TL, estimación de parámetros.

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