Mirza Naveed Shahzad

Transmuted Power Function Distribution : A more flexible Distribution

Abstract Double-bounded data appears in many applications related to engineering, economics, hydrology, social and behavioral sciences. To model the double-bounded data the Power function distribution is an obvious choice. To enhance its applicability, we proposed transmuted Power function distribution in this study. The new distribution relatively more flexible and performs better in reliability and meteorological data analysis than the parent distribution. Its various mathematical properties are derived such as mean, mode, median, variance, quantile function, reliability function and hazard function. The order statistics and generalized TL-moments with its special cases L-, TL-, LL- and LH-moments are also explored. Parameters estimation is approached through method of maximum likelihood estimation and to evaluate their performance a simulation study has been carried out. Finally, the transmuted and parent distributions is illustrated and compared through two real data sets.

Transmuted Dagum distribution: A more flexible and broad shaped hazard function model

In this article, we introduce an extended Dagum distribution, named as transmuted Dagum distribution which can be used for income distribution, actuarial, survival and reliability analysis. The main motivation for generalizing the standard distribution is to provide more flexible distribution to model a variety of data. The extended distribution has been expressed using quadratic rank transmutation map and its tractable properties like moments, moment generating, quantile, reliability and hazard functions are derived. The transmuted Dagum model provides the broader range of hazard behavior than the Dagum model. The densities of its order statistics, generalized TL-moments with its special cases are also studied. The parameters of the new model are estimated by maximum likelihood using Newton-Raphson approach and the information matrix and confidence intervals are also obtained. To illustrate utility and potentiality of the proposed model, it has been applied to rainfall data for the city of Islamabad, Pakistan.