Alpha Power Transformed Extended Bur II Distribution: Properties and Applications

Abstract

This paper presents a new generalization of the extended Bur II distribution. We redefined the Bur II distribution using the Alpha Power Transformation (APT) to obtain a new distribution called the Alpha Power Transformed Extended Bur II distribution. We derived several mathematical properties for the new model which includes moments, moment generating function, order statistics, entropy etc. and used a maximum likelihood estimation method to obtain the parameters of the distribution. Two real-world data sets were used for applications in order to illustrate the usefulness of the new distribution.

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“…The new density function is most tractable when ) and have simple analytical expressions. Based on the generalization in equation 5and (6), several flexible distribution have been proposed and studied not limited to the work of Oguntunde, et al [8] studied the properties of Gompertz inverse exponential distribution, Khaleel, et al [9] studied the Gompertz flexible Weibull distribution and its applications etc.…”

“…On the contrary, in real life situations the hazard rate of many complex phenomena that are often encountered in practice is nonmonotone and cannot be modeled by the Gumbel type-2 distribution. To address this limitation [1] proposed the Exponentiated Gumbel type-2 distribution according to Nadarajah and Kotz [2] version of Gupta, et al [3], Okorie, et al [4] proposed the Kumaraswamy G Exponentiated Gumbel Type-2 Distribution which was obtained by combining Exponentiated Gumbel (EG) and the kumaraswamy distribution [5,6] proposed and studied the properties of Extended Gumbel type-2 ) distribution. Motivated by some of the properties of the generalised distribution with respect to the nature of its hazard function which includes; increasing, decreasing, non-monotone and bathtub shapes as well as the tractability and flexibility of the generalised distribution with improved statistical properties.…”

Transmuted Lower Record Type Power Function Distribution

“…The proposed distributions by using the CRTM are called cubic rank transmuted distributions. Some cubic rank transmuted distributions can be listed as follows: cubic rank transmuted Weibull [7], cubic rank transmuted log-logistic [7], cubic rank transmuted Kumaraswamy [8], cubic rank transmuted inverse Weibull [9], cubic rank transmuted modified Burr III [10]. Balakrishnan and He [11] suggested two new families based on distributions of lower and upper record values.…”