Working Paper Article Version 1 This version is not peer-reviewed

A New Method for Generalizing Burr and Related Distributions

Version 1 : Received: 30 June 2020 / Approved: 3 July 2020 / Online: 3 July 2020 (05:43:57 CEST)

How to cite: CHAKRABORTY, T.; Das, S.; Chattopadhyay, S. A New Method for Generalizing Burr and Related Distributions. Preprints 2020, 2020070013 CHAKRABORTY, T.; Das, S.; Chattopadhyay, S. A New Method for Generalizing Burr and Related Distributions. Preprints 2020, 2020070013

Abstract

A new method has been proposed to generalize Burr-XII distribution, simply called Burr distribution, by adding an extra parameter to an existing Burr distribution for more flexibility. In this method, the exponent of the Burr distribution is modeled using a nonlinear function of the data and one additional parameter. The models of this newly introduced generalized Burr family can significantly increase the flexibility of the former Burr distribution, with respect to the density and hazard rate shapes. Families expanded using the method introduced here is heavy-tailed and belongs to the maximum domain of attractions of the Frechet distribution. Also, the method is applied to yield new three-parameter Pareto and generalized exponentiated distributions. A relevant model of the new generalized Burr family has been considered in detail, with special emphasis on the hazard functions, stochastic orders, expression of the entropies, and the corresponding estimation and testing methods are derived. Finally, as empirical evidence, the new distribution is applied to the analysis of large-scale heavy-tailed network data and compared with other commonly used distributions.

Subject Areas

Burr distribution; exponentiated distributions; stochastic ordering; reliability properties; maximum likelihood

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