Abstract
In this article, Burr III distribution is proposed with a significantly improved functional form. This new modification has enhanced the flexibility of the classical distribution with the ability to model all shapes of hazard rate function including increasing, decreasing, bathtub, upside-down bathtub, and nearly constant. Some of its elementary properties, such as rth moments, sth incomplete moments, moment generating function, skewness, kurtosis, mode, ith order statistics, and stochastic ordering, are presented in a clear and concise manner. The well-established technique of maximum likelihood is employed to estimate model parameters. Middle-censoring is considered as a modern general scheme of censoring. The efficacy of the proposed model is asserted through three applications consisting of complete and censored samples.
Highlights
Burr devised a dynamic family of probability distributions based on the Pearson differential equations
Motivated by a lack of availability of literature related to the modified Burr III (BIII) distribution, we present a much more flexible new modification of BIII distribution
The article is structured as follows: In Section 2, we focus our attention on the idea behind the new modification. {In Section 3, we acquaint the readers with some of the structural properties including the linear expansion, moments, mode, moment-generating functions, order statistics, and stochastic ordering of NMBIII distribution
Summary
Burr devised a dynamic family of probability distributions based on the Pearson differential equations. The two-parameter flexible Weibull extension of [6] has a hazard function that can be increasing, decreasing, or bathtub shaped. A three-parameter model, called exponentiated Weibull distribution, was introduced by [8]. Xie et al [10] proposed a three-parameter modified Weibull extension with a bathtubshaped hazard function. A new modified Weibull distribution by the authors in [11] has been presented with increasing and a bathtub-shaped hazard function. The authors claimed that the newly structured model is a limiting case of generalized inverse Weibull, BIII, and log-logistic distribution. The BIII distribution has a monotonic decreasing and unimodal hazard rate function, but due to its modification, NMBIII has monotonic, decreasing, increasing, unimodal, bathtub, and approximately constant hazard-rate shapes.
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