Abstract
The gamma Burr XII distributions: Theory and applications
Highlights
The Burr XII (BXII) distribution first appears as part of the Burr system of distributions
The likelihood ratio (LR) statistic for testing H0 : a = 1 versus H : a = 1, which is equivalent to compare the Zografos-Balakrishnan Burr XII (ZBXII) and BXII distributions, is given by w = 2{l(a, s, d, c) − l(1, s, d, c)}, where a, s, d and c are the maximum likelihood estimators (MLEs) under H and s, d and c are the estimates under H0
We introduce a four-parameter distribution, called the Zografos-Balakrishnan Burr XII (ZBXII) distribution
Summary
The Burr XII (BXII) distribution first appears as part of the Burr system of distributions. Following Zografos and Balakrishnan (2009) and Ristic and Balakrishnan (2012) proposals, we introduce a new four-parameter distribution called the Zografos-Balakrishnan Burr XII (ZBXII) distribution. Since the RB-G family’s cdf and pdf have a similar structure to the ZB-G family, we present some mathematical properties and expansions for the so-called Ristic-Balakrishnan Burr XII (RBXII) model. These results follow analogously to those of the ZBXII distribution but with different weights in their linear representations (see Section 3).
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