The Extended Marshall-Olkin Burr III Distribution: Properties and Applications

Abstract

We study a new continuous distribution called the Marshall-Olkin modified Burr III distribution. The density function of the proposed model can be expressed as a mixture of modified Burr III densities. A comprehensive account of its mathematical properties is derived. The model parameters are estimated by the method of maximum likelihood. The usefulness of the derived model is illustrated over other distributions using a real data set.

The single and double inverse Pareto–Burr XII distribution: Properties, estimation methods, and real-life data applications

“…Then, some mathematical features of the OIPBXII distribution can be received directly from (13) and the features of the BXII distribution.…”

“…The For the two datasets, we shall compare the fits of the OIPBXII distribution with other competing distributions, including the OLL-BXII, 12 MOMBIII, 13 OLBXII, 14 FTLBXII, 15 GTBX, 16 KEBXII, 6 and BXII distributions.…”

“…• The OIPBXII generalizes nine well-known existing models such as the Marshall-Olkin BXII (MOBXII), exponentiated BXII (Exp-BXII), MO-Lomax, and MO-log-logistic distributions, among others. • It provides consistently better fits than other competing distributions, including the odd log-logistic Burr XII (OLL-BXII), 12 Marshall-Olkin modified Burr III (MOMBIII), 13 odd Lindley Burr XII (OLBXII), 14 Fréchet Topp-Leone Burr XII (FTLBXII), 15 generalized transmuted Burr X (GTBX), 16 Kumaraswamy exponentiated Burr XII (KEBXII), 6 and BXII probability density function.…”