Parameter induction in continuous univariate distributions: Well-established G families

• Published in: Anais da Academia Brasileira de Ciências Vol. 87; no. 2; pp. 539 - 568
• Main Authors: Tahir, Muhammad H, Nadarajah, Saralees
• Format: Journal Article
• Language: English
• Published: Brazil Academia Brasileira de Ciências 01.06.2015
• Subjects: Beta-distribution; exponentiated family; Kumaraswamy distribution; Marshall-Olkin family; McDonald distribution; MULTIDISCIPLINARY SCIENCES; reliability properties; McDonald distribution; Kumaraswamy distribution; reliability properties; exponentiated family; Beta-distribution; Marshall-Olkin family
• ISSN: 0001-3765; 1678-2690; 1678-2690; 0001-3765
• DOI: 10.1590/0001-3765201520140299

The art of parameter(s) induction to the baseline distribution has received a great deal of attention in recent years. The induction of one or more additional shape parameter(s) to the baseline distribution makes the distribution more flexible especially for studying the tail properties. This parameter(s) induction also proved helpful in improving the goodness-of-fit of the proposed generalized family of distributions. There exist many generalized (or generated) G families of continuous univariate distributions since 1985. In this paper, the well-established and widely-accepted G families of distributions like the exponentiated family, Marshall-Olkin extended family, beta-generated family, McDonald-generalized family, Kumaraswamy-generalized family and exponentiated generalized family are discussed. We provide lists of contributed literature on these well-established G families of distributions. Some extended forms of the Marshall-Olkin extended family and Kumaraswamy-generalized family of distributions are proposed.