Thesis (Ph.D.) - Cairo University - Institute of Statistical Studies and Research - Department of Mathematical Statistics

The Generalized Feller-Pareto (GFP) family was defined by Zandonatti (2001) as mentioned in Kleiber and Kotz (2003). Zandonatti (2001) is in Italian and therefore not easily accessible. The GFP is a five parameter family of distributions. Three important four parameter daughter distributions can be obtained from the five- parameter parent GFP distribution as special cases. Two of these distributions are new and will be referred to as the beta Lomax and the generalized Singh-Maddala. The other four parameter daughter distribution is the Feller Pareto distribution. In turn, they give rise to special or limiting case three parameter families of distributions: for example, the generalized gamma and the Burr XII distributions. They also give rise to special or limiting case two parameter families of distributions: for example, the log- normal and the Weibull distributions. Indeed, the GFP family is an attractive, flexible, elegant, and ingenious family but it involves five parameters. Applications of the GFP distribution cover a wide spectrum of areas ranging from lifetime literature, medicine, and economics. For example for lifetime literature and in medicine, Paranaíba et al. (2011) discussed an application of the GFP distribution to a real data set on cancer recurrence

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