A Generalization of Exponentiated Pareto-I Distribution with Applications

Abstract

According to earlier research, transmuting a standard distribution often results in a compound distribution that performs better and is more flexible. In light of this fact, this article proposes two novel generalized versions of the exponentiated Pareto-I distribution, called cubic transmuted exponentiated Pareto-I and fourth rank transmuted exponentiated Pareto-I by using the generalization formula for transmuted distribution. Some statistical properties are derived. Model parameters are estimated using the maximum likelihood method. Finally, an application of the two proposed distributions to two real data sets with diverse shapes is illustrated and compared with some distributions based on the exponential family and the exponentiated Pareto-I distribution. The applications suggest that the fourth version performs better than the cubic one for all shapes of the distribution. The new exponentiated Pareto-I models exhibit constant, upside-down, and bathtub hazard rates. The justification for the practicality of the new lifetime models is based on their ability to model real-life data sets from different perspectives.

Keywords

• pareto distribution
• cubic transmutation
• fourth rank transmutation
• maximum likelihood estimation
• moment generating function