Some extended Pareto Type I distributions

Probability distributions are essential in data modeling. Introduction of parameter(s) into existing probability distributions is a method of extending or generalizing distributions to produce more flexible distributions and for better fit to data. The Pareto type 1 distribution (PT1) is a right skewed continuous distribution originally used in description of wealth and income but also used for modeling other right skewed data. To add flexibility, Pareto type 1 distribution was extended by introducing parameter(s) into its probability distribution to accommodate more types of data. Some functions of the extended Pareto type 1 distributions were derived using five parameter induction methods. Flexibility of extended distributions was demonstrated through comparisons of density and hazard function shapes of some of the extended distributions with those of the PT1. Further study on properties of non-existing extended Pareto Type I distributions and real-life applications are recommended

Modified Frechet distributions and their generalized families

The Frechet distribution is used for modeling extreme events. There are different approaches to developing statistical distributions which include  the use of translation methods, system of differential equations, quantile methods among others. Existing statistical distributions are also modified  or generalized to accommodate other different types of data and improve goodness of fit to data. Addition of extra parameter(s) is one approach  used for generalizing existing distributions such that the base distributions are embedded in the new generalized distributions. Some methods of  parameter induction were used to obtained families of generalized distributions. Parameter(s) were also introduced into the probability  distributions of the Frechet distribution to derive functions of its modified versions belonging to each of the generalized families derived. Further  study is recommended on some of the modified Frechet distributions and their generalized families

A New Log Lindley Distribution with Applications

This paper introduces a new generalization of the Lindley distribution introduced by [1], using the basic idea of [2] and along the lines of [3]. The new distribution is a compound of the Lindley and logarithmic distributions. We refer to the new model as the logarithmic-Lindley (Log-L) distribution. This model is capable of modeling various shapes of aging and failure criteria. The properties of the Log-L model are discussed, and the maximum likelihood estimation method is used to evaluate the parameters involved. Finally, the usefulness of the new model for modeling reliability data is illustrated using a two real data sets with simulation study