An Alternate to the UNH-G Family of Distributions with Illustration

In this short communication we propose an alternate to the UNH-G family of distributions appearing. Further we show a sub-model of the new family is good in fitting real life data. Readers are asked to investigate further properties and applications of the new class of statistical distributions.

AMS Subject Classifications: 62exx

•          Introduction to the New Family

•          Practical Illustration           

•          Open Problem

The new family can be seen as a certain modification of the Weibull or Exponential distributions, to introduce the following as its CDF

Where G is some baseline distribution with parameter vector ?, and a, b, c > 0. Obviously, the PDF can be obtained by differentiating the CDF. The new distribution is a good fit to real life data as shown in the next section [1,2].

We assume a = b = c = 1, and the baseline distribution is Dagum with the following CDF

Where x, f, g, h > 0. Thus the CDF of the new distribution (Modified Weibull-Dagum) is given by

Figure 1: The CDF and PDF of MWD(0.70896,3.48504,2.10098) fitted to the empirical distribution and histogram of the survival times of guinea pigs data.

Notation: We write  if J is a modified Weibull Dagum random variable

It is an open problem to obtain properties and applications of this new class of statistical distributions. The author invites readers to tackle this open problem.

1. Nasiru S, Abubakari AG, Abonongo J. Unit Nadarajah-Haghighi generated family of distributions: properties and applications. Int J Statis. 2020.
2. Adam I. Complementary power series exponentiated nadarajah-haghighi distribution. Master of philosophy degree in applied statistics THESIS Univeri Develop West Africa. 2019.