Article Type : Short commentary
Authors : Ampadu CB
Keywords : UNH-G; Weibull; Exponential; Modified; Guinea pigs data
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.