The idea of transmuted distributions appeared. On the other hand, some contributions to quantile distribution theory appeared. Based on developments, we introduce the class of quantile transmuted-Chen G distributions, and show a sub-model is good in fitting the breast cancer patient’s data recorded.
Breast cancer; Chen-G; Quantile distribution theory; Transmuted distributions
- The New Family Illustrated
- Concluding Remarks and Further Recommendations
The New Family Illustrated
We begin with the following
Definition 1.1. A random variable J is claimed to follow the quantile transmuted- Chen G family of distributions  if its CDF can be represented by the following integral
From the above we have the following
Proposition 1.2. The CDF of the quantile transmuted- Chen G family of distributions [2,3] is given by
For illustrative purposes, let us assume the baseline distribution is Weibull with the following CDF
Theorem 1.3. The CDF of the quantile transmuted Chen-Weibull family is given by
Remark 1.4. We write J* ∼ QTCW(a, b, λ , c, d), if J* is a quantile transmuted Chen-Weibull random variable
This distribution is a good fit to real-life data as shown below (Figure 1).
Figure 1: The CDF of QTCW (1.82675, 125.674, 0.554331, 0.629088, 3.55831) fitted to the empirical distribution of the breast cancer patient’s data recorded in .
Concluding Remarks and Further Recommendations
The quantile transmuted Chen-G class of distributions is presented, a sub-model is shown to be a good fit to real life data  from the health sciences. The author invites the reader to investigate further properties and applications of this  new class of statistical distributions. Potential investigations include
- Application to Other Data Sets in the Health Sciences: We suggest the bladder cancer patient’s data recorded in , which accordingly is taken from .
- Clinical Applications: We suggest the vitamin A data set of . This data set was designed to evaluate the effect of vitamin A supplementation on recurrent diarrheal episodes in small children. In particular, the authors of  modelled the treatment effect in time until the first occurrence of diarrheal episodes, using an appropriate regression model with censored data.