The Quantile Transmuted-Chen G Family of Distributions with Illustration to Breast Cancer Patients Data

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.

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 [1] 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 [5].

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 [5] from the health sciences. The author invites the reader to investigate further properties and applications of this [6] new class of statistical distributions. Potential investigations include