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

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