The Quantile Transmuted-Chen G Family of Distributions with Illustration to Breast Cancer Patients Data
*Corresponding Author(s):
Clement Boateng AmpaduDepartment Of Biostatistics, 31 Carrolton Road, Boston, MA 02132-6303, United States
Tel:+1 6174697268,
Email:drampadu@hotmail.com
Abstract
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.
Keywords
Breast cancer; Chen-G; Quantile distribution theory; Transmuted distributions
CONTENTS
- 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 [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
- Application to Other Data Sets in the Health Sciences: We suggest the bladder cancer patient’s data recorded in [7], which accordingly is taken from [8].
- Clinical Applications: We suggest the vitamin A data set of [9]. 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 [10] modelled the treatment effect in time until the first occurrence of diarrheal episodes, using an appropriate regression model with censored data.
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Citation: Ampadu CB (2020) The Quantile Transmuted-Chen G Family of Distributions with Illustration to Breast Cancer Patients Data. J Pharmacol Pharmaceut Pharmacovig 4: 013.
Copyright: © 2020 Clement Boateng Ampadu, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
