Journal of Pharmacology Pharmaceutics & Pharmacovigilance Category: Medical Type: Short Communication

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

Clement Boateng Ampadu1*
1 Department Of Biostatistics, 31 Carrolton Road, Boston, MA 02132-6303, United States

*Corresponding Author(s):
Clement Boateng Ampadu
Department Of Biostatistics, 31 Carrolton Road, Boston, MA 02132-6303, United States
Tel:+1 6174697268,
Email:drampadu@hotmail.com

Received Date: May 02, 2020
Accepted Date: May 07, 2020
Published Date: May 18, 2020

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

  1. The New Family Illustrated
  2. 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

  1. 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].
  2. 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.

REFERENCES

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.

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