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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:
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

DOI:10.24966/PPP-5649/100013

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

  1. Shaw WT, Buckley IR (2009) The Alchemy of Probability Distributions: beyond Gram-Charlier Expansions, and a Skew-kurtotic-normal Distribution from a Rank Transmutation Map. arXiv preprint arXiv: 0901.0434.
  2. Clement A (2018) Results in Distribution Theory and Its Applications Inspired by Quantile Generated Probability Distributions. Lulu.com ISBN: 0359249957, 9780359249954
  3. Ampadu CB (2020) New Classes of Quantile Generated Distributions: Statistical Measures, Model Fit, and Characterizations. Lulu.com ISBN: 1678166677, 9781678166670
  4. Anzagra L, Sarpong S, Nasiru S (2020) Chen-G class of distributions. Cogent Mathematics & Statistics 7: 1721401
  5. Jayakumar K, Girish Babu M (2017) T-TRANSMUTED X FAMILY OF DISTRIBUTIONS, STATISTICA, anno LXXVII, n. 3.
  6. LEE ET (1992) Statistical Methods for Survival Data Analysis. John Wiley, New York.
  7. Ahmad Z, Elgarhy M, Hamedani GG (2018) A new Weibull-X family of distributions: properties, characterizations and applications. J Stat Distrib App 5.
  8. Lee ET, Wang JW (2003) Statistical Methods for Survival Data Analysis, 3rd edn. Wiley, New York.
  9. Barreto ML, Santos LMP, Assis AMO, Araujo MPN, Farenzena GG, et al. (1994) Effect of vitamin A supplementation on diarrohea and acute lower-respiratory-tract infections in young children in Brazil. Lancet 344: 228-231.
  10. Afify AZ, Cordeiro GM, Bourguignon M, Ortega EMM. Properties of the Transmuted Burr XII Distribution, Regression and its Applications. Journal of Data Science 485-510

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.

Journal Highlights
  • Pharmacology
  • Pharmaceutics
  • Pharmacovigilance
  • Pharmaceutical Sciences
  • Medication Errors

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