On Extended Normal Distribution Model with Application in Health Care
DOI:
https://doi.org/10.6000/1929-6029.2018.07.03.4Keywords:
Normal Distribution, Goodness-of-fit, Characteristics Function, Survival Function, Mixtures, Health Care.Abstract
In this article, the normal distribution model (NDM) is extended. A introduction to a new Extended Normal Distribution (ENDM) and its derivate models used in many applications is proposed. The author proposes the new model (ENDM) which generalizes the normal distribution models. This class of ENDM approximates an unknown risk-neutral density. The paper discusses different properties of the ENDM. In particular, the applicability of the new model with three parameters in a way to justify the representation of combination of normal distributions is presented. The potential of the proposed distribution for modelling and analyzing statistical data with reference to extensive sets of observations. Statistical properties of the proposed distribution have also been studied. The findings of this work will be useful to practitioners in applied fields of health care.
References
Mohammad A, Golam Kibria BM, Mohammad S. Normal and Student ́s t Distributions and Their Applications. Atlantis Studies in Probability and Statistics, Series Editor: C.P.T Sokos 2014.
Lyon A. Why are Normal Distributions Normal? British Journal for the Philosophy of Science 2014; 65(3): 621-649. https://doi.org/10.1093/bjps/axs046 DOI: https://doi.org/10.1093/bjps/axs046
Lahcene B. On Recent Modifications of Extended Weibull Families Distributions and Its Applications Asian Journal Of Fuzzy And Applied Mathematics 2018; 6(1): 1-12.
Lahcene B. On Recent Modifications of Extended Rayleigh Distribution and its Applications. JP Journal of Fundamental and Applied Statistics 2018; 12(1): 1-13.
Box George EP, Tiao C. Bayesian Inference in Statistical Analysis. New York: Wiley 1992. DOI: https://doi.org/10.1002/9781118033197
Cohen J, Cohen P, West SG, Aiken LS. Applied Multiple Regression/ Correlation Analysis for the Behavioral Sciences. Third edition. New Jersey: Lawrence Erlbaum Associates, Inc. 2003.
David FN. Games, Gods, and Gambling. New York, Hafner Pub. Co. 1962.
Feller W. An introduction to probability theory and its Applications. Third Edition, New York: Wiley 1971; 2.
Francis G. F.R.S Results Derived From the Natality Table of Körösi by Employing the Method of Contours or Isogens. Proceedings Royal Society of London 1894; 18(331): 18-23. DOI: https://doi.org/10.1098/rspl.1894.0005
Gravesande GJ. Demonstration Mathematique de la Direction de da Providence Divine. Oeuvres 1774; 2: 221-236.
Hald A. A History of Probability and Statistics and Their Applications before 1750. New York, John Wiley 1990. https://doi.org/10.1002/0471725161 DOI: https://doi.org/10.1002/0471725161
Heyse JF, Cook JR, Carides GW. Statistical Considerations in Analysing Health Care Resource Utilization and Cost Data. In Economic Evaluation in Health Care - Merging Theory with Practice, Edited by Drummond M, McGuire A. New York: Oxford Univers ity Press 2001.
Laplace, Pierre-Simon de. Memoire sur la Probabilite des Causes par les Evenements. Mémoires de l'Académie royale des Sciences de Paris (Savants étrangers), tome(6): pp 621–656. Translated by Stephen M. Stigler in Statistical Science 1774; 1(3): 1986.
Laplace PS. Memoire sur les Approximations des Formules qui sont Fonctions de tres Grand Nombres et sur leur Applications aux Probabilites. M´emoires de l’Academie des sciences de Paris: 1809; pp. 353–415 and 559–565.
Lukas E. A Characterization of the Normal Dstribution. Annals of Mathematical Statistics 1942; 13: 91-93. https://doi.org/10.1214/aoms/1177731647 DOI: https://doi.org/10.1214/aoms/1177731647
Manning WG, Fryback DG, Weinstein MC. Reflecting Uncertainty in Cost-Effectiveness Analysis(In Cost-effectiveness in health and medicine). Edited by Gold MR, Sigel JE, Russell LB, Weinstein MC. Oxford: Oxford University Press 1996.
Jagdish PK, Campbell RB. Handbook of the Normal Distribution", Second Edition, CRC Press 1996.
Pearson ES, Kendall M. Studies in the History of Statistics and Probability. London, Griffin 1970; 1: 185-189.
Karl P. Notes on the History of Correlation. Biometrika 1920; 13(1): 25-45. https://doi.org/10.1093/biomet/13.1.25 DOI: https://doi.org/10.1093/biomet/13.1.25
Pierce RG, Bozic KJ, Hall BL, Breivis J. Health Care Technology Assessment: Implications for Modern Medical –Practice 2007.
Part I. Understanding Technology Adoption and Analyses, Am J Orthop 36(1): 11-14.
Rorty R, Schneewind JB. The Taming of Chance. Edited By Quentin Skinner (General Editor), Lorraine Daston, Wolf Lepenies, University Press 2002.
Stahl S. The Evolution of the Normal Distribution. Mathematics Magazine 2006; 79(2): 96-113. https://doi.org/10.1080/0025570X.2006.11953386 DOI: https://doi.org/10.1080/0025570X.2006.11953386
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2018 Bachioua Lahcene
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Policy for Journals/Articles with Open Access
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are permitted and encouraged to post links to their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work
Policy for Journals / Manuscript with Paid Access
Authors who publish with this journal agree to the following terms:
- Publisher retain copyright .
- Authors are permitted and encouraged to post links to their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work .
