Evaluating the Goodness of the Sample Coefficient of Variation via Discrete Uniform Distribution
Abstract
In this paper we evaluate whether the sample coefficient of variation (CV) is a good estimator for the population coefficient of variation, when the random variable (r.v.) follows the discrete uniform distribution . Samples both with replacement and without replacement are examined and the percentage of the values of the estimator that lie within the bounds of the corresponding population coefficient of variation sqrt(3)/3<CV<1 is calculated as a measure of goodness. The study of the above samples indicates that the goodness of the sample coefficient of variation estimator increases in parallel with the sample size. The overall study gives a good idea of ‘whether the sample coefficient of variation is generally a good estimator’.References
N. Balakrishnan and V. B.Nevzorov, A Primer on Statistical Distributions, Hoboken, N.J. : Wiley, 2003.
H. Belbachir, Determining the mode for convolution powers of discrete uniform distribution, Probability in the Engineering and Informational Sciences, vol. 25, no. 4, pp. 469475, 2011.
H., Belbachir,S. Bouroubi and A. Khelladi, Connection between ordinary multinomials, Fibonacci numbers, Bell polynomials and discrete uniform distribution, Annales Mathematicae et Informaticae 35, pp. 2130, 2008.
S.alikandM.Gngr, On the expected values of the sample maximum of order statistics from a discrete uniform distribution, Applied Mathematics and Computation, vol. 157, no. 3, pp. 695700, 2004.
S. alik, M. Gngr and C. Colak, On The Moments of Order Statistics from Discrete Distributions, Pakistan Journal of Statistics, vol. 26, no. 2, pp. 417426, 2010.
V. Choulakian, R. A. Lockhart and M. A. Stephens, Cramervon Mises statistics for discrete distributions, The Canadian Journal of Statistics, vol. 22, no. 1, pp. 125137, 1994.
A. Christoforidis, V. Perifanis, E. Papadopoulou, M. Dimitriadou, E. Kazantzidou, E. Vlachaki and I. Tsatra, Poor correlations between measurements of bone quality by quantitative ultrasound sonography and dual energy X-ray absorptiometry in patients with beta-thalassaemia major, European Journal of Haematolog, vol. 82, no. 1, pp. 1521, 2009.
N. Farmakis, Introduction to Sampling, A&P Christodoulidi Publishing Co, Thessaloniki (in Greek), 2016.
R. A. Fisher The Design of Experiments, New York: Hafner, 1935.
M.Gharib,B.I.MohammedandW.E.R.Aghel,The Exponentiated Marshall-Olkin Discrete Uniform Distribution With Application In Survival Analysis, International Journal Of Modern Engineering Research, vol. 7, no. 8, pp. 3448, 2017.
J. Hoseini and A. Mohammadi, Estimator and Tests for Coefficient of Variation in Uniform Distribution, Journal of Biometrics and Biostatistics, 3:149, 2012.
C. W. Kang, M. S. Lee, Y. J. Seong and D. M. Hawkins, A control chart for the coefficient of variation, Journal of Quality Technology, vol. 39, no. 2, pp. 151 158, 2007.
K. Krishnamoorthy, Handbook of statistical distributions with applications (2nd edition), Chapman and Hall/CRC, 2015.
F. Kolyva-Machera and E. Bora-Senta, Statistics: Theory and Applications (2nd edition), Ziti Publishing Co, Thessaloniki (in Greek), 2013.
P. S. Levy and S. Lemeshow, Sampling of Populations: Methods and Applications (4th edition), John Wiley Sons, Inc., New York,2008.
R.Mahmoudvand,H.HassaniandR.Wilson, Is the Sample Coefficient of Variationa Good Estimator for the Population Coefficient of Variation?, World Applied Sciences Journal, vol. 2, no. 5, pp. 519522, 2007.
R.Mahmoudvand and T.Oliveira, On the Application of Sample Coefficient of Variation for Managing Loan Portfolio Risks. Preprint, 2018.
F. I. Mahoney and D. Barthel, Functional evaluation: the Barthel Index, Maryland State Medical Journal, 14, pp. 5661, 1965.
L. Mattner and B. Roos, Maximal probabilities of convolution powers of discrete uniform distributions, Statistics and Probability Letters, vol. 78, no. 17, pp. 29922996, 2008.
I.Papatsouma and N.Farmakis, Approximating Symmetric Distributions via Sampling and Coefficient of Variation, Communications in Statistics Theory and Methods, 2018.
K. Pearson, Contributions to the mathematical theory of evolution, II: Skew variation in homogeneous material, Philosophical Transactions of the Royal Society of London, vol. 186, pp. 343414, 1895.
K. Pearson, Mathematical contributions to the theory of evolution: Regression, heredity, and panmixia, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 187, pp. 253318, 1896.
E. J. G. Pitman, Significance tests which may be applied to samples from any population, Royal Statistical Society Supplement 4: 119130 and 225232 (parts I and II), 1937.
C. B. Prasanth and E. Sandhya, A Generalized Discrete Uniform Distribution, Journal of Statistics Applications & Probability, vol. 5, no. 1, pp. 113, 2016.
D.B.Pyne,C.B.TrewinandW.G.Hopkins, Progression and variability of competitive performance of Olympics wimmers, Journal of Sports Sciences, vol. 22, no. 7, pp. 613620, 2004.
S. M. Ross A first course in Probability (9th edition), Pearson, 2012.
E.SandhyaandC.B.Prasanth, Marshall- Olkin Discrete uniform distribution, Journal of probability,Volume2014,10pages,Article ID 979312, Hindawi Publishing Corporation, 2013.
K. Sheeja and S. Lakshmi, The exponentiated Marshall-Olkin discrete uniform distribution with application in survival and hazard analysis on progesterone, estrogen and other various hormones, Arya Bhatta Journal of Mathematics and Informatics,vol.10,no.2, pp. 413420, 2018.
G. Van Belle and D. Martin, Sample Size as a Function of Coefficient of Variation and Ratio of Means, The American Statistician, vol. 47, no. 3, pp. 165167, 1993.
- 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 able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post 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 (See The Effect of Open Access).
