CFP last date
22 April 2024
Call for Paper
May Edition
IJCA solicits high quality original research papers for the upcoming May edition of the journal. The last date of research paper submission is 22 April 2024

Submit your paper
Know more
Reseach Article

Markov Chain Monte Carlo to Study the Estimation of the Coefficient of Variation

by M. A. W. Mahmoud, A. A. Soliman, A. H. Abd Ellah, R. M. El-sagheer
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 77 - Number 4
Year of Publication: 2013
Authors: M. A. W. Mahmoud, A. A. Soliman, A. H. Abd Ellah, R. M. El-sagheer

M. A. W. Mahmoud, A. A. Soliman, A. H. Abd Ellah, R. M. El-sagheer . Markov Chain Monte Carlo to Study the Estimation of the Coefficient of Variation. International Journal of Computer Applications. 77, 4 ( September 2013), 31-37. DOI=10.5120/13384-1000

@article{ 10.5120/13384-1000,
author = { M. A. W. Mahmoud, A. A. Soliman, A. H. Abd Ellah, R. M. El-sagheer },
title = { Markov Chain Monte Carlo to Study the Estimation of the Coefficient of Variation },
journal = { International Journal of Computer Applications },
issue_date = { September 2013 },
volume = { 77 },
number = { 4 },
month = { September },
year = { 2013 },
issn = { 0975-8887 },
pages = { 31-37 },
numpages = {9},
url = { },
doi = { 10.5120/13384-1000 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
%0 Journal Article
%1 2024-02-06T21:49:23.879386+05:30
%A M. A. W. Mahmoud
%A A. A. Soliman
%A A. H. Abd Ellah
%A R. M. El-sagheer
%T Markov Chain Monte Carlo to Study the Estimation of the Coefficient of Variation
%J International Journal of Computer Applications
%@ 0975-8887
%V 77
%N 4
%P 31-37
%D 2013
%I Foundation of Computer Science (FCS), NY, USA

The coefficient of variation (CV ) of a population is defined as the ratio of the population standard deviation to the population mean. It is regarded as a measure of stability or uncertainty, and can indicate the relative dispersion of data in the population to the population mean. In this article, based on the upper record values, we study the behavior of the CV of a random variable that follows a Lomax distribution. Specifically, we compute the maximum likelihood estimations (MLEs) and the confidence intervals of CV based on the observed Fisher information matrix using asymptotic distribution of the maximum likelihood estimator and also by using the bootstrapping technique. In addition, we propose to apply Markov Chain Monte Carlo (MCMC) techniques to tackle this problem, which allows us to construct the credible intervals. A numerical example based on a real data is presented to illustrate the implementation of the proposed procedure. Finally, Monte Carlo simulations are performed to observe the behavior of the proposed methods.

  1. A. H. Abd Ellah, Bayesian one sample prediction bounds for the Lomax distribution, Indian J. Pure Appl. Math. 42 (2011), no. 5, 335–356.
  2. A. H. Abd Ellah, Comparison of estimates using record statstics from Lomax model : Bayesian and non Bayesian approaches, J. Stat. Res. Train. Center 3 (2006), 139-158.
  3. K. Ahn, Use of coefficient of variation for uncertainty analysis in fault tree analysis, Reliab. Engin. System Safety 47 (1995), no 3, 229–230.
  4. B. C. Arnold, Pareto Distributions. In: Statistical Distributions in ScientificWork, International Co-operative Publishing House, Burtonsville, MD, 1983.
  5. B. C. Arnold, N. Balakrishnan and H. N. Nagaraja, Records, Wiley, New York, 1998.
  6. J. O. Berger, Statistical Decision Theory and Bayesian Analysis. New York, Springer Verlag, 1985.
  7. M. C. Bryson, Heavy-tailed distributions: properties and tests, Technometrics 16 (1974), no. 1, 61–68.
  8. M. Chahkandi and M. Ganjali, On some lifetime distributions with decreasing failure rate, Comput. Statist. Data Anal. 53 (2009), no. 12, 4433–4440.
  9. M. M. Dacorogna and E. R¨uttener, Why time-diversified equalisation reserves are something worth having, Converium Research Report, Switzerland, 2006.
  10. B. Efron, The bootstrap and other resampling plans, In: CBMS-NSF Regional Conference Seriesin Applied Mathematics, SIAM, Philadelphia, PA, 1982.
  11. S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images, IEEE Trans. Pattern Anal. Mach. Intell. 6 (1984), 721–741.
  12. W. R. Gilks, S. Richardson and D. J. Spiegelhalter, Markov chain Monte Carlo in Practices, Chapman and Hall, London, 1996.
  13. J. Gong and Y. Li, Relationship between the estimatedWeibull modulus and the coefficient of variation of the measured strength for ceramics, J. Ame. Ceramics Society, 82 (1999), no. 2, 449–452.
  14. W. H. Greene, Econometric Analysis, 5th Ed. New York University, 2002.
  15. M. Habibullah, and M. Ahsanullah, Estimation of parameters of a Pareto distribution by generalized order statstics, Comm. Statist. Theory Methods 29 (2000), 1597-1609.
  16. P. Hall, Theoretical comparison of bootstrap confidence intervals, Ann. Stat. 16 (1988), 927-953.
  17. A. J. Hamer, J. R. Strachan, M. M. Black, C. Ibbotson and R. A. Elson, A new method of comparative bone strength measurement, J. Med. Engin. Tech. 19 (1995), no. 1, 1–5.
  18. W. K. Hastings, Monte Carlo sampling methods using Markov chains and their applications, Biometrika 57 (1970), 97–109.
  19. J. Knight and S. Satchell, Are-examination of Sharpe's ratio for log-normalprices, Appl. Math. Finance, 12 (2005), no. 1, 87–100.
  20. K. S. Lomax, Business failure: Another example of the analysis of the failure data, JASA 49 (1954), 847-852.
  21. A. W. Marshall and I. Olkin, Life Distributions. Structure of Nonparametric, Semiparametric, and Parametric Families, Springer, New York, NY, 2007.
  22. C. Marrison, The Fundamentals of Risk Measurement, McGraw-Hill, New York, 2002.
  23. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller, Equations of state calculations by fast computing machines, J. Chem. Phy. 21 (1953), 1087–1091.
  24. E. G. Miller and M. J. Karson, Testing Equality of Two Coefficients of Variation, Amer. statist. Assoc. Posceed. Business and economics 1 (1977), 278-283.
  25. W. B. Nelson, Applied Life Data Analysis, Wiley, New York, 1982.
  26. W. K. Pang, W. T. Y. Bosco, M. D. Troutt and H. H. Shui, A simulation-based approach to the study of coefficient of variation of dividend yields, European J. Oper. Res. 189 (2008), 559–569.
  27. W. K. Pang, P. K. Leung, W. K. Huang and W. Liu, On interval estimation of the coefficient of variation for the three-parameter Weibull, lognormal and gamma distribution: A simulation based approach, European J. Oper. Res. 164 (2005), 367–377.
  28. S. T. Rachev, I. Huber and S. Ortobelli, Portfolio choice with heavy tailed distributions. Tech. Rep. , University of Karlsruhe, Germany, 2004. .
  29. W. Reh, and B. Scheffler, Significance tests and confidence intervals for coefficient of variation, Comput. Stat. Data Anal. 22 (1996), no. 4, 449–453.
  30. S. Rezaei, R. Tahmasbi and M. Mahmoodi, Estimation of P[Y¡X] for generalized Pareto distribution, J. Statist. Plann. Inference, 140 (2010), 480-494.
  31. C. P. Robert and G. Casella, Monte Carlo Statistical Methods, Second edition, Springer, New York, 2004.
  32. S. K. Upadhyay and M. Peshwani, Choice between Weibull and lognormal models: a smulation based Bayesian study, Comm. Statist. Theory Methods 32 (2003), 381-405. 37
Index Terms

Computer Science
Information Sciences


Lomax distribution Coefficient of variation Markov chain Monte Carlo Upper record value Bootstrap