A Study on Efficiency of Confidence Interval for a Coefficient of Quartile Variation
Abstract
The objective of this study is to learn on the efficiency of confidence interval for coefficient of quartile variation of Bonett on the data with Laplace Distribution, Logistic Distribution, Weibull Distribution, Lognormal Distribution, Skew Normal Distribution and Gamma Distribution, in event of left-skewed, right-skewed and symmetric leptokurtosis distributions. The study reveals that for right-skewed data, the confidence interval for coefficient of quartile variation of Bonett has good efficiency except for the small sample size (=10). For left-skewed data, the confidence interval for a coefficient of quartile variation of Bonett has good efficiency and the efficiency increases as sample size increase and the data distribution is closed to symmetry. Keywords : interquartile range, coefficient of variationReferences
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McKay, A.T., (1932). Distribution of the coefficient of variation and extended ‘t’ distribution. Journal of the Royal Statistical Society, 95, 695 – 698.
Sinsomboonthong, S. (2004). Elementary statistics, (5th Edition). Bangkok : Chamchuri Products. (in Thai)
Vangel, M.G. (1996). Confidence intervals for a normal coefficient of variation. The American Statistician, 50,
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Wilks, S.S. (1959). Nonparametric Statistical Inference. Wiley, New York.
Zar, J.H. (1984). Biostatistical Analysis. second ed. Prentice-Hall, Englewood Cliffs, NJ.
Hettmansperger, T.P., McKean, J.W., (1998). Robust Nonparametric Statistical Methods. Wiley, London.
Stuart, A., Ord, J.K., (1994). Kendalls’ Advanced Theory of Statistics, Volume I: Distribution Theory. sixth ed. Edward
Amold, London
Zwillinger, D., Kokoska, S. (2000). Standard Probability and Statistical Tables and Formula. Chapman & Hall,
Boca Raton.
Niyamangkun, S. (2005). Statistics for Research. (2nd Edition). Bangkok : Kasetsart University Press. (in Thai)
McKay, A.T., (1932). Distribution of the coefficient of variation and extended ‘t’ distribution. Journal of the Royal Statistical Society, 95, 695 – 698.
Sinsomboonthong, S. (2004). Elementary statistics, (5th Edition). Bangkok : Chamchuri Products. (in Thai)
Vangel, M.G. (1996). Confidence intervals for a normal coefficient of variation. The American Statistician, 50,
21 – 26.
Wilks, S.S. (1959). Nonparametric Statistical Inference. Wiley, New York.
Zar, J.H. (1984). Biostatistical Analysis. second ed. Prentice-Hall, Englewood Cliffs, NJ.
Hettmansperger, T.P., McKean, J.W., (1998). Robust Nonparametric Statistical Methods. Wiley, London.
Stuart, A., Ord, J.K., (1994). Kendalls’ Advanced Theory of Statistics, Volume I: Distribution Theory. sixth ed. Edward
Amold, London
Zwillinger, D., Kokoska, S. (2000). Standard Probability and Statistical Tables and Formula. Chapman & Hall,
Boca Raton.
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Published
2018-01-08
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Research Article
