Adjusted generalized confidence intervals for the common coefficient of variation of several normal populations

Abstract This paper proposes the novel approaches to construct confidence intervals for the common coefficient of variation (CV) of several normal populations using the concepts of the adjusted generalized confidence interval (adjusted GCI) approach and the computational approach. The coverage probability and average length of the proposed approaches were evaluated by a Monte Carlo simulation and compared with that of the existing approaches; the generalized confidence interval (GCI) approach and the adjusted method of variance estimates recovery (adjusted MOVER) approach. The results showed that the coverage probability of the adjusted GCI approach is above the nominal confidence level of 0.95 and better than the other approaches when the sample case is small ( 6) for all sample sizes, except when the sample sizes are very small. However, the coverage probability of the computational approach provides much better confidence interval estimate than the other approaches when the sample case is large ( 10). The proposed approaches and the existing approaches are illustrated using three medical science data.

[1]  E. Gökpınar,et al.  A Computational Approach for Testing Equality of Coefficients of Variation in k Normal Populations , 2014 .

[2]  Suparat Niwitpong,et al.  Confidence Intervals for the Ratio of Coefficients of Variation of the Gamma Distributions , 2015, IUKM.

[3]  Suparat Niwitpong,et al.  Confidence Intervals for the Common Mean of Several Normal Populations , 2017, Robustness in Econometrics.

[4]  Ester Samuel-Cahn.  Combining unbiased estimators , 1994 .

[5]  Lili Tian,et al.  Inferences on the common coefficient of variation , 2005, Statistics in medicine.

[6]  A Donner,et al.  Construction of confidence limits about effect measures: A general approach , 2008, Statistics in medicine.

[7]  Ahmed N. Albatineh,et al.  A comparison of some confidence intervals for estimating the population coefficient of variation: a simulation study , 2012 .

[8]  G. E. Miller,et al.  An asymptotic test for the equality of coefficients of variation from k populations. , 1996, Statistics in medicine.

[9]  P. Meier,et al.  Variance of a Weighted Mean , 1953 .

[10]  Nabendu Pal,et al.  A Computational Approach to Statistical Inferences , 2007 .

[11]  Patarawan Sangnawakij,et al.  Confidence intervals for coefficients of variation in two-parameter exponential distributions , 2017, Commun. Stat. Simul. Comput..

[12]  Ren-Dao Ye,et al.  Inferences on the common mean of several inverse Gaussian populations , 2010, Comput. Stat. Data Anal..

[13]  K Krishnamoorthy,et al.  Inferences on the Common Mean of Several Normal Populations Based on the Generalized Variable Method , 2003, Biometrics.

[14]  Samaradasa Weerahandi,et al.  Generalized Confidence Intervals , 1993 .

[15]  Ali Akbar Jafari,et al.  Inferences on the Means of Two Log-Normal Distributions: A Computational Approach Test , 2015, Commun. Stat. Simul. Comput..

[16]  Mark G. Vangel,et al.  Confidence Intervals for a Normal Coefficient of Variation , 1996 .

[17]  Sa-aat Niwitpong,et al.  Confidence intervals for the weighted coefficients of variation of two-parameter exponential distributions , 2017 .

[18]  Allan Donner,et al.  Closed-form confidence intervals for functions of the normal mean and standard deviation , 2012, Statistical methods in medical research.

[19]  W K Fung,et al.  A simulation study comparing tests for the equality of coefficients of variation. , 1998, Statistics in medicine.

[20]  José Dias Curto,et al.  The coefficient of variation asymptotic distribution in the case of non-iid random variables , 2009 .

[21]  Rahim Mahmoudvand,et al.  Two new confidence intervals for the coefficient of variation in a normal distribution , 2009 .

[22]  Jb Jan Dijkstra,et al.  A multi sample test for the equality of coefficients of variation in normal populations , 1983 .

[23]  Tsung-Shan Tsou.  A Robust Score Test for Testing Several Coefficients of Variation with Unknown Underlying Distributions , 2009 .

[24]  Guang Yong Zou,et al.  Confidence interval estimation for lognormal data with application to health economics , 2009, Comput. Stat. Data Anal..