Estimating the Population Standard Deviation with Confidence Interval: A Simulation Study under Skewed and Symmetric Conditions

This paper investigates the performance of ten methods for constructing a confidence interval estimator for the population standard deviation by a simulation study. Since a theoretical comparison among the interval estimators is not possible, a simulation study has been conducted to compare the performance of the selected interval estimators. Data were randomly generated from several distributions with a range of sample sizes. Various evaluation criterions are considered for performance comparison. Two health related data have been analyzed to illustrate the application of the proposed confidence intervals. Based on simulation results, some intervals with the best performance have been recommended for practitioners.

[1]  E. Lehmann,et al.  Testing Statistical Hypothesis. , 1960 .

[2]  B. M. Golam Kibria,et al.  On some confidence intervals for estimating the mean of a skewed population , 2007 .

[3]  Andrija Tomovic,et al.  Nonparametric confidence intervals for population variance of one sample and the difference of variances of two samples , 2007, Comput. Stat. Data Anal..

[4]  J. Tukey.  A survey of sampling from contaminated distributions , 1960 .

[5]  B. M. Kibria,et al.  A simulation study on some confidence intervals for the population standard deviation , 2011 .

[6]  Douglas G. Bonett,et al.  Approximate confidence interval for standard deviation of nonnormal distributions , 2006, Comput. Stat. Data Anal..

[7]  Ayman Baklizi,et al.  One and two sample confidence intervals for estimating the mean of skewed populations: an empirical comparative study , 2009 .

[8]  Shipra Banik,et al.  Comparison of Some Parametric and Nonparametric Type One Sample Confidence Intervals for Estimating the Mean of a Positively Skewed Distribution , 2010, Commun. Stat. Simul. Comput..

[9]  Ricardo Fraiman,et al.  Testing statistical hypothesis on random trees , 2006 .

[10]  A. M. Gross.  Confidence Interval Robustness with Long-Tailed Symmetric Distributions , 1976 .

[11]  Sildenafil for Selective Serotonin Reuptake Inhibitor-Induced Erectile Dysfunction in Elderly Male Depressed Patients , 2003, Journal of sex & marital therapy.

[12]  N Mantel,et al.  Mantel-Haenszel analyses of litter-matched time-to-response data, with modifications for recovery of interlitter information. , 1977, Cancer research.

[13]  P. Rousseeuw,et al.  Alternatives to the Median Absolute Deviation , 1993 .