Bias and mean square error of the common coefficient of variation estimator in some different distributions
(2010) STAM01 20101Department of Statistics
 Abstract
 The validity of the estimator of the coefficient of variation (CV*) can be checked by investigating the bias and mean square error (Mse) of CV*. In this research we simulate the bias and Mse of CV* in normal, exponential, poisson and binomial distributions. We investigate the behavior of the bias and Mse of CV* as a function of sample size and distribution parameters in these distributions. We investigate how fast bias or Mse of CV* tends to zero. We check the effect of CV's on the bias and Mse of dCV in each distribution also. We show that, the bias of CV* in normal, poisson and binomial distributions could be positive or negative so in these distributions we have overestimated or underestimated CV. But in the exponential distribution we... (More)
 The validity of the estimator of the coefficient of variation (CV*) can be checked by investigating the bias and mean square error (Mse) of CV*. In this research we simulate the bias and Mse of CV* in normal, exponential, poisson and binomial distributions. We investigate the behavior of the bias and Mse of CV* as a function of sample size and distribution parameters in these distributions. We investigate how fast bias or Mse of CV* tends to zero. We check the effect of CV's on the bias and Mse of dCV in each distribution also. We show that, the bias of CV* in normal, poisson and binomial distributions could be positive or negative so in these distributions we have overestimated or underestimated CV. But in the exponential distribution we expect to have always negative Bias(CV*) so we expect to have underestimated CV. This biasedness in large sample sizes is not important because CV* is an asymptotically unbiased estimator. But in small samples CV* is not a good estimator. By increasing the sample size, Mse(CV*) tends to zero also. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/1719867
 author
 Keshavarz, Mahtab ^{LU}
 supervisor

 Björn Holmquist ^{LU}
 organization
 course
 STAM01 20101
 year
 2010
 type
 H1  Master's Degree (One Year)
 subject
 keywords
 Bias, Mean square error, Coefficient of variation, Poisson, Exponential, Normal, Binomial
 language
 English
 id
 1719867
 date added to LUP
 20101123 15:03:56
 date last changed
 20101123 15:03:56
@misc{1719867, abstract = {The validity of the estimator of the coefficient of variation (CV*) can be checked by investigating the bias and mean square error (Mse) of CV*. In this research we simulate the bias and Mse of CV* in normal, exponential, poisson and binomial distributions. We investigate the behavior of the bias and Mse of CV* as a function of sample size and distribution parameters in these distributions. We investigate how fast bias or Mse of CV* tends to zero. We check the effect of CV's on the bias and Mse of dCV in each distribution also. We show that, the bias of CV* in normal, poisson and binomial distributions could be positive or negative so in these distributions we have overestimated or underestimated CV. But in the exponential distribution we expect to have always negative Bias(CV*) so we expect to have underestimated CV. This biasedness in large sample sizes is not important because CV* is an asymptotically unbiased estimator. But in small samples CV* is not a good estimator. By increasing the sample size, Mse(CV*) tends to zero also.}, author = {Keshavarz, Mahtab}, keyword = {Bias,Mean square error,Coefficient of variation,Poisson,Exponential,Normal,Binomial}, language = {eng}, note = {Student Paper}, title = {Bias and mean square error of the common coefficient of variation estimator in some different distributions}, year = {2010}, }