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Bias and mean square error of the common coefficient of variation estimator in some different distributions

Keshavarz, Mahtab LU (2010) STAM01 20101
Department 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)
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author
Keshavarz, Mahtab LU
supervisor
organization
course
STAM01 20101
year
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
2010-11-23 15:03:56
date last changed
2010-11-23 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},
}