Some Improved Estimators of Co-efficient of Variation from Bi-variate normal distribution: A Monte Carlo Comparison

Archana V, Aruna Rao K

Abstract


Co-efficient of variation is a unitless measure of dispersion and is very frequently used in scientific investigations. This has motivated several researchers to propose estimators and tests concerning the co-efficient of variation of normal distribution(s). While proposing a class of estimators for the co-efficient of variation of a finite population, Tripathi et al., (2002) suggested that the estimator of co-efficient of variation of a finite population can also be used as an estimator of C.V for any distribution when the sampling design is SRSWR. This has motivated us to propose 28 estimators of finite population co-efficient of variation as estimators of co-efficient of variation of one component of a bivariate normal distribution when prior information is available regarding the second component. Cramer Rao type lower bound is derived to the mean square error of these estimators. Extensive simulation is carried out to compare these estimators. The results indicate that out of these 28 estimators, eight estimators have larger relative efficiency compared to the sample co-efficient of variation. The asymptotic mean square errors of the best estimators are derived to the order of  for the benefit of users of co-efficient of variation.

Keywords


Co-efficient of variation, Finite population, SRSWR, Bivariate normal distribution, Cramer Rao lower bound.

Full Text:

PDF


DOI: http://dx.doi.org/10.18187/pjsor.v10i1.433

Refbacks

  • There are currently no refbacks.




Copyright (c)

Title

Some Improved Estimators of Co-efficient of Variation from Bi-variate normal distribution: A Monte Carlo Comparison

Keywords

Co-efficient of variation, Finite population, SRSWR, Bivariate normal distribution, Cramer Rao lower bound.

Description

Co-efficient of variation is a unitless measure of dispersion and is very frequently used in scientific investigations. This has motivated several researchers to propose estimators and tests concerning the co-efficient of variation of normal distribution(s). While proposing a class of estimators for the co-efficient of variation of a finite population, Tripathi et al., (2002) suggested that the estimator of co-efficient of variation of a finite population can also be used as an estimator of C.V for any distribution when the sampling design is SRSWR. This has motivated us to propose 28 estimators of finite population co-efficient of variation as estimators of co-efficient of variation of one component of a bivariate normal distribution when prior information is available regarding the second component. Cramer Rao type lower bound is derived to the mean square error of these estimators. Extensive simulation is carried out to compare these estimators. The results indicate that out of these 28 estimators, eight estimators have larger relative efficiency compared to the sample co-efficient of variation. The asymptotic mean square errors of the best estimators are derived to the order of  for the benefit of users of co-efficient of variation.


Date

2014-05-15

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol. 10 No. 1, 2014



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810