Estimation of coefficient of variation using linear moments and calibration approach for nonsensitive and sensitive variables

Abstract

AbstractAssessment of coefficient of variation (CV) is of major importance in numerous examinations. However, the appearance of extreme observations raises concerns about the outcomes of CV estimates based on conventional moments. So, motivated by some recent developments in finite sampling theory, we propose some new estimators of CV based on the properties of linear moments (L‐moments and Trimmed L‐moments), which are highly robust whenever outliers or extreme observations appear in a dataset. The proposed estimators are initially established on the premise that the variable of interest is nonsensitive which deals with the subjects that do not embarrass respondents when asked about them explicitly. These estimators are also applied to situations where the variable of interest is associated with sensitive issues that cause measurement errors resulting from nonresponse or unreliable reporting where such issues can be mitigated by increasing respondent participation by scrambled response models which obscure the true value of the sensitive variable. Four models are considered for this article: additive, multiplicative, mixed, and combined additive‐multiplicative models. Finally, in both nonsensitive and sensitive settings, real‐life data sets are employed to undertake simulation‐based analysis. In all cases, the proposed estimators considerably increased efficiency.