In this paper we are studying the coefficient of variation of a continuous random variable and some other concepts, like its inverse (symbol ICv or Cv-1) or its square inverse (symbol ICv^2=q), e.tc. Basically, we try to develop the asymptotic sampling distribution of the inverse coefficient of variation ICV=CV^(-1). This distribution is used to infer statistically significant results for the coefficient of variation or the inverse coefficient of variation of a random variable X without making a hypothesis for the population distribution of the variable X. We are focused on same cases of random variables following specific distributions, dealing with the related parameters of those distributions. E.g. Our attention is mostly focused on extracting results (confidence intervals, hypothesis testing), for parameters of Gamma distribution, Weibull distribution e.tc. Some examples are given in order to illustrate the particulars of the behavior of the ICv and ICv^2, related with the above-mentioned concepts: Confidence intervals, testing hypothesis, etc. for the random variable X and so on.