positive values of the sample mean occur with negligible frequency, the probability distribution of the coefficient of variation for a sample of size of i.i.d. normal random variables has been shown by Hendricks and Robey to be where the symbol indicates that the summation is over only even values of , i.e., if is odd, sum over even values of and if is even, sum only over odd values of . This is useful, for instance, in the construction of hypothesis tests or confidence intervals. Statistical inference for the coefficient of variation in normally distributed data is often based on McKay's chi-square approximation for the coefficient of variation Alternative According to Liu (2012), Lehmann (1986). "also derived the sample distribution of CV in order to give an exact method for the construction of a confidence interval for CV;" it is based on a non-central t-distribution. Similar ratios Standardized moments are similar ratios, where is the kth moment about the mean, which are also dimensionless and scale invariant. The variance-to-mean ratio, , is another similar ratio, but is not dimensionless, and hence not scale invariant. See Normalization (statistics) for further ratios. In signal processing, particularly image processing, the reciprocal ratio (or its square) is referred to as the signal-to-noise ratio in general and signal-to-noise ratio (imaging) in particular. Other related ratios include: Efficiency, Standardized moment, Variance-to-mean ratio (or relative variance), Fano factor, (windowed VMR) See also Omega ratio Sampling (statistics) Sharpe ratio Variance function References External links cvequality: R package to test for significant differences between multiple coefficients of variation Statistical deviation and dispersion Statistical ratios Income inequality metrics