Inference on the Common Coefficient of Variation When Populations Are Lognormal: a Simulation-based Approach

The coefficient of variation is often used as a measure of precision in medical and biological sciences. When it is known a priori that several independent normal populations have equal coefficient of variations, procedures for constructing confidence intervals for the common coefficient of variation based on the concept of generalized variables had been discussed by other researchers. This paper makes use of the same concept applied to lognormal populations. 1. The Lognormal Distribution A random variable is said to have the lognormal distribution if the logarithm of that variable has a normal distribution. A lognormal distribution results if the variable is the product of a large number of independent, identically-distributed variables in the same way that a normal distribution results if the variable is the sum of a large number of independent, identically distributed variables. A lognormal random variable X with parameters L L σ μ , has the probability density function