Srivastava (1974, 1980) and Chaubey and Dwivedi (1982) investigated some es-
timators of mean of a normal population utilizing an estimate of the coefficient
of variation. However, the normal model may not hold for positive or positively
skewed data, hence an alternative model may have to be employed. This paper
uses the inverse Gaussian model for such data and extends the results of Chaubey
and Dwivedi (1982) for the normal population to similar analysis for the inverse
Gaussian population. It is found that the new estimator may result in large gains
in efficiency over the sample mean for large values of the coefficient of variation.