function. A first order Taylor approximation for is: From the equation above, we obtain: and This approximation method is called delta method. Consider now a random variable such that and . Notice the relation between the variance and the mean, which implies, for example, heteroscedasticity in a linear model. Therefore, the goal is to find a function such that has a variance independent (at least approximately) of its expectation. Imposing the condition , this equality implies the differential equation: This ordinary differential equation has, by separation of variables, the following solution: This last expression appeared for the first time in a M. S. Bartlett paper. References Statistical data transformation