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Except for small values of the gamma shape parameter, the best choice of Box-Cox transformation will be close to the cube root (the Wilson-Hilferty transformation). …

(This is the Wilson-Hilferty transformation.) Finally, you can simply accumulate a running total of squared residuals, as shown in the bottom right corner. …

$\ddagger$ you might then wonder -- since the exponential is also a gamma distribution, why would we not use cube roots (power $1/3$ rather than $1/3.6$), as the Wilson-Hilferty transformation would suggest … The answer to that is for gamma with large shape parameter, the Wilson-Hilferty is indeed excellent at achieving near-symmetry and approximate normality, but with small shape parameters it's too weak to …

Also true that If $X \sim \chi^{2}(k)$ then $\sqrt[3]{X / k}$ is approximately normally distributed with mean $1-\frac{2}{9 k}$ and variance $\frac{2}{9 k} \cdot[16]$ This is known as the Wilson-Hilferty …

For considerably smaller degrees of freedom, the Wilson-Hilferty transformation could be used -- it works well down to only a few degrees of freedom -- but the tables should cover that. …

r_D(i) \propto t(y_i/\hat{\mu}_i)$), it's rather similar to (a linear transformation of) a cube root: The cube root is an approximate symmetrizing transformation for the gamma, sometimes called the Wilson-Hilferty …

Since the square of a Rayleigh random variable is a special case of the gamma, the Wilson-Hilferty transformation (cube root in the case of the gamma) should produce a good approximation of normality. … So even though both references seem to be about chi-square distributions, their conclusions apply to gamma distributions more generally) Wilson, E. B., and Hilferty, M. …

If you don't know the d.f. for these variables, the cube root should be approximately normal (the Wilson-Hilferty transformation), so a QQ plot of the cube roots against normal quantiles could be effective …

approximately $\frac{3 \alpha - 0.8}{3 \alpha + 0.2}$ times the mean (as long as $\alpha$ is not too small, say no less than somewhere around 1-2, it works okay): Another way to approach the median is via the Wilson-Hilferty …

. -- ** As Nick Cox mentions below, the usual transformation to approximate normality for the gamma, the Wilson-Hilferty transformation, is weaker than the log - it's a cube root transformation. …

Certainly - you can use a Wilson-Hilferty transformation. Specifically, the cube root of a gamma (or chi-square) random variable is approximately normal. …

To avoid (or at least greatly reduce) the trial and error (not that it takes more than a few moments), we can make use of an approximation that will get us very close to the right answer - the Wilson-Hilferty …

.$$ The Wilson-Hilferty approximation to $\chi^2$ (or, equivalently, a $\Gamma$ distribution)--which has "remarkable accuracy"--can be applied to $F$, which itself is a ratio of $\chi^2$ distributions. …

For example, for an approximate test, one could perform a Wilson-Hilferty type approach (i.e. a cube root transformation) and test normality, though there are other approaches for "gamma-probability" type …