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Results for wilson-hilferty
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7 votes

Estimate Box-Cox Transformation Lambda Using Skewness and Kurtosis

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). …
Glen_b's user avatar
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1 vote

Goodness of fit measurement in Python

(This is the Wilson-Hilferty transformation.) Finally, you can simply accumulate a running total of squared residuals, as shown in the bottom right corner. …
COOLSerdash's user avatar
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11 votes
Accepted

What is a good technique for testing whether data is Rayleigh distributed?

$\ddagger$ 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 …
Glen_b's user avatar
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2 votes
1 answer
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Is true that the sampling distribution of $\ln \left(\chi^{2}\right)$ converges to normality...

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
17 votes

What do you do if your degrees of freedom goes past the end of your tables?

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. …
Glen_b's user avatar
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5 votes

Why do qq-plots appear to show normal residuals from a GAM when the underlying distribution ...

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
Glen_b's user avatar
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12 votes
Accepted

Is it possible to convert a Rayleigh distribution into a Gaussian distribution?

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. …
Glen_b's user avatar
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6 votes

Estimating the distribution of a variable

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 …
Glen_b's user avatar
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5 votes

Prior Gamma distribution: Select appropriate alpha given beta and median

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
Glen_b's user avatar
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38 votes

Which has the heavier tail, lognormal or gamma?

. -- ** 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. …
Community's user avatar
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3 votes
Accepted

Picking the smallest number of i. i. d. exponential variables to satisfy a condition

Certainly - you can use a Wilson-Hilferty transformation. Specifically, the cube root of a gamma (or chi-square) random variable is approximately normal. …
Glen_b's user avatar
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2 votes
Accepted

Calculating a confidence interval and required sample size for the mean time to next event o...

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
Glen_b's user avatar
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6 votes
Accepted

Approximation for Beta distribution when alpha is less than 10

.$$ 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. …
whuber's user avatar
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2 votes
Accepted

Is there a good specification error test against a generalized alternative?

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 …
Glen_b's user avatar
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