Formalized by John Tukey, the Tukey lambda distribution is a continuous probability distribution defined in terms of its quantile function. It is typically used to identify an appropriate distribution (see the comments below) and not used in statistical models directly.
The Tukey lambda distribution has a shape parameter λ. As with other probability distributions, the Tukey lambda distribution can be transformed with a location parameter, μ, and a scale parameter, σ. Since the general form of probability functions can be expressed in terms of the standard distribution, the subsequent formula is given for the standard form of the function.
Read more about Tukey Lambda Distribution: Quantile Function, Moments, Comments
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