Probability Plot Correlation Coefficient Plot - Tukey-lambda PPCC Plot For Symmetric Distributions

Tukey-lambda PPCC Plot For Symmetric Distributions

The Tukey lambda PPCC plot, with shape parameter λ, is particularly useful for symmetric distributions. It indicates whether a distribution is short or long tailed and it can further indicate several common distributions. Specifically,

1. λ = −1: distribution is approximately Cauchy
2. λ = 0: distribution is exactly logistic
3. λ = 0.14: distribution is approximately normal
4. λ = 0.5: distribution is U-shaped
5. λ = 1: distribution is exactly uniform(−1, 1)

If the Tukey lambda PPCC plot gives a maximum value near 0.14, one can reasonably conclude that the normal distribution is a good model for the data. If the maximum value is less than 0.14, a long-tailed distribution such as the double exponential or logistic would be a better choice. If the maximum value is near −1, this implies the selection of very long-tailed distribution, such as the Cauchy. If the maximum value is greater than 0.14, this implies a short-tailed distribution such as the Beta or uniform.

The Tukey-lambda PPCC plot is used to suggest an appropriate distribution. One should follow-up with PPCC and probability plots of the appropriate alternatives.