::Free Statistics and Forecasting Software::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online software (calculator) computes the Tukey lambda PPCC Plot that is used to identify whether a distribution is short or long tailed (only applies to symmetric distributions). In addition it can indicate several common distributions. Specifically,

lambda = -1: distribution is approximately Cauchy lambda = 0: distribution is exactly logistic lambda = 0.14: distribution is approximately normal lambda = 0.5: distribution is U-shaped lambda = 1: distribution is exactly uniform

If the Tukey Lambda PPCC plot gives a maximum value near 0.14, we 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.

source: NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/, 2006-10-03.

Enter (or paste) your data delimited by hard returns.

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Source code of R module

gp <- function(lambda, p) { (p^lambda-(1-p)^lambda)/lambda } sortx <- sort(x) c <- array(NA,dim=c(201)) for (i in 1:201) { if (i != 101) c[i] <- cor(gp(ppoints(x), lambda=(i-101)/100),sortx) } bitmap(file="test1.png") plot((-100:100)/100,c[1:201],xlab="lambda",ylab="correlation",main="PPCC Plot - Tukey lambda") grid() dev.off() load(file="createtable") a<-table.start() a<-table.row.start(a) a<-table.element(a,"Tukey Lambda - Key Values",2,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Distribution (lambda)",1,TRUE) a<-table.element(a,"Correlation",1,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Approx. Cauchy (lambda=-1)",header=TRUE) a<-table.element(a,c[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Exact Logistic (lambda=0)",header=TRUE) a<-table.element(a,(c[100]+c[102])/2) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Approx. Normal (lambda=0.14)",header=TRUE) a<-table.element(a,c[115]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"U-shaped (lambda=0.5)",header=TRUE) a<-table.element(a,c[151]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Exactly Uniform (lambda=1)",header=TRUE) a<-table.element(a,c[201]) a<-table.row.end(a) a<-table.end(a) table.save(a,file="mytable.tab")

Cite this software as:

Wessa P., (2021), Tukey lambda PPCC Plot (v1.0.4) in Free Statistics Software (v1.2.1), Office for Research Development and Education, URL http://www.wessa.net/rwasp_tukeylambda.wasp/

The R code is based on :

NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/, 2006-10-03.

To cite Wessa.net in publications use:
Wessa, P. (2025), Free Statistics Software, Office for Research Development and Education,
version 1.2.1, URL https://www.wessa.net/

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Software Version : 1.2.1
Algorithms & Software : Patrick Wessa, PhD
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