== Percentiles of exponential data and use in outlier detection ==

If the data follows an exponential distribution (test this by using Kolmogorov-Smirnov test in SPSS and choosing the exponential option). Then

- (Mean score) (LN(1- PERC/100 ))  gives the threshold of the PERC% percentile.

This follows from 

P(X < x) = 1 – EXP(-R*x) 
where rate, R, is estimated from the sample data by 1/mean. 

These percentiles may be [[http://www.statsoft.com/textbook/glose.html|used]] to classify a  data point as extreme since outliers are defined as either 

> 75th percentile + 1.5 * (75th perc - 25th perc)

or 

< 25th percentile - 1.5 * (75th perc - 25th perc)