Computing percentile thresholds for exponential data
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*score) where rate, R, is estimated from the sample data by 1/mean.