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 used to classify a data point as extreme since outliers are defined as either
> 75th percentile + 1.5 * (75th perc - 25th perc)
< 25th percentile - 1.5 * (75th perc - 25th perc)