Power transforms for the Weibull and the K‐distribution

Abstract

The Weibull and K-distributions are shown to be very similar over a range of shape parameters ( 1 / 2 ≤ ν < ∞ for the K-distribution), and the mapping k = ( 2 ν + 0.04 ) / ( ν + 0.55 ) gives a means of converting between the shape parameter ν of the K-distribution to the shape parameter k for the Weibull distribution. The Weibull distribution is very like a truncated normal distribution when k = 3.678 , so that a power transform to the power k / 3.678 can transform any Weibull distribution to a good approximation of a truncated normal distribution. The transformation y i = − ( log ⁡ ( x m ) − log ⁡ ( x i ) ) 0.272 was found to transform K-distributed samples to the normal distribution, where x m is the maximum value after clipping at the 0.9995 quantile level.