megamma: Find the maximum-entropy value of the gamma (shift) parameter...
In sethmcg/climod: Bias correction and other tools for climate model output

Description Usage Arguments Details Value Examples

The Box-Cox transform is often used to normalize precipitation data. In practice, the best value of the lambda parameter (the exponent) is usually zero, but the best value of the gamma (shift) parameter is unpredictable. This function finds the best value of gamma by maximizing the entropy of the PDF of the transformed data. This works because (of all distribution on the real line with a given variance) the normal distribution has the maximum possible entropy, which is calculated as minus the integral of p log p. Entropy can therefore be used as a measure of how close a distribution is to normal.

1	megamma(x)

`x`	A vector of values

This function calculates entropy by estimating the PDF of the (transformed) data using KernSmooth::bkde and summing -p log p of the result. Note that because bkde uses a fixed number of bins and uses the variance of the data to scale the gaussian kernel to fit the range of the data, there is no need to explicitly rescale the data to have unit variance or to divide the sum by the bin width; these factors have already been taken into account by the kernel density estimation. This function uses stats::optimize to find the maximum-entropy value of gamma. A more general optimization can be done over both gamma and lambda using optim instead, but it is much, much slower, and tests on real data showed that the lambda parameter strongly tends towards zero in all cases except when the number of data points is very small.

The maximum entropy value of gamma

library(KernSmooth)
set.seed(222)
x <- rgamma(1000, shape=3, rate=2)

plot(bkde(x))

g <- megamma(x)

y <- log(x + g)

plot(bkde(y))
lines(bkde(log(x)), col="red")
lines(bkde(log(x+2*g)), col="blue")