dgammaPlusdexp: The PDF of the sum of gamma and negative exponential...

In forestgeo/ctfs: Tools for the Analysis of Forest Dynamics

Description

The PDF of the sum of gamma and negative exponential distribution. The shape and rate of the gamma are a and r; mean and sd are the mean and sd of the gamma. Lambda is the rate of the exponential.

This is only an appoximation based on the observation that the resulting distribution is very close to a gamma. So I simply work out a new gamma whose mean is the sum of the means of the initial gamma and exponential, and likewise for the new variance.

As long as gamma's rate > the exponential lambda, the distribution can be specified (using pgamma) as in dgammaMinusdexp. But if rate < lambda, this fails.

The gamma approximation fails if the sd is sufficiently higher than the mean, and the mean is low. Then the gamma is absurdly skewed, and the shape of the sum is dominated by the exponential at low z, nothing like a true gamma. It appears to work reasonably well as long as the mean >= sd, or even if mean>=0.5*sd.

Usage

dgammaPlusdexp(z, mean, sd, lambda, draws = 10000, div = 0.01,
  xrange = c(0, 25), xmax = 4, graphit = FALSE)

Arguments

z	A numeric vector.
mean, sd	The mean and sd of the gamma.
lambda	Rate of the exponential.
graphit	Logical; if TRUE adds plot output.

forestgeo/ctfs documentation built on May 3, 2019, 6:44 p.m.