gamma_tools.RdThese functions permit to use alternate parametrisations for Gamma
distributions, from 'shape and scale' to 'mean (mu) and coefficient of
variation (cv), and back. gamma_shapescale2mucv does the first
conversion, while gamma_mucv2shapescale does the second. The function
gamma_log_likelihood is a shortcut for computing Gamma log-likelihood
with the alternative parametrisation (mean, cv). See 'details' for a guide of
which parametrisation to use.
gamma_shapescale2mucv(shape, scale) gamma_mucv2shapescale(mu, cv) gamma_log_likelihood(x, mu, cv, discrete = TRUE, interval = 1, w = 0, anchor = 0.5)
| shape | The shape parameter of the Gamma distribution. |
|---|---|
| scale | The scale parameter of the Gamma distribution. |
| mu | The mean of the Gamma distribution. |
| cv | The coefficient of variation of the Gamma distribution, i.e. the standard deviation divided by the mean. |
| x | A vector of data treated as observations drawn from a Gamma distribution, for which the likelihood is to be computed. |
| discrete | A logical indicating if the distribution should be discretised; TRUE by default. |
| interval | The interval used for discretisation; see
|
| w | The centering of the interval used for discretisation, defaulting to
0; see |
| anchor | The anchor used for discretisation, i.e. starting point of the
discretisation process; defaults to 0; see |
A named list containing 'shape' and 'scale', or mean ('mean') and coefficient of variation ('cv').
The gamma distribution is described in ?dgamma is
parametrised using shape and scale (or rate). However, these parameters are
naturally correlated, which make them poor choices whenever trying to fit
data to a Gamma distribution. Their interpretation is also less clear than
the traditional mean and variance. When fitting the data, or reporting
results, it is best to use the alternative parametrisation using the mean
(mu) and the coefficient of variation (cv), i.e. the standard
deviation divided by the mean.
## set up some parameters mu <- 10 cv <- 1 ## transform into shape scale tmp <- gamma_mucv2shapescale (mu, cv) shape <- tmp$shape scale <- tmp$scale ## recover original parameters when applying the revert function gamma_shapescale2mucv(shape, scale) # compare with mu, cv#> $mu #> [1] 10 #> #> $cv #> [1] 1 #>## empirical validation: ## check mean / cv of a sample derived using rgamma with ## shape and scale computed from mu and cv gamma_sample <- rgamma(n = 10000, shape = shape, scale = scale) mean(gamma_sample) # compare to mu#> [1] 9.835163#> [1] 1.002399