
The Davies distribution is a flexible family of distributions for
non-negative observations; it is particularly suitable for right-skewed
data. Hankin and Lee (2006) set out mathematical properties of the
Davies distribution and the Davies package is showcased
here. It is defined in terms of its quantile function


We may sample from this distribution using
rdavies():
params <- c(2,0.1,0.1)
rdavies(10,params)
#> [1] 1.761097 2.008966 1.767981 2.020754 1.674392 2.003635 1.485477 1.980971
#> [9] 2.253223 2.567022Moments are given by where
is the
beta function. In the package this is given by M(), which
is a convenience wraper for davies.moment(). Numerical
verification for the second (non-central) moment:
c(mean(rdavies(1e6,params)^2),M(2,params))
#> [1] 4.273915 4.275837The least-squares technique described in Hankin and Lee 2006 is not implemented, but the package implements a maximum-likelihood estimate:
x <- rdavies(80,params)
p_estimate <- maximum.likelihood(x)
p_true <- params
p_estimate
#> [1] 1.95306332 0.08418046 0.11483549
(bias <- p_estimate - p_true)
#> [1] -0.04693668 -0.01581954 0.01483549Robin K. S. Hankin and Alan Lee 2006. “A new family of non-negative distributions”. Aust. N. Z. J. Stat, 48(1):67-78