Generate a distribution from a link transform of another

Generates a new distribution by applying a link transformation to an existing distribution dist. If $X \sim \text{dist}$ and $h$ is the link function, this function returns the distribution of $Y = h^{-1}(X)$. The CDF $F_Y$, quantile function $Q_Y$, PDF $f_Y$, and RNG $R_Y$ of the transformed distribution are derived from the original distribution's functions $F_X$, $Q_X$, $f_X$, $R_X$ and the link function $h$ and its inverse $h^{-1}$ as follows: $$ F_Y(y) = F_X(h(y)) $$ $$ Q_Y(p) = h^{-1}(Q_X(p)) $$ $$ f_Y(y) = f_X(h(y)) \cdot |h'(y)| $$ $$ R_Y(n) = h^{-1}(R_X(n)) $$ where $h'(y)$ is the derivative of the link function. This function implements these transformations for the p, q, d, and r functions of the resulting dist_fns object.

Usage

transform(link, dist, ..., name = NULL)

Arguments

link: a link function (or name of a link function)
dist: distribution(s) as a name, function or a dist_fn S3 object
...: parameters for the underlying distribution if dist is a name or function.
name: a name for the link function

Value

a dist_fn or dist_fn_list holding the transformed distribution(s)

Unit tests





t = transform("log","norm")
ps = seq(0,1,0.1)
qs = 0:6
testthat::expect_equal(t$q(ps),qlnorm(ps))
testthat::expect_equal(t$p(qs),plnorm(qs))
testthat::expect_equal(t$d(qs),dlnorm(qs))

t2 = transform("log","norm", 0.4, 0.1)
testthat::expect_equal(t2$q(ps),qlnorm(ps,0.4,0.1))

Examples


n = as.dist_fns("norm",mean=0.5, sd=0.1)
t = transform("log",n)

plot(t)+ggplot2::geom_function(fun=~ dlnorm(.x, 0.5, 0.1), linetype="dashed")