transform_pdf_with_function: Transform a probability density function with a function

In niknap/ScalingFunctions: Collection of functions for scaling of distributions

Description

The PDF of an independent variable x is transformed into the PDF of a dependent variable y based on their relationship y=f(x). Optionally, uncertainty in the x-y-relationship can be incorporated by providing a function that describes the SD of y (assuming Gaussian uncertainty in y direction) either as a function of x or as a function of predicted y.

Usage

transform_pdf_with_function(
  x.vec,
  x.d.vec,
  xy.func = function(x) {     1 * x },
  xsdy.func = NA,
  ysdy.func = NA,
  n.steps = 1000
)

Arguments

x.vec	Vector of values of the independent variable
x.d.vec	Vector of probability densities of each x value
xy.func	Function which relates x to y; Default is y=x
xsdy.func	Function which relates x to SD of y; Default is NA, i.e., no uncertainty
ysdy.func	Function which relates y (i.e., f(x)) to SD of y; Default is NA, i.e., no uncertainty
n.steps	Number of discrete steps between which the PDF is approximated via linear interpolation during the transformation

Value

List containing 1) y values for each input x value, 2) x values for all n steps, 3) y values for all n steps (of x; in the case with uncertainty included the range of y steps is wider than the range of f(x); it ranges from min(f(x)) minus the 99 prediction interval of y), 4) PDF values for all x steps, 5) PDF values for all y steps, as well as the functions for the PDFs of 6) x and 7) y as approxfun functions

Author(s)

Nikolai Knapp, [e-mail]

Examples

# Simulate data from a lognormal distribution
my.x.vec <- rlnorm(200, 3.2, 0.3)
my.x.d.vec <- dlnorm(my.x.vec, 3.2, 0.3)
hist(my.x.vec, breaks=30, freq=F)
curve(dlnorm(x, 3.2, 0.3), add=T, col="blue")
points(my.x.d.vec ~ my.x.vec, col="red")
# Define a power law relationship y=0.1*x^1.8
my.xy.func <- function(x){0.1*x^1.8}
# Apply the transformation
transform.list <- transform_pdf_with_function(x.vec=my.x.vec,
x.d.vec=my.x.d.vec, xy.func=my.xy.func, n.steps=1000)
plot(transform.list$y ~ my.x.vec)
plot(transform.list$x.steps.pdf ~ transform.list$x.steps)
plot(transform.list$y.steps.pdf ~ transform.list$y.steps)
hist(transform.list$y, breaks=30, freq=F)
new.y.steps.vec <- 1:150
new.y.pdf.vec <- transform.list$y.pdf.fun(new.y.steps.vec)
lines(new.y.pdf.vec ~ new.y.steps.vec, col="blue")

niknap/ScalingFunctions documentation built on May 22, 2021, 6:43 a.m.