dirwin.hall: Irwin-Hall density
In unifed: The Unifed Distribution

Description Usage Arguments Details Examples

Irwin-Hall density

1	dirwin.hall(x, n, log = FALSE)

`x`	A number between 0 and `n`.
`n`	Number of uniform distributions in the unit interval to sum.
`log`	If it evaluates to `TRUE` it returns the log of the density instead of the density.

Gives the density of the Irwin-Hall distribution. It is the density of the sum of n uniform distributions on the interval (0,1).

1 __ |_y_| k / n \ n - 1 h(y;n) = --------- \ ( - 1) | | (y - k) (n - 1)! /__ k = 0 \ k /

where x \in [0,1] and n is a positive integer.

This function is not numerically stable. The examples have some cases of this.

dirwin.hall(2,5)

# Numerically unstable example
# Run the following one after the other
# See how it goes from positive to negative (which means overflowing )
dirwin.hall(35,50)
dirwin.hall(36,50)
dirwin.hall(37,50)
dirwin.hall(38,50)