paretoconv: paretoconv.
In mpadge/paretoconv: Calculates the N-Fold Convolution of Two Pareto Distributions

Description Usage Arguments Value Note Author(s) Examples

Convolutes multiple Pareto distributions following

For integer shape parameters: 'The Distribution of Sums of Certain I.I.D. Pareto Variates' by Colin Ramsay (Communications in Statistics - Theory and Methods 35:395-405, 2006);
For non-integer shape parameters: 'The Distribution of Sums of I.I.D. Pareto Random Variables with Arbitrary Shape Parameter' by Colin Ramsay (Communications in Statistics - Theory and Methods 37:2177-2184, 2008).

1 2	paretoconv(x, a, n, x0 = 1, cdf = FALSE, asymp = TRUE, quiet = TRUE)

`x`	value of independent variable (may be a vector)
`a`	The primary shape parameter of the Pareto distribution (single value only)
`n`	Number of convolutions (single value only)
`x0`	Lower cut-off point of classical heavy-tailed distribution (generally obtained emprically with the poweRlaw package).
`cdf`	If TRUE, returns the cumulative distribution function, otherwise returns the probability density function.
`asymp`	If TRUE and `x` is a vector of 10 or more elements, asymptotic convergence is checked for large `x`, with values beyond convergence replaced with directly power-law values
`quiet`	If FALSE, issue progress messages

Value for the CDF or PDF from the convolution of two Pareto distributions of shape a at the value x.

The Pareto distribution may be defined as f(x)=(a/b)(b/x)^(a-1), where a and b are the primary and secondary shape parameters, respectively. It presumed here without loss of generality that b=1 and thus f(x)=a x^(1-a). Convolution of multiple distritions (that is, n>0) are NOT normalised, so CDFs to not sum to unity, and PDFs do not integrate to unity.

Mark Padgham