% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/distrib.R
\name{lossdistrib.fft}
\alias{lossdistrib.fft}
\title{Loss distribution of a portfolio}
\usage{
lossdistrib.fft(p)
}
\arguments{
\item{p}{Numeric vector, the vector of success probabilities}
}
\value{
A vector such that \eqn{q_k=\Pr(S=k)}
}
\description{
\code{lossdistrib.fft} computes the probability distribution of a sum
of independent Bernouilli variables with unequal probabilities
(also called the Poisson-Binomial distribution).
}
\details{
We compute the probability distribution of \eqn{S = \sum_{i=1}^n X_i}
where \eqn{X_i} is Bernouilli(\eqn{p_i}).
This uses the FFT, thus complexity is of order \eqn{O(n \log(n))},
compared to \eqn{O(n^2)} for the recursive algorithm.
}