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authorGuillaume Horel <guillaume.horel@gmail.com>2017-12-18 13:11:07 -0500
committerGuillaume Horel <guillaume.horel@gmail.com>2017-12-18 13:11:07 -0500
commit95adce57909cb778c274ab328ae59c23c8820baa (patch)
tree8a7e078bfbe38fb94bfb90babd6fdeabcbccbd8c /man
parent72549cc50059c32291a33c8933ee4a767438df61 (diff)
downloadlossdistrib-95adce57909cb778c274ab328ae59c23c8820baa.tar.gz
update docs
Diffstat (limited to 'man')
-rw-r--r--man/GHquad.Rd3
-rw-r--r--man/convolve.Rd20
-rw-r--r--man/lossdist.joint.Rd5
-rw-r--r--man/lossdistrib.Rd6
-rw-r--r--man/lossdistrib.fft.Rd11
-rw-r--r--man/lossdistrib2.Rd4
-rw-r--r--man/lossdistrib2.truncated.Rd3
-rw-r--r--man/recovdist.Rd3
8 files changed, 35 insertions, 20 deletions
diff --git a/man/GHquad.Rd b/man/GHquad.Rd
index 1d62281..3a9dfab 100644
--- a/man/GHquad.Rd
+++ b/man/GHquad.Rd
@@ -1,4 +1,4 @@
-% Generated by roxygen2 (4.1.1): do not edit by hand
+% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/distrib.R
\name{GHquad}
\alias{GHquad}
@@ -22,4 +22,3 @@ Gaussian distribution.
if f is a function, then \eqn{\sum_{i=1}^n f(Z_i)w_i \approx
\frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty f(x)e^{-\frac{x^2}{2}}\,dx}.
}
-
diff --git a/man/convolve.Rd b/man/convolve.Rd
new file mode 100644
index 0000000..b2cbbc4
--- /dev/null
+++ b/man/convolve.Rd
@@ -0,0 +1,20 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/distrib.R
+\name{convolve}
+\alias{convolve}
+\title{Convolution of two discrete probability distributions}
+\usage{
+convolve(dist1, dist2)
+}
+\arguments{
+\item{dist1}{Numeric vector of probabilities}
+
+\item{dist2}{Numeric vector of probabilities}
+}
+\value{
+Convolution of the two vectors
+}
+\description{
+This is the probability of the sum of the two random variables
+assuming they are independent.
+}
diff --git a/man/lossdist.joint.Rd b/man/lossdist.joint.Rd
index 1cf7a71..d803252 100644
--- a/man/lossdist.joint.Rd
+++ b/man/lossdist.joint.Rd
@@ -1,4 +1,4 @@
-% Generated by roxygen2 (4.1.1): do not edit by hand
+% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/distrib.R
\name{lossdist.joint}
\alias{lossdist.joint}
@@ -16,7 +16,7 @@ lossdist.joint(p, w, S, N, defaultflag = FALSE)
\item{N}{Integer, number of ticks in the grid}
-\item{defaultflab}{Logical, whether to return the loss or default distribution}
+\item{defaultflag}{Logical, whether to return the loss or default distribution}
}
\value{
q Matrix of joint loss, recovery probability distribution
@@ -27,4 +27,3 @@ rowSums(q) is the loss distribution marginal
For high severities, M can become bigger than N, and there is
some probability mass escaping.
}
-
diff --git a/man/lossdistrib.Rd b/man/lossdistrib.Rd
index 7af12d4..bc68ce4 100644
--- a/man/lossdistrib.Rd
+++ b/man/lossdistrib.Rd
@@ -1,4 +1,4 @@
-% Generated by roxygen2 (4.1.1): do not edit by hand
+% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/distrib.R
\name{lossdistrib}
\alias{lossdistrib}
@@ -14,11 +14,11 @@ A vector q such that \eqn{q_k=\Pr(S=k)}
}
\description{
\code{lossdistrib} computes the probability distribution of a sum
-of independent Bernouilli variables with unequal probabilities.
+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 simple recursive
algorithm of Andersen, Sidenius and Basu
}
-
diff --git a/man/lossdistrib.fft.Rd b/man/lossdistrib.fft.Rd
index c4eae10..3843bdc 100644
--- a/man/lossdistrib.fft.Rd
+++ b/man/lossdistrib.fft.Rd
@@ -1,4 +1,4 @@
-% Generated by roxygen2 (4.1.1): do not edit by hand
+% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/distrib.R
\name{lossdistrib.fft}
\alias{lossdistrib.fft}
@@ -14,13 +14,12 @@ 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.
+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 omplexity is of order \eqn{O(n m) + O(m\log(m))}
-where \eqn{m} is the size of the grid and \eqn{n}, the number of probabilities.
-It is slower than the recursive algorithm in practice.
+This uses the FFT, thus complexity is of order \eqn{O(n \log(n))},
+compared to \eqn{O(n^2)} for the recursive algorithm.
}
-
diff --git a/man/lossdistrib2.Rd b/man/lossdistrib2.Rd
index 4d1dd9c..915deab 100644
--- a/man/lossdistrib2.Rd
+++ b/man/lossdistrib2.Rd
@@ -1,4 +1,4 @@
-% Generated by roxygen2 (4.1.1): do not edit by hand
+% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/distrib.R
\name{lossdistrib2}
\alias{lossdistrib2}
@@ -31,5 +31,5 @@ We compute the probability distribution of \eqn{L = \sum_{i=1}^n w_i S_i X_i}
where \eqn{X_i} is Bernouilli(\eqn{p_i}). If \code{defaultflag} is TRUE, we
compute the distribution of \eqn{D = \sum_{i=1}^n w_i X_i} instead.
This a recursive algorithm with first order correction for discretization.
+Complexity is of ordier \eqn{O(nN)}, so linear for a given grid size.
}
-
diff --git a/man/lossdistrib2.truncated.Rd b/man/lossdistrib2.truncated.Rd
index 9c4854e..7e41c48 100644
--- a/man/lossdistrib2.truncated.Rd
+++ b/man/lossdistrib2.truncated.Rd
@@ -1,4 +1,4 @@
-% Generated by roxygen2 (4.1.1): do not edit by hand
+% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/distrib.R
\name{lossdistrib2.truncated}
\alias{lossdistrib2.truncated}
@@ -30,4 +30,3 @@ This is actually slower than \code{lossdistrib2}, but in C this is
twice as fast. For high severities, M can become bigger than the cutoff, and
there is some probability mass escaping.
}
-
diff --git a/man/recovdist.Rd b/man/recovdist.Rd
index c6da216..16faba2 100644
--- a/man/recovdist.Rd
+++ b/man/recovdist.Rd
@@ -1,4 +1,4 @@
-% Generated by roxygen2 (4.1.1): do not edit by hand
+% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/distrib.R
\name{recovdist}
\alias{recovdist}
@@ -34,4 +34,3 @@ as the pair of values
\eqn{\left\lceil\frac{v}{lu}\right\rceil} so that \eqn{X_i} has
four non zero values.
}
-