https://github.com/mpadge/paretoconv

R package for convolution of Pareto distributions
https://github.com/mpadge/paretoconv

convolution pareto-distributions powerlaw

Last synced: 3 days ago
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R package for convolution of Pareto distributions

• Host: GitHub
• URL: https://github.com/mpadge/paretoconv
• Owner: mpadge
• License: other
• Created: 2016-11-25T11:00:27.000Z (almost 8 years ago)
• Default Branch: master
• Last Pushed: 2020-03-04T14:33:03.000Z (over 4 years ago)
• Last Synced: 2024-10-11T18:46:42.394Z (27 days ago)
• Topics: convolution, pareto-distributions, powerlaw
• Language: R
• Size: 297 KB
• Stars: 2
• Watchers: 3
• Forks: 0
• Open Issues: 2
• Metadata Files:
  • Readme: README.Rmd
  • License: LICENSE

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README

        

```{r, echo = FALSE}

knitr::opts_chunk$set(

  collapse = TRUE,

  comment = "#>",

  fig.path = "README-"

)

```

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[![CRAN_Status_Badge](http://www.r-pkg.org/badges/version/paretoconv)](http://cran.r-project.org/web/packages/paretoconv) 

# paretoconv

An `R` package to calculate the $n$-fold convolution of Pareto distributions.

*f(x)=a x1-a*,

for *x>0*, *a>1* using the techniques devised by Colin Ramsay in

1. 'The Distribution of Sums of Certain I.I.D.  Pareto Variates' (*Communications

   in Statistics - Theory and Methods* **35**:395-405, 2006); and

2. 'The Distribution of Sums of I.I.D. Pareto Random Variables with Arbitrary

   Shape Parameter' (*Communications in Statistics - Theory and Methods*

   **37**:2177-2184, 2008).

The package contains only one function:

```

paretoconv (x, a, n, cdf=FALSE)

```

where `n` specifies the number of convolutions. Both this and `a` must be

single-valued, while `x` can be a vector. `cdf` generates the cumulative

distribution function, otherwise the probability density function is returned.

-----

### Installation

`paretoconv` is not (yet) on CRAN, and can be installed with any of the

following options:

```{r git-install, eval = FALSE}

remotes::install_git("https://git.sr.ht/~mpadge/paretoconv")

remotes::install_bitbucket("mpadge/paretoconv")

remotes::install_gitlab("mpadge/paretoconv")

remotes::install_github("mpadge/paretoconv")

```

```{r install, echo=FALSE, message=FALSE}

devtools::load_all ('.')

#devtools::load_all ('.', recompile=TRUE)

#devtools::document ('.')

#devtools::check ('.')

#goodpractice::gp ('.')

#testthat::test_package ('paretoconv')

```

```{r echo=FALSE, message=FALSE, warning=FALSE, error=FALSE}

options(width=120)

```

-----

## Example

Solid lines in the figure below are a reproduction of Ramsay's (2006) Figure 2

of probability density functions for the first 5 convolutions of the Pareto pdf

with shape parameter of *a=5*. Dashed lines are analogous values for the

non-integer value of *a=4.5*.

```{r example, eval=FALSE}

x <- 1:50 / 10

n <- 1:5

yint <- lapply (n, function (i) paretoconv (x=x, a=5, n=i))

ynon <- lapply (n, function (i) paretoconv (x=x, a=4.5, n=i))

cols <- rainbow (length (n))

plot (NULL, NULL, xlim=range (x), ylim=range (yint, na.rm=TRUE), xlab='x', ylab='p')

for (i in n) {

    lines (x, yint [[i]], col=cols [i])

    lines (x, ynon [[i]], col=cols [i], lty=2)

}

legend ('topright', lwd=1, col=cols, bty='n', 

        legend=sapply (seq (n), function (i) paste0 ('n=', i)))

```

![](./fig/README-example.png)