# DiscreteLaplace: Discrete Laplace distribution In extraDistr: Additional Univariate and Multivariate Distributions

## Description

Probability mass, distribution function and random generation for the discrete Laplace distribution parametrized by location and scale.

## Usage

 ```1 2 3 4 5``` ```ddlaplace(x, location, scale, log = FALSE) pdlaplace(q, location, scale, lower.tail = TRUE, log.p = FALSE) rdlaplace(n, location, scale) ```

## Arguments

 `x, q` vector of quantiles. `location` location parameter. `scale` scale parameter; `0 < scale < 1`. `log, log.p` logical; if TRUE, probabilities p are given as log(p). `lower.tail` logical; if TRUE (default), probabilities are P[X ≤ x] otherwise, P[X > x]. `n` number of observations. If `length(n) > 1`, the length is taken to be the number required.

## Details

If U ~ Geometric(1-p) and V ~ Geometric(1-p), then U-V ~ DiscreteLaplace(p), where geometric distribution is related to discrete Laplace distribution in similar way as exponential distribution is related to Laplace distribution.

Probability mass function

f(x) = (1-p)/(1+p) * p^(|x-μ|)

Cumulative distribution function

F(x) = [if x < 0:] p^-floor(x-μ))/(1+p) [else:] 1-(p^(floor(x-μ)+1))/(1+p)

## References

Inusah, S., & Kozubowski, T.J. (2006). A discrete analogue of the Laplace distribution. Journal of statistical planning and inference, 136(3), 1090-1102.

Kotz, S., Kozubowski, T., & Podgorski, K. (2012). The Laplace distribution and generalizations: a revisit with applications to communications, economics, engineering, and finance. Springer Science & Business Media.

## Examples

 ```1 2 3 4 5 6 7 8``` ```p <- 0.45 x <- rdlaplace(1e5, 0, p) xx <- seq(-200, 200, by = 1) plot(prop.table(table(x))) lines(xx, ddlaplace(xx, 0, p), col = "red") hist(pdlaplace(x, 0, p)) plot(ecdf(x)) lines(xx, pdlaplace(xx, 0, p), col = "red", type = "s") ```

extraDistr documentation built on Sept. 7, 2020, 5:09 p.m.