# DiscreteNormal: Discrete normal distribution In extraDistr: Additional Univariate and Multivariate Distributions

## Description

Probability mass function, distribution function and random generation for discrete normal distribution.

## Usage

 ```1 2 3 4 5``` ```ddnorm(x, mean = 0, sd = 1, log = FALSE) pdnorm(q, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE) rdnorm(n, mean = 0, sd = 1) ```

## Arguments

 `x, q` vector of quantiles. `mean` vector of means. `sd` vector of standard deviations. `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

Probability mass function

f(x) = Φ((x-μ+1)/σ) - Φ((x-μ)/σ)

Cumulative distribution function

F(x) = Φ((floor(x)+1-μ)/σ)

## References

Roy, D. (2003). The discrete normal distribution. Communications in Statistics-Theory and Methods, 32, 1871-1883.

`Normal`

## Examples

 ```1 2 3 4 5 6 7 8``` ```x <- rdnorm(1e5, 0, 3) xx <- -15:15 plot(prop.table(table(x))) lines(xx, ddnorm(xx, 0, 3), col = "red") hist(pdnorm(x, 0, 3)) plot(ecdf(x)) xx <- seq(-15, 15, 0.1) lines(xx, pdnorm(xx, 0, 3), col = "red", lwd = 2, type = "s") ```

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