extraDistr (version 1.9.1)

DiscreteNormal: Discrete normal distribution

Description

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

Usage

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 \(P[X \le x]\) 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

$$ f(x) = \Phi\left(\frac{x-\mu+1}{\sigma}\right) - \Phi\left(\frac{x-\mu}{\sigma}\right) $$

Cumulative distribution function

$$ F(x) = \Phi\left(\frac{\lfloor x \rfloor + 1 - \mu}{\sigma}\right) $$

References

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

See Also

Normal

Examples

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")