Discrete normal distribution
Probability mass function, distribution function and random generation for discrete normal distribution.
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)
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 |
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)
Roy, D. (2003). The discrete normal distribution. Communications in Statistics-Theory and Methods, 32, 1871-1883.
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")
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