Normal
The Normal Distribution

Description

Calculates density, cumulative probability, quantile, and generate random sample for the normal (also called Gaussian) distribution (continuous).

Usage

dnorm(x, mean = 0, sd = 1, log = FALSE) # density
pnorm(q, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE) # probability
qnorm(p, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE) # quantile
rnorm(n, mean = 0, sd = 1) # random

Arguments

x, q numeric vectors in the range (-Inf, Inf) that specify the quantiles.
p a numeric vector in the range [0, 1] that specifies the probabilities.
n an integer scalar in the range [0, Inf) that specifies the number of random samples requested. If the input value is not an integer, it is truncated. If length(n) is greater than 1, the random function returns length(n) random samples.
mean a numeric vector in the range (-Inf, Inf) that specifies means.
sd a numeric vector in the range [0, Inf) that specifies standard deviations.
log a logical value. If FALSE (default), the density function returns the density itself. If TRUE, it returns the log of the density.
lower.tail a logical value. If TRUE (default), the probability supplied to the quantile function or returned by the probability function is P[X <= x]. If FALSE, it is P[X > x].
log.p a logical value. If FALSE (default), the probability supplied to the quantile function or returned by the probability function is the probability itself. If TRUE, it is the log of the probability.

Details

The distribution parameter(s) are replicated cyclically to be the same length as the input x, q, p, or the number of random samples requested.
Missing values (NAs) in the input or the distribution parameter(s) will cause the corresponding elements of the result to be missing.
Value
returns density (dnorm), cumulative probability (pnorm), quantile (qnorm), or random sample (rnorm) for the normal distribution with parameters mean and sd.
Side Effects
If the .Random.seed dataset exists, the random sample function updates its value. The random sample function creates the .Random.seed dataset if it does not exist.
Background
The normal distribution is a family of continuous probability distributions defined on the interval (-Inf, Inf) and parameterized by two parameters, mean and sd.
For more information about the implementation of the uniform random number generator, see set.seed.
References
Johnson, N. L. and Kotz, S. (1970). Continuous Univariate Distributions, vol. 1. Houghton-Mifflin, Boston.
Kinderman, A. J. and Monahan, J. F. (1977). Computer generation of random variables using the ratio of uniform deviates. ACM Transactions on Mathematical Software. 3 257-260.
See Also
Lognormal, dnrange, qqnorm, set.seed
Examples
rnorm(20, 0, 10) # sample of 20, mean 0, standard dev. 10

# Generate a 20x5 matrix of independent Gaussians:
matrix(rnorm(20*5), nrow=20)
Package stats version 6.1.1-7
Package Index