Normal Distribution

Two-parameter Normal (Gaussian) distribution with mean \(\mu\) and standard deviation \(\sigma\). Fitting is performed via closed-form L-moments. The L-moment estimates coincide with the conventional method-of-moments estimates (mean = \(\lambda_1\), sd = \(\lambda_2 \sqrt{\pi}\)).

The probability density function is: $$f(x) = \frac{1}{\sigma\sqrt{2\pi}} \exp\left(-\frac{1}{2}\left(\frac{x - \mu}{\sigma}\right)^2\right)$$ where:

• \(\mu\) — location/mean parameter (mean)

• \(\sigma\) — scale/standard deviation parameter (sd)

Usage

dnorm(x, mean = 0, sd = 1)

pnorm(q, mean = 0, sd = 1)

qnorm(p, mean = 0, sd = 1)

rnorm(n, mean = 0, sd = 1)

Arguments

x, q

vector of quantiles.

mean

mean parameter.

sd

standard deviation parameter.

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken as the number required.