Calculates probablities
from the probability density function
of the normal distribution
\(
X
\sim
\mathcal{N}
\left(
\mu,
\sigma^2
\right)
%(\#eq:dist-X-norm)
\) .
This function is identical to dnorm().
normpdf(x, mu = 0, sigma = 1, log = FALSE)
| x | Numeric vector. Values of the random variable \(X\). |
|---|---|
| mu | Numeric. Location parameter mean \(\mu\). |
| sigma | Numeric. Positive number. Scale parameter standard deviation \(\sigma = \sqrt{\sigma^2}\). |
| log | Logical.
If |
Returns \(f \left( x \right)\)
using the probablity density function
with the supplied parameter/s.
If log = TRUE,
returns \(\log \left( f \left( x \right) \right)\).
The normal (or Gaussian or Gauss or Laplace–Gauss) distribution is given by $$ X \sim \mathcal{N} \left( \mu, \sigma^2 \right) %(\#eq:dist-X-norm) $$ and has the probability density function (PDF) $$ f \left( x \right) = \frac{1}{\sigma \sqrt{2 \pi}} \exp \left[ - \frac{1}{2} \left( \frac{x - \mu}{\sigma} \right)^2 \right] %(\#eq:dist-normpdf-1) $$ or $$ f \left( x \right) = \frac{1}{\sqrt{2 \pi \sigma^2}} \exp \left[ - \frac{ \left( x - \mu \right)^2} {2 \sigma^2} \right] %(\#eq:dist-normpdf-2) $$ with
\(x \in \mathbf{R}\),
\(\mu\) is the location parameter mean \(\left( \mu \in \mathbf{R} \right)\), and
\(\sigma^2\) is the scale parameter variance \(\left( \sigma^2 > 0 \right)\).
Wikipedia: Normal Distribution