normpdf

Normal probability density function

📝Syntax

y = normpdf(x)
y = normpdf(x, mu)
y = normpdf(x, mu, sigma)

📥Input Arguments

Parameter	Description
x	scalar value or array: Values at which to evaluate pdf.
mu	scalar value, 0 (default) or array: Mean.
sigma	positive scalar value, 1 (default) or array of positive values: Standard deviation.

📤Output Arguments

Parameter	Description
y	scalar value or array: pdf values.

📄Description

normpdf computes the probability density function of the normal (Gaussian) distribution.

The general formula for the normal distribution PDF is:

$$f(x|\mu,\sigma^2) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}}$$

where

$$\mu$$

is the mean and

$$\sigma^2$$

is the variance.

For the standard normal distribution (

$$\mu = 0, \sigma = 1$$

):

$$\phi(x) = \frac{1}{\sqrt{2\pi}} e^{-\frac{x^2}{2}}$$

💡Examples

x = [-0.2, -0.1, 0, 0.1, 0.2];
R = normpdf(x);

x = [-0.2, -0.1, 0, 0.1, 0.2];
R = normpdf(x, 2, 1);

R = normpdf(0, [-0.2, -0.1, 0, 0.1, 0.2], 1);

🔗See Also

📚Bibliography

Evans, M., N. Hastings, and B. Peacock. Statistical Distributions. 2nd ed. Hoboken, NJ: John Wiley and Sons, Inc., 1993.

🕔Version History

Version	Description
1.0.0	initial version