normpdf

Normal probability density function

📝 Syntax

• y = normpdf(x)

• y = normpdf(x, mu)

• y = normpdf(x, mu, sigma)

📥 Input argument

• 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 argument

• 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 ( $\mu = 0, \sigma = 1$

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

📚 Bibliography

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

💡 Example

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

mean.

🕔 History

Version	📄 Description
1.0.0	initial version