# normstat

Normal mean and variance

## Description

example

[m,v] = normstat(mu,sigma) returns the mean and variance of the normal distribution with mean mu and standard deviation sigma.

The mean of the normal distribution with parameters µ and σ is µ, and the variance is σ2.

## Examples

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Compute the mean and variance of the normal distribution with parameters mu and sigma.

mu = 1;
sigma = 1:5;
[m,v] = normstat(mu,sigma)
m = 1×5

1     1     1     1     1

v = 1×5

1     4     9    16    25

## Input Arguments

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Mean of the normal distribution, specified as a scalar value or an array of scalar values.

To compute the means and variances of multiple distributions, specify distribution parameters using an array of scalar values. If both mu and sigma are arrays, then the array sizes must be the same. If either mu or sigma is a scalar, then normstat expands the scalar argument into a constant array of the same size as the other argument. Each element in m and v is the mean and variance of the distribution specified by the corresponding elements in mu and sigma.

Example: [0 1 2; 0 1 2]

Data Types: single | double

Standard deviation of the normal distribution, specified as a positive scalar value or an array of positive scalar values.

To compute the means and variances of multiple distributions, specify distribution parameters using an array of scalar values. If both mu and sigma are arrays, then the array sizes must be the same. If either mu or sigma is a scalar, then normstat expands the scalar argument into a constant array of the same size as the other argument. Each element in m and v is the mean and variance of the distribution specified by the corresponding elements in mu and sigma.

Example: [1 1 1; 2 2 2]

Data Types: single | double

## Output Arguments

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Mean of the normal distribution, returned as a scalar value or an array of scalar values. m is the same size as mu and sigma after any necessary scalar expansion. Each element in m is the mean of the normal distribution specified by the corresponding elements in mu and sigma.

Variance of the normal distribution, returned as a scalar value or an array of scalar values. v is the same size as mu and sigma after any necessary scalar expansion. Each element in v is the variance of the normal distribution specified by the corresponding elements in mu and sigma.

## Alternative Functionality

• normstat is a function specific to normal distribution. Statistics and Machine Learning Toolbox™ also offers generic functions to compute summary statistics, including mean (mean), median (median), interquartile range (iqr), variance (var), and standard deviation (std). These generic functions support various probability distributions. To use these functions, create a NormalDistribution probability distribution object and pass the object as an input argument.

## References

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

## Version History

Introduced before R2006a