Normal random numbers
collapse all in page
Syntax
r = normrnd(mu,sigma)
r = normrnd(mu,sigma,sz1,...,szN)
r = normrnd(mu,sigma,sz)
Description
example
r = normrnd(mu,sigma) generates a random number from the normal distribution with mean parameter mu and standard deviation parameter sigma.
r = normrnd(mu,sigma,sz1,...,szN) generates an array of normal random numbers, where sz1,...,szN indicates the size of each dimension.
example
r = normrnd(mu,sigma,sz) generates an array of normal random numbers, where vector sz specifies size(r).
Examples
collapse all
Generate Normal Random Number
Open Live Script
Generate a single random value from the standard normal distribution.
rng('default') % For reproducibilityr = normrnd(0,1)
r = 0.5377
Reset Random Number Generator
Open Live Script
Save the current state of the random number generator. Then create a 1-by-5 vector of normal random numbers from the normal distribution with mean 3 and standard deviation 10.
s = rng;r = normrnd(3,10,[1,5])
r = 1×5 8.3767 21.3389 -19.5885 11.6217 6.1877Restore the state of the random number generator to s, and then create a new 1-by-5 vector of random numbers. The values are the same as before.
rng(s);r1 = normrnd(3,10,[1,5])
r1 = 1×5 8.3767 21.3389 -19.5885 11.6217 6.1877Clone Size from Existing Array
Open Live Script
Create a matrix of normally distributed random numbers with the same size as an existing array.
A = [3 2; -2 1];sz = size(A);R = normrnd(0,1,sz)
R = 2×2 0.5377 -2.2588 1.8339 0.8622You can combine the previous two lines of code into a single line.
R = normrnd(1,0,size(A));
Input Arguments
collapse all
mu — Mean
scalar value | array of scalar values
Mean of the normal distribution, specified as a scalar value or an array of scalar values.
To generate random numbers from multiple distributions, specify mu and sigma using arrays. If both mu and sigma are arrays, then the array sizes must be the same. If either mu or sigma is a scalar, then normrnd expands the scalar argument into a constant array of the same size as the other argument. Each element in r is the random number generated from the distribution specified by the corresponding elements in mu and sigma.
Example: [0 1 2; 0 1 2]
Data Types: single | double
sigma — Standard deviation
nonnegative scalar value | array of nonnegative scalar values
Standard deviation of the normal distribution, specified as a nonnegative scalar value or an array of nonnegative scalar values.
If sigma is zero, then the output r is always equal to mu.
To generate random numbers from multiple distributions, specify mu and sigma using arrays. If both mu and sigma are arrays, then the array sizes must be the same. If either mu or sigma is a scalar, then normrnd expands the scalar argument into a constant array of the same size as the other argument. Each element in r is the random number generated from the distribution specified by the corresponding elements in mu and sigma.
Example: [1 1 1; 2 2 2]
Data Types: single | double
sz — Size of each dimension (as a row vector)
row vector of integers
Size of each dimension, specified as a row vector of integers. For example, specifying [5,3,2] generates a 5-by-3-by-2 array of random numbers from the probability distribution.
If either mu or sigma is an array, then the specified dimensions sz must match the common dimensions of mu and sigma after any necessary scalar expansion. The default values of sz are the common dimensions.
If you specify a single value
[sz1], then r is a square matrix of sizesz1-by-sz1.If the size of any dimension is
0or negative, thenris an empty array.Beyond the second dimension,
normrndignores trailing dimensions with a size of 1. For example, specifying[3,1,1,1]produces a 3-by-1 vector of random numbers.
Example: [5,3,2]
Data Types: single | double
Output Arguments
collapse all
r — Normal random numbers
scalar value | array of scalar values
Normal random numbers, returned as a scalar value or an array of scalar values with the dimensions specified by sz1,...,szN or sz. Each element in r is the random number generated from the distribution specified by the corresponding elements in mu and sigma.
Alternative Functionality
normrndis a function specific to normal distribution. Statistics and Machine Learning Toolbox™ also offers the generic function random, which supports various probability distributions. To userandom, create a NormalDistribution probability distribution object and pass the object as an input argument or specify the probability distribution name and its parameters. Note that the distribution-specific functionnormrndis faster than the generic functionrandom.Use randn to generate random numbers from the standard normal distribution.
To generate random numbers interactively, use randtool, a user interface for random number generation.
References
[1] Marsaglia, G, and W. W. Tsang. “A Fast, Easily Implemented Method for Sampling from Decreasing or Symmetric Unimodal Density Functions.” SIAM Journal on Scientific and Statistical Computing. Vol. 5, Number 2, 1984, pp. 349–359.
[2] Evans, M., N. Hastings, and B. Peaco*ck. Statistical Distributions. 2nd ed. Hoboken, NJ: John Wiley & Sons, Inc., 1993.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
The generated code can return a different sequence of numbers than MATLAB® if either of the following is true:
The output is nonscalar.
An input parameter is invalid for the distribution.
For more information on code generation, see Introduction to Code Generation and General Code Generation Workflow.
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Version History
Introduced before R2006a
See Also
random | mvnrnd | lognrnd | NormalDistribution | randn | normcdf | normpdf
Topics
- Random Number Generation
- Normal Distribution
MATLAB Command
You clicked a link that corresponds to this MATLAB command:
Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list:
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- Deutsch
- English
- Français
- United Kingdom (English)
Asia Pacific
- Australia (English)
- India (English)
- New Zealand (English)
- 中国
- 日本 (日本語)
- 한국 (한국어)
Contact your local office
