MATLAB: How to generate random number from a given Normal distribution

distributionnormal distributionrandom number generator

Hello

I need to generate random numbers (e.g. n = 100) from a parameter, x, with a Normal distribution that the Mean and Standard Deviation is also given (and do a Monte Carlo simulation by hand). Is there any command in Matlab that by giving the X = Normal (M, S.D.) it generates n numbers from that distribution?

Thank you,

Best Answer

There are several options. One is the core MATLAB function randn. The Statistics and Machine Learning Toolbox has the normrnd funciton, and others.

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MATLAB: How to go about finding the standard normal probability based on the z-score

doc normcdf
doc normpdf

When you know what you want but not sure the name, try something like

>> lookfor normal
realmin                        - Smallest positive normalized floating point number.
randn                          - Normally distributed pseudorandom numbers.
sprandn                        - Sparse normally distributed random matrix.
surfnorm                       - Surface normals.
isonormals                     - Isosurface normals.
cde                            - cd elliptic function with normalized complex argument.
sne                            - sn elliptic function with normalized complex argument.
addfreqcsmenu                  - Add a cs menu to switch between linear and normalized frequency
convertfrequnits               - converts between Normalized, Hz, kHz, etc
histfit                        - Histogram with superimposed fitted normal density.
jbtest                         - Jarque-Bera hypothesis test of composite normality.
lhsnorm                        - Generate a latin hypercube sample with a normal distribution
logncdf                        - Lognormal cumulative distribution function (cdf).
lognfit                        - Parameter estimates and confidence intervals for lognormal data.
logninv                        - Inverse of the lognormal cumulative distribution function (cdf).
lognlike                       - Negative log-likelihood for the lognormal distribution.
lognpdf                        - Lognormal probability density function (pdf).
lognrnd                        - Random arrays from the lognormal distribution.
lognstat                       - Mean and variance for the lognormal distribution.
mvncdf                         - Multivariate normal cumulative distribution function (cdf).
mvnpdf                         - Multivariate normal probability density function (pdf).
mvnrnd                         - Random vectors from the multivariate normal distribution.
normcdf                        - Normal cumulative distribution function (cdf).
normfit                        - Parameter estimates and confidence intervals for normal data.
norminv                        - Inverse of the normal cumulative distribution function (cdf).
normlike                       - Negative log-likelihood for the normal distribution.
normpdf                        - Normal probability density function (pdf).
normplot                       - Displays a normal probability plot.
normrnd                        - Random arrays from the normal distribution.
normspec                       - Plots normal density between specification limits.
normstat                       - Mean and variance for the normal distribution.
logn3fit                       - Fit a 3-param lognormal dist'n using cumulative probabilities.
wgtnormfit                     - Fitting example for a weighted normal distribution.
wgtnormfit2                    - Fitting example for a weighted normal distribution (log(sigma) parameterization).
>>

Judicious search terms help but seeing the list of things related to "normal" lets you find the two functions of interest (plus a lot more depending upon which toolboxes are available, maybe) that might be of use/interest...

MATLAB: How to calculate the inverse cumulative density function of a Gaussian mixture with Statistical Toolbox

Assuming that a univariate mixture of Gaussians is required (otherwise the inverse cumulative density function (CDF) does not exist), compute the CDF over a grid of, say, 1000 values, and compute the inverse CDF by reverse interpolation.

There is an example of this idea in the demo "Nonparametric Estimates of Cumulative Distribution Functions and Their Inverses" that ships with Statistics Toolbox, but which is not in the web documentation yet. That demo does this in a slightly different context, but the idea carries over.

Best Answer

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MATLAB: How to go about finding the standard normal probability based on the z-score

MATLAB: How to calculate the inverse cumulative density function of a Gaussian mixture with Statistical Toolbox

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