MATLAB: Probability distribution of a multiple variable sum

histogramsmultiple variablesprobability

Hi everyone,

I’m coming here for really advance statistic/probability advice, which I'm a beginner in this field.

I would like to know the probability of a variable TAU_total such as TAU_total=TAU1+TAU2+….+TAU129.

The variables TAUi are independent of each other.

For each one of them, I have a sample of 20,000 values which you can see some examples of their distribution on the histograms in the attachment.

My question is the following: I would like to be able to determine the probability of TAU_total to be superior to a certain value Xmax.

Thank you for your help,

Regards,

Rémy

Best Answer

Take samples from your empirical data and use Monte-Carlo-simulation to determine the above probability.

This code should help to take the samples:

https://de.mathworks.com/matlabcentral/fileexchange/7976-random-number-from-empirical-distribution

Related Solutions

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: Plot pdf from histogram – dice

hist function is not recommended. Please use histogram function instead.

And by setting the 'Normalization' option, PDF can be plotted, like:

AllRoll = randi(6,50000, 1);
SumRoll = sum(AllRoll, 2);
Edges = 0.5:1:6.5;
histogram(SumRoll,Edges,'Normalization','probability');
title(sprintf('PDF'));
xlabel(sprintf('1-6'));
ylabel(sprintf('Probability'));
grid on
hold on

Best Answer

Related Solutions

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

MATLAB: Plot pdf from histogram – dice

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