MATLAB: KStest for unimodal and bimodal models

goodness of fitkstestmixture models

Hi, i would like to perform a KStest of an unimodal and bimodal models with observed data X.

Please find an example of X in attachement.

The unimodal model is a lognormal distribution defined as:

where

The bimodal model is a lognormal & lognormal PDF defined as:

where

How can i use the KStest for evaluate the goodness of fit of both models with observed data?

Is there a quick way to evaluate this with KS statistic?

T PLOCOSTE

Best Answer

Hi,

Kstest(x) returns a test decision for the null hypothesis that the data in vector x comes from a specified standard normal distribution or it does not come from such a distribution

If the result is one the test rejects the null hypothesis at default significance level(5%)

From your data

Data=ObservedData(:,1); 
x=(Data-3.2)/0.44; %specified mean and standard deviation
r=kstest(x) ;

Similarly ,for a bimodal distribution, check the kstest for each distribution seperately

Refer to the link kstest for more information

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: Kstest and hypothesis rejecting

When in doubt, use help()

help kstest
 kstest Single sample Kolmogorov-Smirnov goodness-of-fit hypothesis test.
    H = kstest(X) performs a Kolmogorov-Smirnov (K-S) test to determine if
    a random sample X could have come from a standard normal distribution,
    N(0,1). H indicates the result of the hypothesis test:
       H = 0 => Do not reject the null hypothesis at the 5% significance

       level. 
       H = 1 => Reject the null hypothesis at the 5% significance
       level.

The null hypothesis depends on your inputs. Again, from the documentation using doc(ktest):

Test the null hypothesis that the data comes from a normal distribution with 
a mean of 75 and a standard deviation of 10. Use these parameters to center 
and scale each element of the data vector since, by default, kstest tests for 
a standard normal distribution.
x = (test1-75)/10;
h = kstest(x)

Best Answer

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

MATLAB: Kstest and hypothesis rejecting

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