MATLAB: Hi,i want to write matlab code for the given eq. plese help me

MATLAB

INt=eye(100,1);
mean=0;
sigma_2=1/100;
r1=1/(sqrt(2*pi*sigma_2));
zgk=r1*exp(-INt.^2/(2*sigma_2));

Best Answer

Here is the definition of the complex normal distribution:

https://en.wikipedia.org/wiki/Complex_normal_distribution

You used the standard real normal distribution in your code.

Best wishes

Torsten.

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MATLAB: How to calculate standard errors for estimated parameters for a 3-parameter Weibull Distribution

One method is to use Fisher information; another method is to use bootstrapping. Google will explain these if you are not already familiar with them.

Here is some code implementing each method:

%%Demo showing 2 methods of computing standard errors of 3-parameter Weibull distribution.
% Both methods require Cupid available at https://github.com/milleratotago/Cupid
% Method 2 also requires RawRT available at https://github.com/milleratotago/RawRT
% Here are some sample data to be used for this demo.
myDist = Weibull(550,1.9,300);  % Arbitrary parameter values to generate some data.
myDist.PlotDens;
data = myDist.Random(300,1);  % Replace this with your own data.
figure; histogram(data);
%%Method 1: Estimate SEs using Fisher Information
myDist = Weibull(500,1.8,200);  % Use your best guesses for the initial parameter values.
myDist.EstML(data);   % Estimate the parameter values.
estparms = myDist.ParmValues;
[SEs, Cov] = myDist.MLSE(data,'rrr');  % This step computes the standard errors.
%%Method 2: Estimate the SEs using bootstrapping.
% This option requires Cupid, as above, and also RawRT.
datatbl = table(data);  % Data must be in a MATLAB table
nBootSamples = 100;  % Probably you would want a lot more for any real analysis.
sEval = 'CondFitDist(OneSample,''data'',{},Weibull(500,1.8,200))';
ManyEstimates = CondBootstrap(datatbl,{},sEval,nBootSamples);
SEparm1 = std(ManyEstimates.scale);
SEparm2 = std(ManyEstimates.power);
SEparm3 = std(ManyEstimates.origin);

MATLAB: Transforming uniform variables to normal variables

I will assume that your uniform random variables are stored in an array just like the one created with the commands

X = rand(2000,1); % the number of points is arbitrary

To create a sample of random variables drawn from a normal distribution with parameters (mu,sigma) defined as

mu = 0;
sigma = 1;

use the command

Y = mu + sqrt(2)*sigma*erfinv(2*X-1);

The right hand side of the equation above is the inverse of the CDF associated with a Normal(mu,sigma) random variable... see http://en.wikipedia.org/wiki/Inverse_transform_sampling

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MATLAB: How to calculate standard errors for estimated parameters for a 3-parameter Weibull Distribution

MATLAB: Transforming uniform variables to normal variables

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