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From: Argon on 10 Aug 2010 14:13
Dear All,

I have some data vectors x and y, and using these data I need to fit the distribution y=N(0,a+b*x), where N is the normal distribution (i.e. zero mean, standard deviation linearly dependent on x).
Anyone has any idea on how to do it in Matlab (how to find the values of a and b and possibly their distributions as well)?

Help is appreciated.
From: Rogelio on 10 Aug 2010 14:26
"Argon " <kineros(a)yahoo.it> wrote in message <i3s4rg$3sa$1(a)fred.mathworks.com>...
> Dear All,
>
> I have some data vectors x and y, and using these data I need to fit the distribution y=N(0,a+b*x), where N is the normal distribution (i.e. zero mean, standard deviation linearly dependent on x).
> Anyone has any idea on how to do it in Matlab (how to find the values of a and b and possibly their distributions as well)?
>
> Help is appreciated.

you can do maximum likelihood estimation. program the loglikelihood of the normal distribtion and specify the variance of it as a in your case, i.e. a function of x. Then a and b are your parameters to be found. You would like to use fminunc to minimize the minus loglikelihood, which is equivalent to maximize the log likelihood. a and b are coefficients so they are non stochastic.
From: Peter Perkins on 10 Aug 2010 16:41
On 8/10/2010 2:13 PM, Argon wrote:
> Dear All,
>
> I have some data vectors x and y, and using these data I need to fit the
> distribution y=N(0,a+b*x), where N is the normal distribution (i.e. zero
> mean, standard deviation linearly dependent on x).
> Anyone has any idea on how to do it in Matlab (how to find the values of
> a and b and possibly their distributions as well)?

If you have access to the Statistics Toolbox, you can use MLE. That
function is usually used to fit a univariate distribution with no
covariates, but this is one of the cases where you can trick it into
fitting a distribution with covariates, by using an anonymous function.

a = 1.23;
b = 2.34;
x = rand(1000,1);
y = normrnd(0,a+b*x,size(x));

mypdf = @(y,a,b) normpdf(y,0,a+b*x);
[paramEsts,paramCIs] = ...
mle(y,'pdf',mypdf,'start',[1 1],'lowerbound',[0 0])

Hope this helps.
From: Argon on 10 Aug 2010 17:04
Peter Perkins <Peter.Perkins(a)MathRemoveThisWorks.com> wrote in message <i3sdhf$mqc$1(a)fred.mathworks.com>...
> On 8/10/2010 2:13 PM, Argon wrote:
> > Dear All,
> >
> > I have some data vectors x and y, and using these data I need to fit the
> > distribution y=N(0,a+b*x), where N is the normal distribution (i.e. zero
> > mean, standard deviation linearly dependent on x).
> > Anyone has any idea on how to do it in Matlab (how to find the values of
> > a and b and possibly their distributions as well)?
>
> If you have access to the Statistics Toolbox, you can use MLE. That
> function is usually used to fit a univariate distribution with no
> covariates, but this is one of the cases where you can trick it into
> fitting a distribution with covariates, by using an anonymous function.
>
> a = 1.23;
> b = 2.34;
> x = rand(1000,1);
> y = normrnd(0,a+b*x,size(x));
>
> mypdf = @(y,a,b) normpdf(y,0,a+b*x);
> [paramEsts,paramCIs] = ...
> mle(y,'pdf',mypdf,'start',[1 1],'lowerbound',[0 0])
>
> Hope this helps.

Immense thanks.
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