Thread Subject: Fitting CDF of Beta distribution data

Right now I am fitting the CDF data using the normal
distribution via the GLMFIT. Are there any way I can do the
same fitting but assuming the BETA distribution.

The current code I am using to fit Normal CDF data is as
shown below:
x = [0.1294;0.2211;0.3779;0.5559;0.7034;0.8901;1.1263;];
y = [0;0;0.004;0.007;0.029;0.078;0.192;];

Y = roundn( [y*100 100*ones(length(y), 1)], 0);
b = glmfit( x, Y, 'binomial', 'link', 'probit');

% Equivalent Normal parameters are (From Tom Lane):
mean = -b(1)/b(2);
stdDev = 1/b(2);

Thank you very much for your help,

Pete, with the "probit" link function you are saying the binomial
probabilities follow the form of a normal cdf. The b(1) and b(2) parameters
adjust the mean and standard deviation of the distribution function.

That's not the case with a beta distribution. It's not a location/scale
family. It would be possible to use a beta distribution function with
parameters that you specify in advance, and then let the b(1) and b(2)
parameters define a location/scale transformation of that. I'll bet that's
not what you intend, though. Also, unlike the normal, this distribution has
zero probability outside a finite range; this may or may not cause troubles
for you..

I can't think of any way to use glmfit and estimate the beta function
parameters. I have seen work people have done to estimate parameters in a
link function. If that's what you really want, let me know. Maybe I can
find a reference.

-- Tom

"Pete sherer" <tsh@abg.com> wrote in message
news:g0v407$9e9$1@fred.mathworks.com...
> Right now I am fitting the CDF data using the normal
> distribution via the GLMFIT. Are there any way I can do the
> same fitting but assuming the BETA distribution.
>
> The current code I am using to fit Normal CDF data is as
> shown below:
> x = [0.1294;0.2211;0.3779;0.5559;0.7034;0.8901;1.1263;];
> y = [0;0;0.004;0.007;0.029;0.078;0.192;];
>
> Y = roundn( [y*100 100*ones(length(y), 1)], 0);
> b = glmfit( x, Y, 'binomial', 'link', 'probit');
>
> % Equivalent Normal parameters are (From Tom Lane):
> mean = -b(1)/b(2);
> stdDev = 1/b(2);
>
> Thank you very much for your help,

Hi Tom,

It doesn't have to use the GLMFIT. Any function that can be
used to estimate the parameters of beta distribution would do.

Thanks a lot.

Pete

> It doesn't have to use the GLMFIT. Any function that can be
> used to estimate the parameters of beta distribution would do.

Okay, Pete. Usually I tell people that they need to be clear about whether
to approach something as a distribution fitting problem or a curve fitting
problem. Let's just say you have a curve fitting problem, which just
happens to use a curve in the form of a distribution function.

Your largest x value is bigger than 1. So the beta distribution on [0,1] is
not appropriate. Let's say you have a beta distribution with parameters A
and B on the interval [0,C] where there are now three parameters to
estimate. Here's one way of going about that. I exponentiated all the
parameters just as a convenient way to force them to be positive.

I hope this is enough to get you started.

-- Tom

x = [0.1294;0.2211;0.3779;0.5559;0.7034;0.8901;1.1263;];
y = [0;0;0.004;0.007;0.029;0.078;0.192;];

f = @(p,x) betacdf(x/exp(p(1)),exp(p(2)),exp(p(3)));

p = nlinfit(x,y,f,[2 1 1])
fmt = 'Beta distributionon on [0,%g] with parameters %g and %g \n',...
t = sprintf(fmt, exp(p));

xx = linspace(0,1.2);
plot(x,y,'bo',xx,f(p,xx),'r-')
title(t)