Thread Subject: Curve fitting using Gaussian model

Dear Sir/Madam,

In curve fitting toolbox, the Gaussian model is:

Y = a * exp(-((x-b)/c)^2)

and Matlab returns the coefficients a, b and c.
Where a is the amplitude
b is the centriod (location)
c is related to the peak width

The question is: what is the relation between a and c?

Comparing general Gaussian model with the previous model we
find:

c = 1/(a*(sqrt(pi)))

By the returned values for a and c from the fitting process
do not validate this relation.

The general Gaussian model is:

Y = (1/(sigma*(sqrt(2*pi)))) * exp(-((x-b)^2)/((2*sigma)^2))

"Osama Zahran" <zahran@liverpool.ac.uk> wrote in message
<g09k3o$j0f$1@fred.mathworks.com>...
> Dear Sir/Madam,
>
> In curve fitting toolbox, the Gaussian model is:
>
> Y = a * exp(-((x-b)/c)^2)
>
> and Matlab returns the coefficients a, b and c.
> Where a is the amplitude
> b is the centriod (location)
> c is related to the peak width
>
> The question is: what is the relation between a and c?
>
> Comparing general Gaussian model with the previous model we
> find:
>
> c = 1/(a*(sqrt(pi)))
>
> By the returned values for a and c from the fitting process
> do not validate this relation.
>
> The general Gaussian model is:
>
> Y = (1/(sigma*(sqrt(2*pi)))) * exp(-((x-b)^2)/((2*sigma)^2))

Hi,
I guess you already know it, but in your
last equation the coefficient a is expressed
in terms of sigma because the integral of
the function must be 1 (this is, for example,
when you have a normal probability distribution function
like randn). So if you simulate some x=randn(1,N)
and then you calculate the hist(x,...),
and normalize the integral to unity, then the
result can be fitted by a gaussian like
Y = (1/(sigma*(sqrt(2*pi)))) * exp(-((x-b)^2)/((2*sigma)^2))
Otherwise, if you just want to fit some data
with a gaussian fucntion, the amplitude (a) has no
relation with the widht (c).

Regards

Osama Zahran wrote:
> Dear Sir/Madam,
>
> In curve fitting toolbox, the Gaussian model is:
>
> Y = a * exp(-((x-b)/c)^2)
>
> and Matlab returns the coefficients a, b and c.
> Where a is the amplitude
> b is the centriod (location)
> c is related to the peak width
>
> The question is: what is the relation between a and c?

Osama, You might find this demo helpful:

<http://www.mathworks.com/products/statistics/demos.html?file=/products/demos/shipping/stats/cfitdfitdemo.html>