fitting a gamma model to a data set

Hello,

I have a horrible equation that I need to fit some data to. How may I go about doing this?

This is the function:

where the gamma presumably is this thing:

I have 32 data points evenly spaced from 1 to 32.

Any ideas on how to start would be really appreciated!

[Torsten]

Which parameters do you want to fit ? For which variable(s) in the equation do you have these 32 data ?

Answer 1

[Rohit Kulkarni]

Hi,

In my understanding you want to model the above functions and then fit the a vector of values from 1 to 32 in these. You can use symbolic equation to model such expressions:

syms f(mu) N(D,mu)
f(mu) = ((6/3.67^4)) * ((3.67 + mu)^(mu + 4))/gamma(mu+4);
N(D,mu) = Nw * f(mu) * ((D/D_0)^mu) * exp(-(3.67 + mu) * (D/D_0));

MATLAB offers a built-in function called gamma that allows you to calculate the values of the gamma function.

From the equation provided, it can assumed that 'D' and 'mu' are variables and all others are constants.

Then create a vector v and substitute it for mu, also provide the values for 'D' variable.

v = 1:32;
ans = N(D,v);

Hope it helps!