How to fit a dataset with two independant variables (of different dimensions) and one dependant variable?

I need to fit data points of an Intensity-Duration-Frequency curve into a non-linear equation of the form

i=K*(T^a)/((t+b)^n)

where i is the intensity(dependant),T the return period(independant) and t the duration(independant).

K,a,b,n are the coefficients to be found.

t={ 1 2 4 5 10 12 15 24 36 48 }

T={2 5 10 25 50 100}

I was attempting nlinfit with the two independant variable data sets to be in one single matrix,but dimensions do not agree for the two.How would i fit these?

[Matt J]

What are the dimensions of i?

[Ashok Jacob]

there are 10*6= 60 data points in i,one for each combination of t and T.

Apologies for the oversight.

Answer 1

[Jeff Miller]

You need give nlinfit the corresponding 60 values of t and T. Something like this (but check the order of the resulting 60 points):

t=[   1   2  4  5  10  12  15  24  36  48];
T=[2 5 10 25 50 100];
[t2, T2] = ndgrid(t,T);
t2 = reshape(t2,60,1);
T2 = reshape(T2,60,1);
% now pass t2 and T2 to nlinfit