Thread Subject:

Creating Custom Equation for Gravity Model

Hi all,
I am trying to create a custom distribution for the 'gravity' model used for modelling traffic distribution for a N-node network. The volume of traffic entering network at node i and leaving at node j is defined by the gravity model as:

V(i,j) = (exprnd(alfa(i)) * exprnd(beta(j)))/sum(exprnd(alfa));

where i = 1, 2, ....N; j = 1, 2, ...., N
alfa and beta are N-dimensiona vectors of mean traffic volume. For example alfa(i) is the mean traffic volume entering the network via node i and beta(j) is the mean traffic volume leaving the network via node j. The traffic entering or leaving the network is assumed to be exponentially distributed.

So given a set of data for V(i,j), and the value of N, I want to used the above custom equation to estimate the parameters alfa and beta of the data. I also want to see how well a data fits this distribution.

Can anyone exist in creating a custom distribution based on the above equation?