How to create fitting plots using data and a parametric function, whose parameter I estimated through maximum likelihood?

Dear all,

I want to plot data vs fitted function I found through Maximum Likelihood Estimation.

The following 4 plots are needed:

- observed and fitted densities

- observed and fitted densities in log

- observed vs fitted frequencies in log

- Q-Q plot in log

The function I used is a double Pareto-lognormal function. I managed to estimate the parameters of the function but now I'm struggling with the plots. Any help would be great.

The function is as follows:

Y = log(X)
n = length(Y);
m = mean(Y);
theta(1)= 3.3025;
theta(2)= 2.2771;
theta(3)= 0.9303;
p = theta(1)*theta(3) - (Y-m + 1/theta(1) - 1/theta(2) )/theta(3);
q = theta(2)*theta(3) + (Y-m + 1/theta(1) - 1/theta(2) )/theta(3);
M = log(  (1-normcdf(p)).*normpdf(q) + (1-normcdf(q)).*normpdf(p) ) + .5*(log(2*pi)+p.^2) + .5*(log(2*pi)+q.^2);
function F=n*log(theta(1)) + n*log(theta(2)) - n*log(theta(1)+theta(2)) + ...
    sum(-.5*(log(2*pi) + ( (Y-m + 1/theta(1) - 1/theta(2))/theta(3) ).^2)   ) + sum(M);
end
F = -F;

[dpb]

function F=n*log(theta(1)) + n*log(theta(2)) - n*log(theta(1)+theta(2)) + ...
    sum(-.5*(log(2*pi) + ( (Y-m + 1/theta(1) - 1/theta(2))/theta(3) ).^2)   ) + sum(M);
end
F = -F;

What's the negation of F after the function? Shouldn't be either

function F=n*log(theta(1)) + n*log(theta(2)) - n*log(theta(1)+theta(2)) + ...
    sum(-.5*(log(2*pi) + ( (Y-m + 1/theta(1) - 1/theta(2))/theta(3) ).^2)   ) + sum(M);
  F = -F;
end

or

function F=-(n*log(theta(1)) + n*log(theta(2)) - n*log(theta(1)+theta(2)) + ...
    sum(-.5*(log(2*pi) + ( (Y-m + 1/theta(1) - 1/theta(2))/theta(3) ).^2)   ) + sum(M));
end

?

Also, where are X, Y? Nobody can do nuttin' without the data.

Lastly, what have you tried and where did you run into a problem, specifically?

[Alessandro Calabrese]

Thanks for your answer dpb.

X are just income data of a survey. Actually from 0 to 541879.19, and are called before by

X = LabourIncSHIW2002(:,18);

after correctly loading the file with

cd('/Users/******.*******/Desktop/******/Italy/Matlab/Data')

[LabourIncSHIW2002, txt2002]= xlsread('Matlab_2002_data_excel.xlsx');

The problem is, that I don't get the values calculated as it says "The current use of n (in the function) is inconsistent".

I guess the plotting is the easy part.