using mle in matlab

for a given dataset i need to calculate parameters value using mle where cdf = a*(1-exp(-b*A)) and pdf = a*b*exp(-b*A),if i use following code

A=[6 10 17 20 29 34 38 41 50 55 ];
[phat,pci] = mle(A,'pdf',@(A,x,y) x*y*exp(-y*A),'start',[1,1])

i get

 Error using mlecustom>llf_pdfcdf
(line 440)
The PDF function returned negative
or zero values.

Error in fminsearch (line 330)
        x(:) = xe; fxe =
        funfcn(x,varargin{:});

Error in mlecustom (line 184)
            fminsearch(llf,start,opts,uncensData,censData,uncensFreq,censFreq,fun1Args,fun2Args,checkFunVals,lb,ub);

Error in mle (line 247)
            [phat, pci] =
            mlecustom(data,varargin{:}); 
            

I am not able to understand what is wrong and how to rectify it as i am new to matlab.Please help how sholud i evaluate parameters a and b using mle function in matlab.

Answer 1

[w w]

try 'lowerbound'

Answer 2

[Jeff Miller]

One problem is that mle's search function (fminsearch) may try negative parameter values, in which case your pdf function returns a negative value. You could avoid that problem by squaring the parameter values, like this:

[phat,pci] = mle(A,'pdf',@(A,x,y) x^2*y^2*exp(-y^2*A),'start',[1,1])

If you do that, just keep in mind that the "real" x and y values you want are the squares of the phat values returned by mle.

Another problem, though, is that these are not legitimate pdf and cdf functions except when a=1. So, I think you really only have one parameter to estimate here--namely, your y parameter. It looks to me, anyway, like you are fitting an exponential distribution to these A values and looking for the best-fitting rate parameter. That value is 0.03333 = 1/mean(A)

[shalini sharma]

thanks but squaring the values give

Warning: Maximum likelihood

estimation did not converge.

Iteration limit exceeded.

> In mlecustom (line 241)

In mle (line 247)

Warning: Matrix is close to singular

or badly scaled. Results may be

inaccurate. RCOND = 3.426193e-22.

> In mlecov (line 291)

In mlecustom (line 260)

In mle (line 247)

phat =

1.0e+20 *

3.8864 -0.0000

pci =

1.0e+20 *

2.1832 -0.0000

5.5897 -0.0000

[shalini sharma]

using fsolve i am able to find out the values of parameters a and b (for cdf = a*(1-exp(-b*A)) and pdf = a*b*exp(-b*A)) but i want to evaluate parameters of a cdf and pdf having 5 unknowns which is estimating incorrect values using fsolve (not matching the given results) and therefore i want to compare the results of mle and fsolve to estimate the correct output. So i tried using simpler pdf having known parameters to check which method will be best suited for my model,but i am not able to find correct values of a and b for the given pdf using mle(above mentioned problem). Moreover i dont understand why fsolve,mle and coding (newton ralphson) all gives different values. Since i dont have deep understanding of matlab so i am very confuse which method is best fsolve or mle for estimating parameters (5 to 10) .

thanks...

[Elifnur Öztürk]

Did you find the answer to your question? @shalini sharma

[shalini sharma]

I tried using the square of parameters in equation to be evaluated...and also with used different PDF and cdf but every time I got error....anyway thanks ....will try again