Error when using custom pdf for mle

Hello,

I am trying to use the mle function with a custom pdf defined by:

function[frequency] = myfun(data,x) frequency = data.^(x);

myhandle = @(data, x) myfun(data,x)

My starting value for x is -1, so I enter: [phat] = mle (data, 'pdf', myhandle, 'start', -1);

(Physically, I have data where I the freqency of occurrence to be approximately inversely proportional to the energy signal observed.)

None of my data is negative or zero. However, I get the following error:

??? Error using ==> mlecustom>llf_pdfcdf at 441 The PDF function returned NaN or infinite values.

I have input my data into the defined function and checked that it does not produce any NaNs or infinities. Does anyone know how I can solve this error or a different way I can estimate my parameter x?

Thankyou!

Answer 1

[Tom Lane]

The mle function needs a real pdf. Yours isn't normalized to integrate to 1. Here's an example that integrates to 1 from 0 to +Inf for parameters a>1:

>> f = @(x,a) (a-1)*x.^-a;
>> quad(@(x) f(x,2),1,100)
ans =
    0.9900
>> quad(@(x) f(x,5),1,100)
ans =
    1.0000
>> quad(@(x) f(x,15),1,100)
ans =
    1.0000
>> mle(x,'pdf',f,'start',2)
ans =
    2.7134

[Francesca]

Thanks! I understand what the problem is now. Sadly, I think (for physics reasons) that my exponent will be around -0.9. So maybe I will try defining a function with a cutoff to zero for high input so that it is normalizable?