I am trying to use mle()
function in MATLAB to estimate the parameters of a 6-parameter custom distribution.
The PDF of the custom distribution is
![enter image description here](https://i.stack.imgur.com/kCGVZ.png)
and the CDF is
![enter image description here](https://i.stack.imgur.com/UPvYL.png)
where Γ(x,y) and Γ(x) are the upper incomplete gamma function and the gamma function, respectively. α, θ, β, a, b, and c are the parameters of the custom distribution. K is given by
![enter image description here](https://i.stack.imgur.com/3lv7T.png)
Given a data vector 'data
', I want to estimate the parameters α, θ, β, a, b, and c.
So, far I have come up with this code:
data = rand(20000,1); % Since I cannot upload the acutal data, we may use this
t = 0:0.0001:0.5;
fun = @(w,a,b,c) w^(a-1)*(1-w)^(b-1)*exp^(-c*w);
% to estimate the parameters
custpdf = @(data,myalpha,mybeta,mytheta,a,b,c)...
((integral(@(t)fun(t,a,b,c),0,1)^-1)*...
mybeta*...
igamma(myalpha,((mytheta/t)^mybeta)^(a-1))*...
(mytheta/t)^(myalpha*mybeta+1)*...
exp(-(mytheta/t)^mybeta-(c*(igamma(myalpha,(mytheta/t)^mybeta)/gamma(myalpha)))))...
/...
(mytheta*...
gamma(myalpha)^(a+b-1)*...
(gamma(myalpha)-igamma(myalpha,(mytheta/t)^mybeta))^(1-b));
custcdf = @(data,myalpha,mybeta,mytheta,a,b,c)...
(integral(@(t)fun(t,a,b,c),0,1)^-1)*...
integral(@(t)fun(t,a,b,c),0,igamma(myalpha,(mytheta/t)^mybeta)^mybeta/gamma(myalpha));
phat = mle(data,'pdf',custpdf,'cdf',custcdf,'start',0.0);
But I get the following error:
Error using mlecustom (line 166)
Error evaluating the user-supplied pdf function
'@(data,myalpha,mybeta,mytheta,a,b,c)((integral(@(t)fun(t,a,b,c),0,1)^-1)*mybeta*igamma(myalpha,((mytheta/t)^mybeta)^(a-1))*(mytheta/t)^(myalpha*mybeta+1)*exp(-(mytheta/t)^mybeta-(c*(igamma(myalpha,(mytheta/t)^mybeta)/gamma(myalpha)))))/(mytheta*gamma(myalpha)^(a+b-1)*(gamma(myalpha)-igamma(myalpha,(mytheta/t)^mybeta))^(1-b))'.
Error in mle (line 245)
phat = mlecustom(data,varargin{:});
Caused by:
Not enough input arguments.
I tried to look into the error lines but I can't figure out where the error actually is.
Which function lacks fewer inputs? Is it referring to fun
? Why would mle
lack fewer inputs when it is trying to estimate the parameters?
Could someone kindly help me debug the error?
Thanks in advance.
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