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
and the CDF is
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
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.
exp()
is a function, not a variable, precise the argument
exp^(-c*w) ---> exp(-c*w)
- The starting point concerns the
6 parameters
, not only one0.1*ones(1,6)
- In custcdf
mle
requires the upper bound of the integral to be a scalar, I did some trial and error and the range is [2~9]
. for the trial some values lead to negative cdf or less than 1 discard them. - Then use the right one to compute the upper bound see if it's the same as the one you predefined.
I re-write all the functions, check them out
The code is as follow
Censored = ones(5,1);% All data could be trusted
data = rand(5,1); % Since I cannot upload the acutal data, we may use this
f = @(w,a,b,c) (w.^(a-1)).*((1-w).^(b-1)).*exp(-c.*w);
% to estimate the parameters
custpdf = @(t,alpha,theta,beta, a,b,c)...
(((integral(@(w)f(w,a,b,c), 0,1)).^-1).*...
beta.*...
((igamma(alpha, (theta./t).^beta)).^(a-1)).*...
((theta./t).^(alpha.*beta + 1 )).*...
exp(-(((theta./t).^beta)+...
c.*igamma(alpha, (theta./t).^beta)./gamma(alpha))))./...
(theta.*...
((gamma(alpha)).^(a+b-1)).*...
((gamma(alpha)-...
igamma(alpha, (theta./t).^beta)).^(1-b)));
custcdf = @(t,alpha,theta,beta, a,b,c)...
((integral(@(w)f(w,a,b,c), 0,1)).^-1).*...
(integral(@(w)f(w,a,b,c), 0,2));
phat = mle(data,'pdf',custpdf,'cdf',custcdf,'start', 0.1.*ones(1,6),'Censoring',Censored);
Result
phat = 0.1017 0.1223 0.1153 0.1493 -0.0377 0.0902
来源:https://stackoverflow.com/questions/56522903/using-mle-function-to-estimate-the-parameters-of-a-custom-distribution