how can i write t truncated distribution as a likelihood?

i have this function

f(x)=  [(gamma((v+1)/2))/(gamma(v/2)(2π).^(1/2)* σ] *(1+((x-μ)^2)/(v*σ^2 ))).^(-(v+1)/2)*(1/ (F(b)-F(a)))

i want to write the function as likelihood function(L)?

Answer 1

[Jeff Miller]

Not entirely clear what you are asking. Without looking too closely, your equation looks like the conditional density of x for a truncated distribution such that a<=x<=b. One normally computes "likelihood" with respect to a set of data, say y_i, i=1..n. Here, you could compute that with L=prod(f(y_i)). If that isn't what you are after, can you explain a bit more?

[elham kreem]

thank you sir very much to reply you write what are you say, this is the function for t truncated distribution : i will write it as :

f(x) = k * (1+((x-μ)^2)/(vσ^2 ))).^(-(v+1)/2)*(1/ (F(b)-F(a)))

i want to write it as a likelihood function, how can i sum the bracts , if i arise it to n , can i derivative it with respect x. i want the answer as a writing not as a code.please

with my respect

[Jeff Miller]

As I understand it, the likelihood function is the same as the density function, just viewed as a function of the parameters rather than a function of the data. So you might write:

L(μ,σ|x,k,a,b) = k * (1+((x-μ)^2)/(vσ^2 ))).^(-(v+1)/2)*(1/ (F(b)-F(a)))

But I suspect that you already know this and that you are actually asking math questions that are well beyond me (sum the brackets, raise to n, and differentiate). Sorry I cannot be more helpful.

[elham kreem]

thank you at all