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how can i write t truncated distribution as a likelihood?

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elham kreem
elham kreem 2018-3-21
关闭： MATLAB Answer Bot 2021-8-20
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)?

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Jeff Miller
Jeff Miller 2018-3-21
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?
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Jeff Miller
Jeff Miller 2018-3-22
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.

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