Attached is my project if you'd like more information. I'm not asking for a way out, I'm asking for advice. I've hit a snag and I'd like to do the project myself.
Hi all, this is my first post.
Here's the challenge:
f(x; θ) =1/θ x^((1/θ) −1)
for x ∈ [0, 1]
Is the function we're dealing with, so depending on theta, we can have either uniformly distributed (namely if theta = 1) or skewness to the right (theta < 1) or skewness to the left (theta > 1)
I've been trying to develop a statistic for theta, the most obvious one that comes to mind is the mean. From there I attempted to find a sufficient estimator of theta (or perhaps I should be trying to use the maximum likelihood estimator?)
I hit a snag in my algebra, here's what I got after simplifying their products:
((1/θ)^n) x^(∑1/θ - n)
I'm not sure whether x should be raised to the Nth power or what i'm doin...
Normally I'd break this down into ((1/θ)^n) x^(∑1/θ - n) equalling g(Θ,θ) and h(x.....xn) = 1
help out if ya'll can!
Okay, I've made some progress;
f(x1|θ) x f(x2|θ) x ..... (fxn|θ) = 1/θ Prod<xsubi> ^ ((n/θ)-1)
sorry for the crappy notation, if anyone knows an easier way to type, lemme kno
Edit:
(1/θ)^n ∏x ^ ((n/θ) - n)
I'm checking to see if theta is a sufficient estimator, but can't deal with the product of x's unless they're factored out to h(x1,x2....xn)
Should I replace the values of x with my statistic estimate of ?