A set of 10 observations from the given distribution calculate the values of the maximum likelihood estimate and the method-of-moments estimate of theta: .9960, .3125, .4374, .7464, .8278, .9518, .9924, .7112, .2228, .8609
I think the formula to use is estimate theta = -n/ln(a pie symbot with n above and i=1 below and to the right X and sub i.

Question

A set of 10 observations from the given distribution calculate the values of the maximum likelihood estimate and the method-of-moments estimate of theta: .9960, .3125, .4374, .7464, .8278, .9518, .9924, .7112, .2228, .8609
I think the formula to use is estimate theta = -n/ln(a pie symbot with n above and i=1 below and to the right X and sub i.

zarkon · Answer

"from the given distribution"

what distribution?

anonymous · Answer

i don't for sure. Let f(x,theta) = thetax^(thata-1), 0 < x <1, theta belongs to omega = {theta: 0 < theta < infinity}. Let X1, X2, ....Xn denote a random sample of size n from this distribution.