sorry for unformatted question, but advanced editor doesn\'t seem to be working atm
let p > 0 and X_n be from a random sample with distribution f(x)=p(1-x)^(p-1), 0 <= x <= 1
Find the log likelihood of p.
What I\'ve got:
L(p) = prod(f(x)) = p(1-x_1)^(p-1)*p(1-x_2)^(p-1)...= p^n(1-x)^n(p-1)
l(p) = ln(L(p)) = ln(p^n)(1-x)^(n*ln(p)-n)
Solution
ln L(p) = ln f(xi) = ln(p(1-xi)^(p-1)) = (ln p + (p-1)ln(1-xi))
= ln p + (p-1)ln(1-xi)
= n ln p + (p-1) ln(1-xi)
= n ln p + (p-1)(ln(1-x_1) + ln(1-x_2) + ln(1-x_3) + ..... + ln(1-x_n)).
sorry for unformatted question, but advanced editor doesnt seem to.pdf
1. sorry for unformatted question, but advanced editor doesn't seem to be working atm
let p > 0 and X_n be from a random sample with distribution f(x)=p(1-x)^(p-1), 0 <= x <= 1
Find the log likelihood of p.
What I've got:
L(p) = prod(f(x)) = p(1-x_1)^(p-1)*p(1-x_2)^(p-1)...= p^n(1-x)^n(p-1)
l(p) = ln(L(p)) = ln(p^n)(1-x)^(n*ln(p)-n)
Solution
ln L(p) = ln f(xi) = ln(p(1-xi)^(p-1)) = (ln p + (p-1)ln(1-xi))
= ln p + (p-1)ln(1-xi)
= n ln p + (p-1) ln(1-xi)
= n ln p + (p-1)(ln(1-x_1) + ln(1-x_2) + ln(1-x_3) + ..... + ln(1-x_n))
