设X概率密度 f(x)=(θ+1)x^θ,0

问题描述:

设X概率密度 f(x)=(θ+1)x^θ,0

矩估计:E(x)=∫_(0,1) x * (θ+1)x^θ dx=∫_(0,1) (θ+1)x^(θ+1) dx=(θ+1)/(θ+2)*x^(θ+2) |_(0,1)=(θ+1)/(θ+2)令E(x)=(Σxi)/n则θ=1/(1-(Σxi)/n) - 2极大似然估计:ln p(x1,x2,...,xn) = ln f(x1) + ln f(...