Recall the lifetime (in months) of a battery is modeled by a random variable X that...

Recall the lifetime (in months) of a battery is modeled by a random variable X that has pdf fθ(x)=Kθx1(x>0)where K=ln(1/θ) for an unknown parameter θ∈(0,1) .

Assume instead that we cannot actually observe the lifetime of the batteries. Instead, we only observe if the battery is still working after τ months for some known τ to be chosen later (this is called censored data ).

Let Y1,…,Yn be our observations where Yi=1(Xi>τ) indicates that the i th battery is still working after τ months. Our goal is to estimate θ∈(0,1) (the parameter for the pdf of X ) based on this new data.

The quantity n−−√(θ~−θ) converges in distribution to N(0,σ2~) . Find the asymptotic variance σ2~ . σ2~=

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milcah answered 2 weeks ago

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