Confidence interval; exponential distribution (normal or student approximation?)Let's say we have got a sample of size n from an exponential distribution with an unknown mean λ.We want to construct a confidence interval and so we can compare this:X―−λS2nto a student t-distribution with n−1 degrees of freedom.However, as in the case of the exponential distribution, we know that Var[X]=(E[X])2, so rather than introducing an estimator for variance, we can simply use one estimator, i.e:X―−λX―2n.And now the question is:Do we compare this statistic with normal distribution or again with student t-distribution?

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Confidence interval; exponential distribution (normal or student approximation?)Let&#039;s say we have got a sample of size n from an exponential distribution with an unknown mean λ.We want to construct a confidence interval and so we can compare this:X―−λS2nto a student t-distribution with n−1 degrees of freedom.However, as in the case of the exponential distribution, we know that Var[X]=(E[X])2, so rather than introducing an estimator for variance, we can simply use one estimator, i.e:X―−λX―2n.And now the question is:Do we compare this statistic with normal distribution or again with student t-distribution?

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I do not recommend to use the Student approximation. Instead, it is better to observe that ︎X1+⋯+Xn≃︎Γ(n,θ)&amp;nbsp;with&amp;nbsp;θ=1λ.Therefore,&amp;nbsp;2λ(X1+⋯+Xn)≃︎Γ(n,12)=χ2n2. Hence you can construct the required interval through the quantiles of&amp;nbsp;χ{2n}2.

Confidence interval; exponential distribution (normal or student approximation?) Let's

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