What is non asymptotic confidence interval?
Non asymptotic confidence intervals for a binomial proportion p can be calcu- lated by the use of the F distribution, which is related to the binomial distribution via the incomplete beta function. Such confidence intervals can be easily calculated using modern statistical software.
How do you show something is a pivotal quantity?
The random variable Q is said to be a pivot or a pivotal quantity, if it has the following properties: It is a function of the observed data X1, X2, X3., Xn and the unknown parameter θ, but it does not depend on any other unknown parameters: Q=Q(X1,X2,⋯,Xn,θ).
How to find a confidence interval using as pivotal quantity?
Find a confidence interval for θ using as pivotal quantity a function of the maximum likelihood estimator for θ. Well, using the logaritmic version of the likelihood function, I got that the MLE of θ is T1 = − n n ∑ i = 1logxi. Is this correct? And how could I use a function of it as a pivotal quantity?
Is the CI an asymptotic interval or a confidence interval?
No it’s not wrong. Pivot the quantity $ heta \\bar{X}$ to get the CI in terms of $ heta$.$\\endgroup$– JohnKJun 6 ’15 at 21:11 $\\begingroup$But this is also an asymptotic interval?
Can a pivotal quantity be a function of θ?
I know that a pivotal quantity is a function of the sample and the parameter, whose distribution doesn’t depend on θ. Assuming you want a confidence interval for θ, you may use the CLT or a known chi distribution for variances and some integrals to get an interval for the parameter.
How to find confidence interval for exponential distribution?
Confidence interval for exponential distribution Ask Question Asked6 years, 1 month ago Active3 years, 2 months ago Viewed17k times 4 1 $\\begingroup$ Let $X_1,…,X_n$ random sample of $X$~$exp( heta)$. i) Find a exact confidence interval for $ heta$ with coefficient of confidence equal to $\\gamma$