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tommik
tommik
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Assume that $Y_1, Y_2,\dots, Y_n$ are iid samples from the exponential distribution with the density function $f_{\theta}(x) = \frac{1}{\theta}e^{\frac{-x}{\theta}}$$f_{\theta}(y) = \frac{1}{\theta}e^{\frac{-y}{\theta}}$. Assume that $\hat{\theta}$ is the MLE estimate for $\theta$. How can we given a approximately confidence interval for $\theta$ based on the asymptotic distribution of $\hat{\theta}$?

We know that $\hat{\theta}$ indicated above is $\frac{Y_1+Y_2+\dots+Y_n}{n}$ and I know that $Y1+Y2+\dots+Y_n$ has a $Gamma(n,\frac{1}{\theta})$ distribution. But I do not know how to relate this to the confidence interval?

Assume that $Y_1, Y_2,\dots, Y_n$ are iid samples from the exponential distribution with the density function $f_{\theta}(x) = \frac{1}{\theta}e^{\frac{-x}{\theta}}$. Assume that $\hat{\theta}$ is the MLE estimate for $\theta$. How can we given a approximately confidence interval for $\theta$ based on the asymptotic distribution of $\hat{\theta}$?

We know that $\hat{\theta}$ indicated above is $\frac{Y_1+Y_2+\dots+Y_n}{n}$ and I know that $Y1+Y2+\dots+Y_n$ has a $Gamma(n,\frac{1}{\theta})$ distribution. But I do not know how to relate this to the confidence interval?

Assume that $Y_1, Y_2,\dots, Y_n$ are iid samples from the exponential distribution with the density function $f_{\theta}(y) = \frac{1}{\theta}e^{\frac{-y}{\theta}}$. Assume that $\hat{\theta}$ is the MLE estimate for $\theta$. How can we given a approximately confidence interval for $\theta$ based on the asymptotic distribution of $\hat{\theta}$?

We know that $\hat{\theta}$ indicated above is $\frac{Y_1+Y_2+\dots+Y_n}{n}$ and I know that $Y1+Y2+\dots+Y_n$ has a $Gamma(n,\frac{1}{\theta})$ distribution. But I do not know how to relate this to the confidence interval?

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K.N
K.N
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Assume that $Y_1, Y_2,\dots, Y_n$ are iid samples from the exponential distribution with the density function $f_{\theta}(x) = \frac{1}{\theta}e^{\frac{-x}{\theta}}$. Assume that $\hat{\theta}$ is the MLE estimate for $\theta$. How can we given a approximately confidence interval for $\theta$ based on the asymptotic distribution of $\hat{\theta}$?

We know that $\hat{\theta}$ indicated above is $\frac{Y_1+Y_2+\dots+Y_n}{n}$ and I know that $Y1+Y2+\dots+Y_n$ has a $Gamma(n,\frac{1}{\theta})$ distribution. But I do not know how to relate this to the confidence interval?

Assume that $Y_1, Y_2,\dots, Y_n$ are iid samples from the exponential distribution with the density function $f_{\theta}(x) = \frac{1}{\theta}e^{\frac{-x}{\theta}}$. Assume that $\hat{\theta}$ is the MLE estimate for $\theta$. How can we given a approximately confidence interval for $\theta$ based on the distribution of $\hat{\theta}$?

We know that $\hat{\theta}$ indicated above is $\frac{Y_1+Y_2+\dots+Y_n}{n}$ and I know that $Y1+Y2+\dots+Y_n$ has a $Gamma(n,\frac{1}{\theta})$ distribution. But I do not know how to relate this to the confidence interval?

Assume that $Y_1, Y_2,\dots, Y_n$ are iid samples from the exponential distribution with the density function $f_{\theta}(x) = \frac{1}{\theta}e^{\frac{-x}{\theta}}$. Assume that $\hat{\theta}$ is the MLE estimate for $\theta$. How can we given a approximately confidence interval for $\theta$ based on the asymptotic distribution of $\hat{\theta}$?

We know that $\hat{\theta}$ indicated above is $\frac{Y_1+Y_2+\dots+Y_n}{n}$ and I know that $Y1+Y2+\dots+Y_n$ has a $Gamma(n,\frac{1}{\theta})$ distribution. But I do not know how to relate this to the confidence interval?

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K.N
K.N
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Confidence interval for exponential distribution with MLE

Assume that $Y_1, Y_2,\dots, Y_n$ are iid samples from the exponential distribution with the density function $f_{\theta}(x) = \frac{1}{\theta}e^{\frac{-x}{\theta}}$. Assume that $\hat{\theta}$ is the MLE estimate for $\theta$. How can we given a approximately confidence interval for $\theta$ based on the distribution of $\hat{\theta}$?

We know that $\hat{\theta}$ indicated above is $\frac{Y_1+Y_2+\dots+Y_n}{n}$ and I know that $Y1+Y2+\dots+Y_n$ has a $Gamma(n,\frac{1}{\theta})$ distribution. But I do not know how to relate this to the confidence interval?