Questions tagged [conditional-distribution]
8 questions
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Predictive Posterior Distribution of Normal Distribution with Unknown Mean and Variance
Suppose that $x_{i}|\mu,\sigma^{2} \sim \mathcal{N}(\mu,\sigma^{2})$ for $i = 1,...n$. Assume that the assigned prior distributions are $\mu$ ~ $\mathcal{N}$($\mu_{0}$, $\sigma^{2}_{0}$) and $\tau \sim Gamma(ξ_{0}, ξ_{0})$ with $\tau =…
StatBeginner
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How do I find the conditional distribution of a normal r. v. z, given that I know the sum of z and another normal r. v. x is greater than some value?
Suppose I have two independent normal random variables, $X$ and $Z$ with $\mu_x$, $\sigma^2_x$ and $\mu_z$, $\sigma^2_z$. Suppose I also know that $x+z\geq y$. How do I find the conditional distribution of $z$, that is $f(Z|x+z\geq y)$?
What I have…
thagomizer
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Find the conditional distribution of $(x_2, x_3),$ given $x_1$
If we let $x∼N_3(\mu, \Sigma)$ with $\mu^T=(\mu_1,\mu_2,\mu_3)$ and $\Sigma=\begin{pmatrix}\sigma ^2&\sigma ^2\rho &\sigma \:^2\rho \:\\ \sigma \:^2\rho \:&\sigma \:^2&\sigma \:^2\rho \:\\ \sigma \:^2\rho \:&\sigma \:^2\rho \:&\sigma…
PythonDaniel
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Strict stationarity in terms of conditional distributions
Let's start with the definition of a strictly stationary process: The process $\{X_t\}=\{X_1,X_2,X_3,X_4\}$ is strictly stationary if the joint distribution of the vector $(X_1,...,X_n)$ and the time shifted vector $(X_{1+h},...,X_{n+h})$ is the…
ColorStatistics
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How to Interpret Conditional Distribution
Considering the following contingency table:
We calculate the conditional distribution for the city Manchester:
Why do we need the conditional distribution and how we interpret the result?
Is conditional distribution different from conditional…
Infinity
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1
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Identity of ${{\mathit f}({\mathbf z} {\mid} {\mathbf x)}}$ and ${\mathit f}$($\mathbf {z}$) under normality - a peculiar case
I am a newbie to econometrics, so kindly excuse me if I sound too naive.
This is what Fumio Hayashi says on page 34 of "Econometrics":
Recall from probability theory that the normal distribution has several convenient
features:
• The…
eisendon
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1
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1 answer
Gibbs sampling example of a bivariate normal with unknown correlation
I'm looking for an example of using Gibbs sampling with a bivariate normal, where the correlation parameter is not fixed or known. In other words, what is the conditional distribution of the correlation $\rho$?
There are many examples out there…
Shravan Vasishth
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Use Kernel Density Estimation for Prediction
I would like to use the KDE to predict future positions of surrounding vehicles. So given a set of data [I: some input features, O: future position] I learn the joint distribution of the input and output with KDE. Then I compute the distribution…
