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The normal, or Gaussian, distribution has a density function that is a symmetrical bell-shaped curve. It is one of the most important distributions in statistics. Use the [normality-assumption] tag for asking about testing for normality.
1
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Evaluate high-dimensional Gaussian with variance matrix $\sigma^{2}I_{n_{t}\times n_{t}}+\bo...
I need to compute the log-likelihood function in a high-dimensional
Gaussian time-series. I have the following model:
$\mathbf{y}_{t}\left|\mathcal{F}_{t-1}\sim\mathcal{N}\left(\mathbf{\boldsymbol{\m …
4
votes
2
answers
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Inference on $P\left(\left.\sum_{i=1}^{N}X_{i}\ \right|\ \sum_{i=1}^{N}X_{i}^{2}\right)$ whe...
Let:
$$X_{i}\overset{i.i.d}{\sim}\mathcal{N}\left(0,1\right)$$
Hence:
$$\sum_{i=1}^{N}X_{i}\sim\mathcal{N}\left(0,N\right)$$
and
$$\sum_{i=1}^{N}X_{i}^{2}\sim\chi^{2}\left(N\right)$$
What can b …