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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 vote
1 answer
759 views

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 …
BLaursen's user avatar
  • 303
4 votes
2 answers
367 views

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 …
BLaursen's user avatar
  • 303