1
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0answers
6 views

References to papers/books that uses a kernel to smooth a discrete distribution

Since a kernel, such as Gaussian, is often used to smooth out the distribution of discrete points in 1D, 2D or 3D, I believe there must be some study materials or research work that have used this, ...
0
votes
0answers
27 views

$(X, Y)^T$ ~ multivariate normal does NOT implies that X | Y $\in$ [a,b] has normal distribution??

I just found a rather surprising fact about the multivariate normal distribution. Suppose $(X,Y)^T$ has bivariate normal distribution; $$ \begin{bmatrix} X\\ Y \end{bmatrix} \sim MVN_2 \Big( ...
1
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1answer
64 views

Importance of estimating $\sigma^2$ in linear Statistical model

Statistical model for Complete Randomized design $y_{ij} = \mu + \tau_i + \epsilon_{ij}$ where, $i$ denotes treatment and $j$ denotes observation. $i=1,2,...,k\quad and \quad j=1,2,..., n_i$ ...
1
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1answer
190 views

Well known probability distributions defined on a $n$-dimensional simplex besides the Dirichlet distribution?

Are there well known probability distributions defined on a n-dimensional simplex besides the Dirichlet distribution where the variation of of each component doesn't vary as much when the mean of the ...
1
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0answers
126 views

How can I find Multivariate normal distribution original paper? And other nature-revealing articles by the way

I want to see how Gauss get this distribution function representation. I want to understand deeper of Multivariate normal distribution. I tried but failed to search the original paper of Gauss ...