# Tag Info

Accepted

### Sampling from $P(x) \propto \cosh^{m}(a x) e^{-x^{2}/2}$

The distribution that the OP seeks is a straightforward extension of the formula for the case $m=1$ that Xi'an derived in the linked answer. Suppose that $P(x) \propto (\cosh(ax))^m \exp(-x^2/2)$. ...
• 46.3k

### Sampling from $P(x) \propto \cosh^{m}(a x) e^{-x^{2}/2}$

Building on the answer of Dilip, for non-integer $m$, letting $\{m\}=m-\lfloor m\rfloor$ denote the fractional part of $m$, and using the fact that $\cosh x\le \exp|x|$, the (unnormalized) target ...
• 10.7k

### Density Forecasts with GAMLSS

GAMLSS uses distributional assumptions, and estimates and forecasts conditional distribution parameters. So you would need to use the what parameter to ...
• 121k
Accepted

### Zero variance but non-zero skewness

If the variance is 0 then all the values have to be the same and there can't be any skew.
• 117k

### A problem on bivariate random variables

Remember, when $\mathbf X\mapsto \mathbf Y$ via a one-one onto transformation, say $y_i:= g_i(x_1, \ldots, x_n),$ and $h_i:=g_i^{-1},$ then if $\frac{\partial h_i}{\partial y_j}$ are continuous for ...
• 7,887
1 vote
Accepted

### comparing pdf in log scale

The big advantage of using a log-scale here is that it allows you to see the relative comparison properly in the tails where the relevant probability density is extremely low. If you looked at this ...
• 123k
1 vote
Accepted

### Understanding the multivariate normal density proportional

$\mu^\top \Sigma^{-1} x$ is a scalar (which you can think of as a $1 \times 1$ matrix), so it is equal to its transpose: \mu^\top \Sigma^{-1} x = (\mu^\top \Sigma^{-1} x)^\top = x^\top (\Sigma^{-1})^...
• 2,188
1 vote

### Sampling from $P(x) \propto \cosh^{m}(a x) e^{-x^{2}/2}$

This is just an extended comment. With the restriction of the values of $m$ being positive integers there is an analytic solution of a mixture of normals each with variance 1 as shown by @DilipSarwate ...
• 3,684

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