probability or statistics – How to generate random variate in custom domain for a distribution?

I have a distribution defined in a particular domain of the variable but now I want to generate a random variable not in the entire domain but only in a subset of the domain. Here is what I’m trying to do

a=0.25*(Pi);
pdf= ProbabilityDistribution(1/Cos(x)^2, {x, -a, a}, Method -> "Normalize");
RandomVariate(pdf)

This will generate a random variable from the given distribution between (-a,a). But I want to generate the variable between some subset, say (-a/2,a/2). How do I do this?

I have tried changing the domain of the distribution itself but it is easy to see that this will redefine the whole distribution and is not the same as what I want.

What is the distribution of eigenvalues of $A^TA$, where $A sim N(mu, Sigma)$?

Let $A$ be a random matrix following multivariate normal distribution $N(mu, Sigma)$.

What is the distribution of the eigenvalues of $A^TA$?

A reference to the literature would be most welcome.

st.statistics – Negative binomial or Poisson distribution

I’m not sure if this problem has to be solved with a negative binomial distribution or a poisson distribution:

If the probability is 0.005 that any one person attending a parade on a
very hot day will suffer from heat exhaustion, what is the probability
that 18 of the 3000 persons attending the parade will suffer from heat
exhaustion?

st.statistics – Can the same dataset be described as Chaotic & Pareto/ Power law distribution?

I’m trying to abstract the mathematical part of the problem as much as possible before the details follow,
There’s this dynamic data set that’s $O(2^{32})$, a recent result described it as a power-law distribution, as average is approaching $1-2$ with a peak at $100$ as said. I was just motivated by the fact that there is a subset known to have sometimes values of $O(10^5)$ inside, and the 1st lesson on Statistics is that average is not enough to represent the data in such cases. Then I found previous results describing the same dataset as:

  • “is impossible to be modeled mathematically, since it is purely chaotic” (Stanford report Dec2015)

  • “Nevertheless, in the above graph there’s a distinct linear formation within the phenomenal chaos” (2017).

I came to this group to ask the Scientific opinion of the most specialized, all the complete files r downloadable & available online.

References

The Stanford Report poster

The median results 2017, although I think it has 2 groups/clusters one with a linearly increasing median & one adjacent to the X-axis (the majority by the newer results)

A 3rd fig in 2017

The Utreexo graph 2019, with green text & colored lines added by me

statistics – Fisher information of joint distribution of transformed Normal distribution

Suppose $X_1=theta+epsilon_1$ and $$X_i=sqrt{gamma}X_{i-1}+sqrt{1-gamma}epsilon_i+theta(1-sqrt{gamma})$$
Where $gamma in (0,1)$ and $theta$ is the parameter of the model. Also $epsilon_1,epsilon_2,…epsilon_n$ are iid $N(0,1)$.

What is the Fisher information of this model and for what values of $gamma$ does it tensorise. I’ve tried using the Jacobian to find the joint distribution but I’m not sure, especially when determining for which values we have tensorisation. Any help would be much appreaciated.

permissions – Sharepoint Online custom app distribution failed for co-worker, not for me

I’ve been developing and deploying a custom web part on our SPO tenant for a while. Today, my co-worker tried to deploy a new version of the app.

He successfully uploaded to the app to https://tenant.sharepoint.com/sites/apps/AppCatalog/Forms/AllItems.aspx, and pressed the “Deploy” button that popped up – just like I always do.

But in the right most column on mentioned site (which I believe in English is named something like “Error from application package”) he got a “distribution failed” error message (and a correlation ID).

I have no idea how to debug this, as I wouldn’t know even where to find any logs. As this procedure works for me, I suspect it has something to do with access rights or something.

Does anyone here have an idea why this is happening, and how we can fix it?

PS. I originally posted this over at Microsoft’s tech community, but didn’t get any responses so I’m re-posting it here.

pr.probability – Finding the K-means of the normal distribution

Let $Kinmathbb N^+$ be a parameter.

Given a distribution $q$ over the real numbers, K-means clustering aims to find $K$ centroids $c_1,ldots,c_kinmathbb R$ that minimize
$$
int_{-infty}^infty q(x)cdot min{(x-c_i)^2mid iin{1,ldots,k}}dx.
$$

We can, without loss of generality, assume that $c_1le c_2leldotsle c_k$.

What are the resulting centroids for the standard normal distribution $q=N(0,1)$?


The solution for $K=2$ is given by $c_1=-sqrt{2/pi}$ and $c_2=sqrt{2/pi}$. The reason is that the distribution is symmetric around $0$ and the expected value given that the variable is positive equals the mean of a half-normal random variable.
I am interested in computing the result for a larger $K$, e.g.,

  • What are the centroids for $K=4$?

Using WolframAlpha, after some simplifications, it seems that the solution is approximately $c_1approx -1.51, c_2approx-0.453,c_3approx 0.453, c_4approx1.51$.

How can I efficiently check if a given email address is included in a distribution list in Microsoft Outlook OWA?

From what I can see, clicking on the distribution list in Microsoft Outlook OWA doesn’t give any efficient way to check if a given email address is included in a distribution list, since would have to go through the list of email addresses included in a distribution list (which is inconvenient if the distribution list contains many email addresses):

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How can I efficiently check if a given email address is included in a distribution list in Microsoft Outlook OWA?

How to install a desktop GNU/Linux distribution on remote VPS without virtualization?

How to install a desktop GNU/Linux distribution on remote VPS without virtualization?
I want to have Desktop distro installed on some VPS. I would use it thru RDP. Is there a way to install it like on local PC?

How to use TransformedDistribution to infer The Sampling Distribution of the sample mean?

As we know the TransformedDistribution can infer a distribution of transformation like

TransformedDistribution(A*X + B, X (Distributed) NormalDistribution(μ, σ))

NormalDistribution(A μ + B, σ Abs(A))

But can we use it get The Sampling Distribution of the sample mean? Such as $X_1,X_2,cdots,X_n sim text{NormalDistribution}(μ, σ)$ then the $overline{X}=frac{X_1,X_2,cdots,X_n}{n}sim text{NormalDistribution}(μ, σ/sqrt{n})$.Can we do such symbolic derivation? My current try is

TransformedDistribution(Mean({x, y, z}), {x, y, z} (Distributed) NormalDistribution())

TransformedDistribution( 1/3 ((FormalX)1 + (FormalX)2 +
(FormalX)3), {(FormalX)1, (FormalX)2, (FormalX)3} (Distributed)
NormalDistribution(0, 1))

I have to say is not a real symbolic derivation. I hope to get $text{NormalDistribution}(μ, σ/sqrt{n})$ result. I don’t sure I have missed anything.