Not seeing axis labels in Power Statistics ubunto 20.04

I have freshly installed ubunto 20.04 and quite new to the ecosystem so any help would be great.
Here’s what is see in Power Statistics.

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.

statistics – Can Mutual Information based feature selection be used when the input variables are numerical and the output is categorical?

I am working on a machine learning project for a classification problem. In the dataset the input variables are numerical and the output is categorical. Is it appropriate to apply the Mutual Information based feature selection approach here? I am confused as I have gone through some articles and they have suggested applying ANOVA/ Kendall’s rank correlation coefficient while using numeric inputs and categorical output.

Selecting Feature Selection Method

statistics – How many BTC transactions happened in 2019?

I’m interested in a comparison between different blockchains and payment networks.

Bitcoin has a block time of around 10 minutes, so there should be roughly 52,560 blocks in one year. However, the number of transactions per block varies.

Is the number of BTC transactions that happened in 2019 document somewhere?

(Extra question: Is the volume in BTC or even USD at the time of the trade available?)

statistics – Problem about Multivariate Probability Distributions

I was solving this problem and I have faced a doubt regarding part c].

I attach you the statement:
enter image description here

My question was regarding part c], maybe it is so simple, but I do not know how to correctly approach it.

Thank you,

A.N.J.

statistics – Sliding window max/min algorithm without dynamic allocations

I’m working on a suite of DSP tools in Rust, and one of the features of the library is a collection of windowed statistics (mean, rms, min, max, median, etc) on streams of floating-point samples. The user provides an iterator of floats and a fixed-size mutable slice/array of floats as inputs, and get back a iterator that lazily calculates the desired stat one sample at a time. The contents of the float slice/array become the initial window, and can be used as scratch space internally. This slice/array also determines the sliding window size.

// A sliding mean with a window size of 64, initially filled with 0.42.
let sample_iter = /* an iterator that yields floats */;
let buffer = (0.42; 64);
let sliding_mean_iter = SlidingMean::new(sample_iter, buffer);

I’d ideally like to have my library also usable in an embedded environment, and so far I’ve been able to do so by not using any dynamic memory allocations.

As of now, I have efficient mean and rms implementations, but I’m stumped on the windowed min/max. Looking up sliding window min/max algorithms online(1)(2), I see that:

  1. A naive approach of scanning the window after each update leads to a O(nk) runtime, where n is the length of the input iterator and k is the window length. This feels like it could be inefficient for larger window sizes.
  2. Using a deque allows for an efficient implementation of O(n) (with amortized insertion of O(1)), but using a deque would require dynamic allocations.
  3. Since the passed-in buffer is overloaded to both set the initial window contents as well as to serve as scratch space, I can’t mess with the type of that, it has to stay as a slice/array of plain floats. This means I can’t make it an array of (int, float) to store array indices alongside the data, for example.

Are there any clever tricks or optimizations I can use to have my cake (efficient sliding min/max) and eat it too (avoid having memory allocations)?

statistics – Dice mechanic that handles very easy and very difficult tasks

I’ve always liked the Ars Magica stress dice mechanic.

Roll a d10 – a zero indicates a potential problem, a one doubles the next roll (where a subsequent 0 is a 10) and anything else is the value given.

If a zero is rolled, you then get to roll a number of botch dice according to how risky the action was, a single die if it was not particularly risky, up to dozens or more (botching a casting roll in a divine aura when using raw vis to boost your spell casting *8′). If a botch die comes up zero, something has gone badly wrong – the character has actually botched. If you rolled more than one botch dice and more than one of them came up zero multiple zero’s you have the potential for a double botch or triple botch etc. which allow for more extreme failures. If non of the botch dice come up zero, then you’ve been lucky and you just got a zero on the roll – which may still be enough to succeed if your stat/skill is high enough.

It doesn’t have the ugly discontinuities that the shadow-run exploding dice mechanic has (what use is difficulty 6?), it allows botches to be 1 in a 100 or worse depending on risk and very occasionally allows really quite awesome rolls (one time in 10,000 you could roll 80 with the sequence 1,1,1,10).

It also leads to the amusing “Yes! Going up!” only to be followed by “Oh, only to 4” moments later.

Ars also has the concepts of simple and quality dice. Simple dice are just a straight 1-10 roll, for un-stressful situations where there is no chance of a catastrophic failure, but no chance of an exceptional success either. Quality dice rolls are the best kind. These rare beasts are for situations where there is no chance of a botch, but a small chance of things going exceptionally well.

The combination of these three basic dice mechanics provides a rich set of options for the Ars Magica GM to call upon to randomise outcomes.

Ars also has lovely rules for long term development. Want to research a level 30 spell but only have a lab total of 32, then that will take you 15 seasons (3.75 years) of downtime†, so it would be better to spend a few seasons studying your arts to bring your lab total up to 38 and then you can complete the research in 4 seasons‡. †2 (32-30) and ‡ 8 (38-30) points per season towards the 30 points required.

If you want, you could allow rolls to be re-rolled with whatever PC luck mechanic you use (Fate points in Warhammer, confidence in Ars, possibilities in Torg etc.). Each re-roll you allow makes it 10x less likely that characters are will botch and gives the players the chance to decide whether they use up that re-roll on the easy, but unlucky roll, or save it for an important roll later.

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.

probability or statistics – Stochastic noise with known propability density function

How can I generate samples for random function, which functional “probability density” is known? When I say “probability density” for random function $xi(mathbf{q},t)$, I mean, that there is such a functional $P(xi(mathbf{q},t))$, that all the mean values due to the $xi$ realizations should be calculated as following path integral:

$langle A(xi)rangle_{xi}=int mathcal{D}xi A(xi) P(xi)$.

In my particular case this PDF is the following:

$
P(xi(mathbf{q},t))= exp left(- int d z int frac{d^{2} q}{(2 pi)^{2}} q^{11/3}|{xi}|^{2}right)
$

So the process is gaussian in a functional sense. I understand, that it is always possible to make your model discrete and manually simulate the process, but is there some built-in instrument in Mathematica, which allows you to deal with such things?

Thank everyone in advance!