Questions tagged [probability-or-statistics]

Questions about systematic data collection and organization, or the application of probability theory to model the inherent patterns and properties of sampled data, underlying data distribution(s) or random processes.

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How to extract viewership data and what kind of distribution should describe youtube viewership for events in a video?

This is actually a 2-in-one question. I am a big chess fan, and I have been following the FIDE candidates tournament closely. I was watching an older interview where IM Levi Rozman interviews GM Ian ...
ydd's user avatar
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1 vote
1 answer
40 views

Issue with FullSimplify in StirlingS2 definition

I have previously asked a question about a problem simplifying an expression in Mathematica. The solution was to expand the definition of StirlingS2. This time, I ...
Cardstdani's user avatar
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1 answer
37 views

Problem calculating mean of probability distribution

I have a discrete probability distribution where $P(X=x)=(Factorial[n]/(n^x))*StirlingS2[x-1,n-1]$. So, when trying to calculate its mean with the following property: $\mu = \sum_{i} x_i \cdot P(x_i)$,...
Cardstdani's user avatar
-1 votes
0 answers
30 views

Higher moments dominated by mean and variance [closed]

Let {$X_{k}$} be i.i.d variables, $\mathbb{E}(X_{k})=0$,$Var(X_k)=1$. Fix $u > 0$, denote $\widetilde{X}_{k}=X_{k}\mathbb{I}_{|X_{k}|>u}-m(u)$, where $m(u)=\mathbb{E}(X_{k}\mathbb{I}_{|X_{k}|>...
Guocheng Zhen's user avatar
0 votes
1 answer
57 views

Attempting Data Analysis with FlightData information

I am trying to use data collected from the FlightData[] command to analyze departure delay data for a school project. I am getting as far as using a command to get the data, taking it into a named ...
rnb95312's user avatar
1 vote
0 answers
72 views

Is there a difference in the definition of the pth percentile in Mathematica? [closed]

The pth percentile of a set of n data can be calculated by the following steps: Step 1: arrange the original data in ascending order. Step 2: calculate i=n*p%. Step 3: if i is not an integer and the ...
csn899's user avatar
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1 answer
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How to solve a problem about data when a certain percentile number is known?

Given that the 75th percentile of the data set is 6, how can we find the value of parameter a? data = {1, 1, a, 4, 5, 5, 6, 7} Why didn't the following method ...
csn899's user avatar
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1 answer
50 views

Computation of critical value in F-distribution [closed]

Is there a way to manually compute the critical value of f-distribution from this table for df1=df2=417? It should be 1.21194 Thanks
johnniem's user avatar
3 votes
3 answers
155 views

How to use Mathematica to find the mode of a set of data? [closed]

Mode[{2, 3, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10}] Why can't the mode command be used to find the mode of a set of data?
csn899's user avatar
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48 views

How to quickly sample points according to the given distribution?

Consider the following points sampler: ...
John Taylor's user avatar
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2 answers
78 views

NExpectation with complex condition

When I run a computation for NExpectation with a condition of the following form -- T>R>P -- the computation runs fine. But when I add another inequality -- T>R>P>S -- it gives me an '...
Paul Studtmann's user avatar
5 votes
1 answer
207 views

P-Values For LinearModelFit Changing Due To Ordering Of Features

The arbitrary ordering in a linear model of the independent variables should not impact the p-values for the coefficients of said model. However that is exactly what is happening here ...
Daniel Berkowitz's user avatar
9 votes
5 answers
830 views

Create n random points on [0,1] with minimum distance

Given a positive integer n and a small positive real number s. How to create distribution for ...
imida k's user avatar
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2 votes
0 answers
58 views

Equivalent of `MomentConvert` for free moments/free cumulants? [closed]

I'm looking for Mathematica implementation of conversion between free moments and free cumulants. For instance, for traditional moments we have from ...
Yaroslav Bulatov's user avatar
5 votes
1 answer
90 views

Alternative Representation for Energy Levels and Energy Level Density (II)

Following my previous question, I want a graph that must look like this (the lower image is taken from the Wikipedia page for the Microcanonocal Ensemble-->> Quantum Mechanical), The code for ...
user444's user avatar
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1 answer
65 views

Estimating the shape of the distribution of histogram

Here is the data: data = {37., 76, 81, 81, 28, 29, 18, 18, 27, 44, 18, 17, 70, 87, 45, 32, 88, 20, 18, 44, 17, 51, 24, 37, 24, 21, 18, 18, 17, 44, 25, 16, 45, 31, 74, 38, 16, 35, 17, 44, 34, 27, 87, ...
SciJewel's user avatar
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1 vote
1 answer
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How to compute a weighted mean as a measure of central tendency?

Imagine I have data points in triplicates, as follows $$ L=\begin{pmatrix} p_{11} & p_{12} & p_{13}\\ p_{21} & p_{22} & p_{23}\\ & \vdots &\\ p_{n1} & p_{n2} & p_{n3} \...
sam wolfe's user avatar
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1 vote
2 answers
150 views

The best way to guess the needed data using Mathematica?

I have a question, which is not entirely related to Mathematica, and would appreciate any help on this matter. I have the following dataset, which shows the growth of a bacterium in a specific medium: ...
A novice's user avatar
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7 votes
4 answers
360 views

Getting formulas like $E[\operatorname{Tr}(A^3 (A^T)^3]=n^4+10n^2+4n$

Suppose $A$ is an random $n\times n$ matrix with standard normal entries. A user was able to obtain the following formula by enumerating all diagrams by hand: $$E[\operatorname{Tr}(A^3 (A^T)^3]=n^4+...
Yaroslav Bulatov's user avatar
2 votes
1 answer
67 views

Joint Moments of Stochastic Process at Different Times

Suppose I have a random process defined in Mathematica, e.g. h = TelegraphProcess[a] I know you can use Mathematica to calculate different statistics like the mean,...
Sahand Tabatabaei's user avatar
1 vote
1 answer
152 views

How to randomly sample small rotations?

I need a random rotation matrix that rotates random vectors by $\approx \arccos 0.9$ RandomVariate[CircularRealMatrixDistribution[n]] gives rotation matrices that ...
Yaroslav Bulatov's user avatar
1 vote
1 answer
140 views

How to do BayesianMinimization in 2D?

Studying a new experimental BayesianMinimization command in 14.0 and following an example from the documentation ...
user64494's user avatar
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4 votes
2 answers
179 views

`Expectation` of a positive random variable gives negative results

Using Expectation to find $E[\operatorname{score}^2]$ evaluates to $-\frac{1}{6}$ below, why is this happening? ...
Yaroslav Bulatov's user avatar
2 votes
1 answer
69 views

"Piecewise" in "ProbabilityDistribution" would not affect the result

...
Y. zeng's user avatar
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3 votes
1 answer
87 views

Why can't "TransformedDistribution" give a result but finding the probability first and then the derivative can?

PDF[TransformedDistribution[Sin[X], Distributed[X, ProbabilityDistribution[2*x/(Pi^2), {x, 0, Pi}]]], y] // Simplify produces ...
Y. zeng's user avatar
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2 votes
2 answers
204 views

Calculating conditional expectation for uniform distribution over a trapezoid

I have a bivariate uniform distribution, defined over a trapezoid $\Omega$ with vertices $(2, 2), (1, -2), (-2, -2), (-2, 2)$: $$\vec{\xi} = (\xi_1, \xi_2) \sim \mathcal U (\Omega).$$ How can I ...
Maks's user avatar
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0 votes
1 answer
73 views

Computing statistics of sample average over $n$ IID variables

I need to plot $E[\log|1-a X|]=0$ as a function of $a$ where $X$ is sample average of $n$ IID draws from standard $\chi$^2. The following is a symbolic approach (borrowed from here) which works for $n=...
Yaroslav Bulatov's user avatar
1 vote
0 answers
55 views

Solving a System of Recursively Defined Equations in Mathematica

I am trying to solve a system of equations in Mathematica where the variables are recursively defined. The system represents a probability distribution, and I want to find the values of the variables ...
Resting Platypus's user avatar
2 votes
1 answer
93 views

Numerical differentiation of summation of implicit regions

I'm very new to mathematica and this forum, so I apologize for the poor formatting. I am trying to find a probability density function, given a continuous and piecewise differentiable cumulative ...
Carson Newman's user avatar
2 votes
0 answers
56 views

Deriving Expressions for R1, R2, and R12 , Normalized Coincident Detection Probability, and LG Mode Formalism

I am currently reviewing a research paper on orbital angular momentum entanglement between two photons (signal and idler) generated from a pump photon via SPDC. The paper introduces the following ...
Qubit's user avatar
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5 votes
2 answers
271 views

Nearest-neighbor density estimation in Mathematica

I want to use SmoothHistogram-like plot using smoothing kernel $f(x)$ which is uniform $(a,b)$ with $a,b$ adjusted for each $x$ to include 11 points on the left, ...
Yaroslav Bulatov's user avatar
1 vote
1 answer
54 views

Leading significant digits

Given that the initial area in a Sierpinski triangle is A_0 and the subsequent areas $$(A_n) =A_0 (3/4)^n$$ , what is the formula to calculate the leading ...
Rubens Vilhena Fonseca's user avatar
0 votes
1 answer
98 views

Bandwidth selection for histograms in bounded domain?

Does anyone have tips how to do proper bandwidth selection to visualize density which is known to be strictly positive? Example below uses SmoothHistogram and ...
Yaroslav Bulatov's user avatar
2 votes
1 answer
143 views

One more incorrect result of CDF

In 13.3.1 on Windows 10 I find ...
user64494's user avatar
  • 26.4k
5 votes
2 answers
236 views

An incorrect result of CDF

In 13.3.1 on Windows 10 I execute ...
user64494's user avatar
  • 26.4k
0 votes
1 answer
80 views

Any luck estimating a multivariate hidden Markov process?

I am having problems using EstimatedProcess to estimate a multivariate HiddenMarkovProcess. I'm following the work of a paper, so I know this method is feasible. In brief, given 2 economic variables: ...
XXX's user avatar
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3 votes
1 answer
105 views

Fast multivariate Cauchy sampling?

I've been using the code below to efficiently sample from multivariate Gaussian with diagonal covariance matrix. Now I want to try the same for Cauchy samples, however replacing ...
Yaroslav Bulatov's user avatar
3 votes
4 answers
355 views

Sampling from intersection of $n$-sphere and hyperplane

Edit How do I uniformly sample from intersection of $n$-sphere centered at 0 and an arbitrary hyperplane for $n\ge3$? Below is an approach using FindInstance to ...
Yaroslav Bulatov's user avatar
-3 votes
1 answer
131 views

How to calculate the Poisson index of dispersion? [closed]

I came across the Poisson index of dispersion. I find it very interesting. But I didn't understand how to apply it. It is simply necessary: ...
Zollikofen4's user avatar
0 votes
2 answers
77 views

Gamma Distribution: what to do after calculating Shape and Rate? How to proceed? [closed]

I got stuck while applying Gamma Distribution. Having Mean = 5 and Standard Deviation = 2, here's how I preceded: ...
Zollikofen4's user avatar
1 vote
1 answer
97 views

How can we plot horizontal prediction bands?

1. Problem statement Some game days before the end of a league season I want to show the possible final rankings (depending upon the results of the outstanding games). 2. Example data (situation after ...
eldo's user avatar
  • 69.8k
3 votes
1 answer
181 views

CorrelationTest vs PearsonCorrelationTest

I understand that these two functions consider different null hypotheses. However, although I can reproduce the calculation related to PearsonCorrelationTest from scratch, I cannot reproduce the p-...
Luis Diambra's user avatar
0 votes
0 answers
64 views

A geometric application of Benford's law [duplicate]

I would like some help solving the following problem using Mathematica: Show that, no matter what the initial area of an equilateral triangle is, the sequence of areas (painted in black) of the ...
Rubens Vilhena Fonseca's user avatar
3 votes
2 answers
192 views

Sort sequences by their "randomness"

Example matrix (rows always have equal lengths) ...
eldo's user avatar
  • 69.8k
1 vote
2 answers
121 views

Compute Central Moments of Vector

Say we have three stochastic variables defined as follows: ...
Mirko Aveta's user avatar
  • 2,192
5 votes
4 answers
403 views

An accumulated moving average

1. Problem statement In accordance with the standard definitions the inbuilt MovingAverage ...
eldo's user avatar
  • 69.8k
8 votes
6 answers
1k views

Problem on geometric probability

This is a problem from the recent 18th Kolmogorov competition on probability theory and statistics 2023. A random point P is chosen in an equilateral triangle. What ...
user64494's user avatar
  • 26.4k
1 vote
1 answer
113 views

Pick random value based on list of probabilities

I'm pretty sure this must have been asked before, but I can not find the duplicate. Given a list of values with their probabilities ...
infinitezero's user avatar
  • 1,419
0 votes
0 answers
40 views

CompiledFunction fails for Variance with a rank 3 input

Why does compiling Variance for a rank 3 input fail but Mean works? ...
IntroductionToProbability's user avatar
0 votes
1 answer
59 views

Function to generate analytic solution of StandardDeviation of a list given sublists

Motivation I have the Mean and StandardDeviation of several lists of equal size but I don't know the elements of those lists. I ...
IntroductionToProbability's user avatar

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