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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7 votes
3 answers
234 views
+100

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+...
-3 votes
0 answers
33 views

what is event space [closed]

i want to know about event space completely what is event space and what is the requirement of event space, i mean we already know the all possible out comes in sample space(S) and we can get P( ...
1 vote
1 answer
138 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 ...
2 votes
1 answer
61 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,...
6 votes
2 answers
233 views

How do you create the Commonest function

How does the Commonest function work? How can I implement that functionality without using that command?
1 vote
1 answer
129 views

How to do BayesianMinimization in 2D?

Studying a new experimental BayesianMinimization command in 14.0 and following an example from the documentation ...
15 votes
2 answers
741 views

How can the Theil-Sen estimator be made to work on larger datasets?

The Theil-Sen estimator finds the slope and intercept of a line passing through a set of points by calculating the median slope and median intercept of the set of lines passing through all possible ...
1 vote
1 answer
149 views

Non-Gaussian Hidden Markov Process

I'm using EstimatedProcess to simulate a HiddenMarkovProcess with two states using data derived from different ARIMA processes <...
3 votes
1 answer
86 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 ...
4 votes
2 answers
178 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? ...
2 votes
1 answer
69 views

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

...
2 votes
2 answers
201 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 ...
0 votes
1 answer
72 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=...
1 vote
5 answers
426 views

How to map the second highest value in each row of a matrix?

I have a matrix with three or more columns called mat. I would like to map the second highest value in each row of mat into its ...
1 vote
0 answers
51 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 ...
0 votes
2 answers
529 views

How to plot this pdf?

Let $x\sim N(\mu,\sigma^2)$ and $y=\max\{e^{x-1}-\kappa,0\}$. How to get and plot the pdf of y? In particular, there will be a probability mass at $y=0$, which is a nondifferentiable point. I tried <...
2 votes
1 answer
255 views

Second Order Probability

The literature has considerable discussion of higher order probabilities and in particular second-order probability, which is the probability that the true probability of something has the value P. ...
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 ...
1 vote
2 answers
950 views

Integration of linked PDFs over probability simplex

I'm trying to integrate the following expression: f[a1,p1+p2+p3+p4]*f[a2,p2+p3+p4]*f[a3,p3+p4]*f[a4,p4] Where ...
2 votes
0 answers
51 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 ...
1 vote
1 answer
151 views

Can this previously solved three-dimensional constrained integration also be solved with certain added products in the integrand?

In Solved3DConstrainedIntegration the constrained three-dimensional (Hilbert-Schmidt-metric-based HSmetric) integration problem for the absolute separability probability of the two-qubit (quantum bit)...
5 votes
2 answers
269 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, ...
1 vote
1 answer
53 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 ...
0 votes
1 answer
96 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 ...
2 votes
1 answer
142 views

One more incorrect result of CDF

In 13.3.1 on Windows 10 I find ...
1 vote
1 answer
298 views

Evaluate 3D- and 5D-constrained integrals for absolute separability probabilities

In a recent posting, TwoQubits user JimB, employing a change-of-transformations put forth by N. Tessore, was able to confirm a formula for the "two-qubit absolute separability Hilbert-Schmidt ...
8 votes
1 answer
431 views

Can LearnDistribution learn conditionality?

I would like to apply LearnDistribution to multivariate conditional distributions. Here's a simple artificial example: ...
2 votes
2 answers
105 views

Optimization of a Markov сhain with symbolic transition rate

I am trying to work on 1D random walk that can move to left, right or stay with probabilities $p_i$,$q_i$,$r_i$ that changes with the site $i$. I am trying to simulate this by using a recurrence ...
5 votes
2 answers
236 views

An incorrect result of CDF

In 13.3.1 on Windows 10 I execute ...
6 votes
1 answer
33k views

Reversing Autocorrect, aka how to find the word that was supposed to be there

When I receive messages from people using their smartphones I usually see typos and, worst, typos corrected by Autocorrect. Now, I receive messages in English, which is not my first language. I can ...
7 votes
6 answers
313 views

Manually modify lists for survival analysis

I have a series of lists of this form: {1, 1, 1, 1, 0, 0, 1, 1}. I would like to perform a survival analysis on these lists. To do that, I need a code that would ...
0 votes
1 answer
77 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: ...
5 votes
2 answers
161 views

TransformedDistribution using $k$ iid random variables, but $k$ not fixed

Can I create a TransformedDistribution that uses $k$ independent identically distributed (i.i.d.) random variables where $k$ is not fixed? This question is closely ...
3 votes
1 answer
104 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 ...
3 votes
4 answers
346 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 ...
1 vote
1 answer
148 views

Express the PDF of StableDistribution in terms of FoxH for the case of alpha values grater than 1

The PDF of StableDistribution in terms of FoxH for the case $\alpha\leq 1$ is available at https://reference.wolfram.com/language/ref/FoxH.html namely ...
2 votes
1 answer
95 views

Computing the MultinormalDistribution density gives sometimes different values from in-built function

I'm trying to define the density of the Multivariate Normal distribution, since it will be faster to compute for greater dimensions (vectors of size 50 or more), specially when I have to do those ...
-3 votes
1 answer
122 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: ...
0 votes
2 answers
76 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: ...
1 vote
1 answer
95 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 ...
8 votes
3 answers
2k views

Contour lines over SmoothDensityHistogram

I am using SmoothDensityHistogram on a data set of the form {{x1, y1}, {x2, y2}, …, {x_n, y_n}}, and I would like to also show ...
2 votes
1 answer
135 views

How to find the expectation $\mathbb{E}\left[ a \mathcal{Q} \left( \sqrt{b } \gamma \right) \right]$?

I'm trying to find the following expectation $$\mathbb{E}\left[ a \mathcal{Q} \left( \sqrt{b } \gamma \right) \right],$$ where $a$ and $b$ are constant values, $\mathcal{Q}$ is the Gaussian Q-function,...
3 votes
1 answer
178 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-...
4 votes
3 answers
613 views

Applying an exponential decay fit with uncertainties

I have some data from a radioactive decay experiment that I'm trying to fit an exponential decay curve on that will take account of the uncertainties on the data, and then ideally return the data for ...
0 votes
0 answers
63 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 ...
3 votes
2 answers
192 views

Sort sequences by their "randomness"

Example matrix (rows always have equal lengths) ...
1 vote
2 answers
121 views

Compute Central Moments of Vector

Say we have three stochastic variables defined as follows: ...
5 votes
4 answers
397 views

An accumulated moving average

1. Problem statement In accordance with the standard definitions the inbuilt MovingAverage ...
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 ...
1 vote
1 answer
108 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 ...

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