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.
1,852
questions
5
votes
2
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258
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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, ...
- 8,135
1
vote
1
answer
52
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
91
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 ...
- 8,135
2
votes
1
answer
123
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5
votes
2
answers
231
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0
votes
1
answer
69
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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: ...
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3
votes
1
answer
103
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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 ...
- 8,135
3
votes
4
answers
341
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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 ...
- 8,135
-3
votes
1
answer
110
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: ...
- 95
0
votes
2
answers
70
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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:
...
- 95
1
vote
1
answer
92
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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 ...
- 49.1k
3
votes
1
answer
174
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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-...
- 33
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
189
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1
vote
2
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116
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Compute Central Moments of Vector
Say we have three stochastic variables defined as follows:
...
- 2,150
5
votes
4
answers
390
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An accumulated moving average
1. Problem statement
In accordance with the standard definitions the inbuilt MovingAverage
...
- 49.1k
8
votes
6
answers
1k
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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 ...
- 24.5k
1
vote
1
answer
101
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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
...
- 1,357
0
votes
0
answers
39
views
CompiledFunction fails for Variance with a rank 3 input
Why does compiling Variance for a rank 3 input fail but Mean works?
...
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 ...
0
votes
2
answers
59
views
Modifying horizontal axis of a PDF plot
I have a bunch of particles that I can measure their volume.
PDFs of the size distribution by volume of particles, v(a), measured are reasonably well represented by lognormal distributions of the ...
- 337
3
votes
0
answers
71
views
How can I calculate P-Value for a custom distribution?
I used DistributionFitTest but it works only with a defined distribution.
This is the distribution that I used:
...
- 59
2
votes
2
answers
104
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 ...
- 160
6
votes
5
answers
335
views
0
votes
1
answer
40
views
Trying to use ProbabilityDistribution for custom distribution - Getting errors/warnings I don't understand
I have this custom distribution that I want to use in Mathematica, but there
appears to be some sort of problem I don't understand.
Also, when I compute the mean for the custom distribution via
...
- 427
6
votes
4
answers
404
views
Visualizing empirical PDF from monotonically decreasing density
I have a sample from distribution whose density is known to be monotonically decreasing. What's the easiest way to incorporate this information into Mathematica for an empirical density plot?
Looking ...
- 8,135
0
votes
0
answers
55
views
Obtaining moments from the *inverse* of the moment-generating function?
I have a moment generating function $z=\phi(t)$ whose inverse has the following form for integer $k>0$
$$t=\frac{z}{(1+z)^{k+1}}$$
How would I get the moments?
Code below uses ...
- 8,135
-5
votes
1
answer
97
views
Unable to check own distribution
Good afternoon I need to estimate different distributions from some data. Among these distributions, it is necessary to use the Kritsky-Menkel distribution. I set a formula for the distribution ...
- 1
1
vote
0
answers
79
views
Getting behavior around 0 for spectrum of product of Gaussian matrices?
Edit the math part was answered in mathoverflow, I'm now looking on how to port this to Mathematica to check against observed fit
Consider a product of $k$ independent square matrices with IID ...
- 8,135
2
votes
1
answer
207
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. ...
- 71
0
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0
answers
69
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Identifying $X^2$ relationships between random variables
Given $X$ coming from a known distribution faily, how do I identify distribution family of of $X^2$ and $\sqrt{X}$?
Code below uses ...
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0
votes
1
answer
60
views
Fitting data to peaks visually with manipulate - how to compactly implement for many peaks
I am trying to create a visual aid for peak fitting. There should be a background profile and on top, I want to place peaks. So far, I am stuck with the following issue. For simplicity, I am using a ...
- 3,733
3
votes
1
answer
121
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FindPeaks in a 2d list and half values
FindPeaks is a nice little help. But it only works on 1D lists and tends to return half integer values for positions of the peaks which are ultimately very useless ...
- 3,733
2
votes
2
answers
85
views
Grouping expressions by their $O(..)$ rate of growth around 0
Given a list of expressions like $3 x^2,\frac{\sqrt{x}}{\sqrt{2}},\frac{2 \sqrt{x}}{\pi },\frac{9 x^3}{2},x,$, how could I group them based on their rates of growth around 0?
IE, $2x$ and $3x$ are ...
- 8,135
1
vote
1
answer
118
views
Sampling from density specified in terms of spacing ratios?
Given a sorted vector of positive reals $\{\lambda_1,\lambda_2,\ldots,\lambda_P\}$ and corresponding vector of spacing ratios $r_i=\frac{\lambda_i-\lambda_{i-1}}{\lambda_{i-1}-\lambda_{i-2}}$, I know ...
- 8,135
0
votes
1
answer
178
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How to Draw a Probability Tree Diagram to Calculate the Probability of Badminton Competition Game?
Question：
A, B, and C students will participate in a badminton competition, and the agreed format is as follows:
Those who have accumulated two losses are eliminated;
Draw lots before the competition ...
- 2,905
5
votes
2
answers
160
views
Can the type 3 SS be obtained using the ANOVA function or an adaptation that is readily available in Mathematica?
The default output for the ANOVA function is that of a type 1 Sum of Squares (SS) table. This is sufficient for a one-way ANOVA, however, when running an n-way ANOVA (with n greater than 1) and ...
- 53
1
vote
3
answers
81
views
Visualizing range of possible CDFs of $X\in (0,1]$ such that $E[X]=1/3$
What's an elegant way to visualize the range of possible CDFs for a random variable $X\in (0,1]$ such that $E[X]=\frac{1}{3}$?
Below is an attempt by discretizing (0,1] interval and using ...
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2
votes
2
answers
121
views
Calculating Distributions that Have Dependencies
I want to calculate a distribution from a function that depends on several variables, where there is an interdependency between the variables. This works:
...
- 133
5
votes
1
answer
140
views
Visualizing density given by its Stieltjes transformation?
How can I use Mathematica to get $f(y)$, the PDF of a random variable given its Stieltjes transform $g(s)$?
$$g(s)=E\left[1/(s-X)\right]$$
I need to visualize probability density of a random variable ...
- 8,135
1
vote
3
answers
208
views
Finding a continuous distribution that fits the empirical density of dataset $1,1/4,1/9,1/16\ldots$
I have a list of coefs of the form $1,1/4,1/9,1/16,\ldots,1/d^2$ sampled with relative sampling frequencies $1,1/4,1/9,1/16,\ldots,1/d^2$.
How do I find a nice continuous density whose CDF closely ...
- 8,135
0
votes
1
answer
62
views
`MomentGeneratingFunction` producing a function with negative moments
I'm getting moment generating function which is negative and all moments are $-\infty$ which seems wrong...1) is this a bug in MomentGeneratingFunction? 2) what is ...
- 8,135
2
votes
2
answers
155
views
Getting distribution of squared coordinate on a sphere?
Suppose $\mathbf{x}$ is on a surface of n-sphere, how do I get the distribution of $x_1^2$?
Distribution of $x_1$ is shifted Beta so we can use ...
- 8,135
1
vote
1
answer
76
views
Deriving variance component of 1-Way ANOVA?
My goal is to drive $E(MSA)$ for this design(the 1-way ANOVA);
$$y_{ij}=\mu +\alpha_i + \epsilon_{ij}$$for i=1,2,...,a (that is, there are a groups)and j=1,2,...,n. $\epsilon_{ij}$ and $\alpha_i$ are ...
- 399
1
vote
2
answers
89
views
The problem of finding the maximum coefficient term in the binomial expansion,Find the value range of K
The problem is shown in the figure, and the result should be the range of K obtained at the end of the image
...
- 2,905
2
votes
3
answers
133
views
How to find the K value in the probability inequality of binomial distribution?
dist = BinomialDistribution[100, 1/3]
Solve[{PDF[dist, k] >= PDF[dist, k - 1],
PDF[dist, k] >= PDF[dist, k + 1]}, k] // FullSimplify
In this binomial ...
- 2,905
7
votes
5
answers
329
views
Quickly simulating "mean-time until collision"
Edit high-level summary of problem/solutions in Mathematica community post
Suppose I draw (with replacement) $k$ colored balls from bins with probabilities $h_1,\ldots,h_d$ until some color is drawn ...
- 8,135
2
votes
2
answers
79
views
Work-arounds to InverseFunction not evaluating?
Inverse CDF of Marchenko Pastur fails to evaluate at seemingly random points as you can see below. Is there an easy workaround?
...
- 8,135
3
votes
2
answers
141
views
Non-uniform birthday problem in Mathematica
Suppose my year has $d$ days. I have a vector of probabilities of being born on those days as $h=p_1,\ldots,p_d$, and want to estimate the smallest $k$ such that probability of of birthday collision (...
- 8,135
3
votes
0
answers
168
views
FindDistribution analog: automated data modeling with all Wolfram statistical distributions
BOUNTY GOAL
To get bounty I am asking to build a function that serves as an analog of FindDistribution. You can also simply re-implement ...
- 71.9k