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.
1,880
questions
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2
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960
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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
...
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 ...
0
votes
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: $\mu = \sum_{i} x_i \cdot P(x_i)$,...
-1
votes
0
answers
30
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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}|>...
1
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1
answer
162
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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)...
0
votes
1
answer
57
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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 ...
6
votes
5
answers
1k
views
How to calculate the number of prime numbers in a group of numbers?
If two different numbers are randomly selected from seven integers from 2 to 8, what is the probability of the two numbers being mutually prime?
Take 2 different numbers randomly from 7 integers from ...
7
votes
3
answers
176
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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 ...
0
votes
1
answer
76
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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 ...
3
votes
3
answers
155
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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?
1
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0
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71
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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 ...
0
votes
1
answer
50
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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
4
votes
4
answers
84
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Mean of List of Coordinates
Imagine I have the following list
l = {{1, 2}, {1, 3}, {2, 4}, {2, 2}, {2, 3}}
I want to take the mean only regarding the second element. That is, I want to find ...
0
votes
0
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48
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How to quickly sample points according to the given distribution?
Consider the following points sampler:
...
0
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2
answers
78
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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 '...
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 ...
1
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1
answer
73
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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}
\...
5
votes
1
answer
207
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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
...
1
vote
1
answer
151
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 ...
1
vote
1
answer
308
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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 ...
9
votes
1
answer
447
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Can LearnDistribution learn conditionality?
I would like to apply LearnDistribution to multivariate conditional distributions. Here's a simple artificial example:
...
2
votes
0
answers
58
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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 ...
2
votes
4
answers
220
views
Does TTest taking into account the Welch's t-test?
TTest has an option VerifyTestAssumptions for "EqualVariance", does it automatically switch to Welch's t-test when variance of the two data sample differ a lot?
5
votes
1
answer
90
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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 ...
0
votes
1
answer
65
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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, ...
7
votes
4
answers
360
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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+...
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:
...
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,...
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
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1
answer
139
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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
746
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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
150
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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
87
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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
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?
...
2
votes
1
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69
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2
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2
answers
204
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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
73
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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
427
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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
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0
answers
54
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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
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1
answer
287
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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
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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 ...
2
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0
answers
56
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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 ...
5
votes
2
answers
271
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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, ...
1
vote
1
answer
54
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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
98
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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
143
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One more incorrect result of CDF
In 13.3.1 on Windows 10 I find
...
2
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2
answers
107
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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
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An incorrect result of CDF
In 13.3.1 on Windows 10 I execute
...
6
votes
1
answer
34k
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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 ...