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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2
votes
1answer
45 views

Numerically Inverting Characteristic Function with Inverse Fourier Transform

I'm trying to numerically invert this characteristic function: ...
1
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0answers
33 views

ParameterPValues

I am currently translating a Mathematica notebook for model fitting into Python, and I need to understand one property of NonLinearModelFit. Could anyone link to a ...
4
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2answers
85 views

Chi^2 fitting for correlated data

Suppose you have $N$ correlated data points $\vec{y}_\mathrm{data}$ and a model that is a function of $M$ parameters $\vec{x}$. The associated $\chi^2$ statistic is $\chi^2 = (\vec{y}_\mathrm{data} - ...
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0answers
33 views

Quantifying the similarity/difference of two probability histograms in Mathematica

I am trying to estimate the similarity/overlap or conversely the difference between two probability histograms in Mathematica. There are two built-in measures I have discovered in Mathematica, namely ...
1
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1answer
50 views

How to make specific physics animation

I'm thinking about adding some animations in Mathematica to my last Physics assignment and I don't quite know where to start. Id like to make somthing like this image: which I made using PowerPoint ...
1
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0answers
109 views

Introduction to Probability with Mathematica

Is there any newer book that would be good introductory text to probability with Mathematica? I have Introduction to Probability with Mathematica by Hastings but it is over 10 years old and it overly ...
2
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1answer
55 views

About AbsoluteCorrelation

In my understanding, "the absolute correlation" is not such a common expression. Can anyone kindly explain the significance of the built-in symbol ...
0
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0answers
43 views

Code optimization

I designed this Gillespie's algorithm by the First Reaction method, and I would like this runs faster. I mean, to reduce the absolute timing of the Do bucle. So, I was thinking what kind of ...
0
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0answers
71 views

Is it possible to create the following simulation in mathematica?

Consider a set of discrete "states" $|1\rangle,|2\rangle,|3\rangle,\dots,|N_{\text{max}}\rangle$). Next, assume that there are 1000 "particles" occupying the state 1 at the initial moment of "time". ...
6
votes
3answers
363 views

Sum of dependent random variables

Suppose that $X$ and $Y$ are jointly distributed in such a way that $X\sim U[-1,1]$ and $Y\sim U[-|X|,|X|]$. I am interested in obtaining the PDF of $X+Y$ using Mathematica. Without much hope, I ...
0
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0answers
25 views

Problem when integrating a discontinuous function

I have this simple code: ...
2
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2answers
77 views

Plotting function takes forever

I have this simple code, but it takes ages to plot the last function: FS12... how to speed it up? Thank you ...
1
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0answers
49 views

CDF looks OK but Integral of PDF does not sum to 1.0

I defined a CDF as a function of another CDF of a well known probabilistic distribution. Now I want to obtain the PDF of the former CDF. To check if the PDF is correct I integrate it over the range ...
0
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0answers
20 views

How could I use Mathematica to prove the equality of these binomial distribution CDF formulas?

I noticed that I get seemingly very different outputs when I try the following things, which, if I am not mistaken, should be mathematically equivalent. ...
3
votes
0answers
72 views

Finding percentage of points within tilted ellipse?

I am trying to find the number of data points that I have that are within a tilted ellipse that I have generated to represent the 68% confidence region. I generated some data using: ...
0
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1answer
41 views

Solving equation issue

I have a very simple trial that tries to get the value with a specific probability of not being exceeded, F, based on a Gaussian PDF ...
1
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0answers
56 views

Combined probability function

I have two PDFs given by: ...
2
votes
1answer
62 views

Computing the entropic risk measure symbolically in MMA

Using the link Definition, it is possible to compute the entropic risk measure as follows: $$ EVaR=\text{inf}_{z>0}\{z^{-1}\ln\left(\frac{M_X(z)}{\alpha}\right)\}, $$ wherein $X$ is a random ...
2
votes
1answer
57 views

How to find a CDF of Y(X) given that we know a probability distribution of X?

Suppose we know probability distribution of X. For simplicity let's say X~UniformDistribution[]. There is also a defined function Y of X (e.g. Y=1/X). How to find a ...
2
votes
0answers
36 views

What is the best way to obtain a numerical probability distribution from a big two-dimensional set of data?

Let us suppose that I have a set of N points described by x-y couples, i.e., I have a table such that, for example, table[[4]]={0.234,0.678}. For every element of ...
1
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2answers
135 views

Inaccuracy of the Difference between two $\chi^2$ Cummulative Distribution Functions

I have an algorithm which needs to calculate the difference of two Gamma distributions evaluated at some large values. I cannot do this over CDFs because they give $1$ if a large value is evaluated. ...
0
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0answers
57 views

Small issue with PDE initial condition

I'm trying to solve the Fokker-Planck equation $$\frac{\partial p}{\partial L}(L, \eta)= \frac{\partial}{\partial \eta}\left[\left(\eta^{2}-1\right) \frac{\partial p}{\partial \eta}(L, \eta)\right] = ...
0
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0answers
19 views

Algorithm used for variance of WeightedData

There are multiple definitions of the sample variance of weighted data in the literature. Which one does Mathematica use? An equation in terms of the arguments provided to WeightedData[] would be ...
0
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0answers
58 views

Strange behavior with Conditioned[]

I am using Mathematica 12.0 on Windows and I recently tried to evaluate a conditional expectation, namely ...
3
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0answers
107 views

Kolmogorov backward PDE with boundary conditions

I am trying to solve numerically Kolmogorov backward PDE with boundary conditions: ...
0
votes
1answer
32 views
0
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1answer
35 views

Simplifying / approximating compound negative binomial - binomial distribution

Suppose we have that the distribution of a count $x$ is given by a binomial distribution: $x\sim \mathcal{B}(n,\theta)$. Further, suppose that the sample size $n\sim NB(\lambda,\kappa)$, where this ...
1
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1answer
97 views

Find PDF of a stochastic process

I consider the following Ito process ...
0
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0answers
37 views
0
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0answers
77 views

Integration of multidimensional Gaussian

How could the following integration of a 6-dimensional Gaussian be achieved? Are there some techniques? (MMA code below) $$\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\int _{-\infty }^{\infty ...
4
votes
0answers
59 views

CDF of an order distribution derived from a sum of gamma random variables

I am interested in finding an analytic expression for the below cdf of an order distribution, whose form I now describe. Suppose that the time until a particular process occurs can be modelled as the ...
0
votes
0answers
35 views

Optimal way to approximate initial condition for PDE?

I have a Fokker-Planck PDE \begin{align} \frac{\partial p}{\partial L}(L,\eta) = \eta^2\frac{\partial^2 p}{\partial\eta^2}(L,\eta) +(1-2\eta)\frac{\partial p}{\partial\eta}(L,\eta)+\frac{2(\eta-1)}{\...
3
votes
1answer
134 views

Wrong definition of auto-correlation function(ACF)

Consider $X$ to be a random variate with defined expectation $\mu$ and finite variance $\sigma^2$ . Consider a ton of points $X_1,X_2,..X_n$ generated via some process. The points need not be all ...
2
votes
0answers
34 views

Strange result in LinearModelFit ANOVATable

For one of the models I'm building, the p-value in the ANOVA table obtained from the "ANOVATable" properties of a LinearModelFit ...
4
votes
2answers
91 views

TableView: How to change column headings?

I am not even sure whether it is possible. I would like to change column headings of TableView output to letters such as A, B, C etc instead of 1,2,3. Here is an example: ...
2
votes
2answers
313 views

Expectation of function of random variables (example Euclidean distance)

How the expectation value of a nonlinear transform of normal distributed variables can be approximated by Mathematica in case there is no analytical solution? Let's take the Euclidian distance of 2 ...
8
votes
2answers
536 views

How does BoxWhiskerChart detect outliers?

BoxWhiskerChart can detect and show outliers: ...
7
votes
1answer
139 views

About Silverman's bandwidth selection in SmoothKernelDistribution

I asked the following question in the site Cross Validated: https://stats.stackexchange.com/questions/444320/convergence-of-kernel-density-estimate-as-the-sample-size-grows/444479#444479. It was about ...
2
votes
2answers
373 views

Integration of probability density function

I would like to integrate the function so that I know the probability between values between 0 and 90000 ...
2
votes
2answers
83 views

Fit probability distribution from weighted observations?

Consider an observable $X$ which follows some unknown statistical distribution $P$, with elements $x\in X$ in the interval $-1<x<1$. Consider also an observable $Y$ which follows a uniform ...
7
votes
1answer
67 views

Logistic Regression classifier in Versions 12 vs 11.3

There is a mysterious "LogisticRegression" method in MMA, which could be applied as a substitution for missing multinomial logit functionality. In version 11.3 I had the following simple 3-category ...
3
votes
1answer
74 views

How can I normalize a dataset relative to data already given previously?

Some scientific libraries, like Scikit-Learn for Python are able to create normalizing/standardizing functions based on data that is previously given. Looking at the documentation for ...
3
votes
1answer
68 views

White noise at non integer intervals, bug or my mistake?

I'm intending to add white noise to a simple periodic signal ...
2
votes
0answers
71 views

Random Number Generation using LogNormalDistribution

I have a problem that I can't seem to figure out on my own due to limited knowledge of mathematics, and I was hoping I could seek help from the community. I would like to use ...
8
votes
2answers
135 views

Fitting in mathematica when dealing with non-gaussian noise and errors on the data points

How is it best to deal with fitting in Mathematica when the data has a non-normal or non-Gaussian noise on top of it? This could also be phrased as how to fit correctly in Mathematica when your data ...
0
votes
1answer
84 views

How I can Normalize the below given PDF?

I have tried to Normalize the below Code PDF with a such Constant K But I didn't succeed , I have used this instruction: ...
1
vote
1answer
67 views

Real Results from NSolve

I have the following equation that I am solving with NSolve, but Mathematica is giving unusual results when I use the Reals option with the function. Here is the equation: ...
4
votes
4answers
190 views

Setting up uniform distribution over non-rectangular support

$X$ and $Y$ are uniformly distributed over the triangle $T$ in the first quadrant of the $x$-$y$ plane with vertices $(0,0)$, $(1,0)$, and $(0,1)$, so that $$T=\{(x,y)\mid0\le x\le1,0\le y\le1-x\}$$ ...
4
votes
1answer
66 views

Getting dataset whose cumulants match user-provided values?

I'm interested in getting list of numbers whose cumulants match user-specified list of values. Below is an example that works for list of length 2, but I'm interested in generalizing it to higher ...

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