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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Introduction to Univariate Regression and Sum of Squared Errors

On google I find that you can manipulate a linear regression on mathemtica. If you search "Introduction to Univariate Regression and Sum of Squared Errors, Mathematica" you'll see what I'm talking ...
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63 views

Least Square with quadratic constraint [closed]

I have the following problem:For $\theta \in \mathbb{C}^{n\times1}$, $\quad$ $Y=X\theta+W$ where $W \in \mathbb{C}^{m\times1}$ is the complex additive white Gaussian noise. $X \in \mathbb{C}^{m\...
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1answer
140 views

Best way of transforming random variable

I am working with the following code: ...
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19 views

Plotting CDFs of transformed normal random variables

I'm using the following transformed random variables ...
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1answer
96 views

Conditional Random Walk

I am attempting to model a physical process I'm observing in the lab with a random walk generator. I need to find a way to impose a condition such that when the random walk runs into a point in the ...
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2answers
75 views

Compute expectation of K independent random variables

I am trying to write Mathematica code to symbolically compute the expectation of $g(X_1, \ldots X_K)$, where $X_1, \ldots, X_K$ are Bernoulli random variables with probabilities $p_1, \ldots, p_K$, ...
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38 views

Count data fitting with Nonhomogeneous Poisson process

Following is count data needed to model with a nonhomogeneous Poisson process (NHPP). For each row-wise e.g. 8:15-8:30, every 12 intervals of 15 minutes size and 15 days of data collected. I have ...
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43 views

How is a Lévy stabile process pdf normalized?

I'm interested in how to deal with α-stabile probability density functions, for example one with the Laplace image like: $ \phi(s) = s^{(\alpha-1)}*e^{-\nu s^{\alpha}} $ I can work with this ...
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1answer
44 views

Count based hypothesis test for inhomogeneous Poisson process

I am intended to fit the following data using InhomogeneousPoissonProcess[] in v12.0. The original form of data tabulated given as below Such a table contains ...
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20 views

What is the reason StandardDeviation doesn't cooperate with Quantity “Percent”?

Consider the following list of numbers y = {13, 0.2, 11.201}; Turning y into a list of ...
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1answer
62 views

Numerically Inverting Characteristic Function with Inverse Fourier Transform

I'm trying to numerically invert this characteristic function: ...
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0answers
43 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 ...
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2answers
125 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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1answer
72 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 ...
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119 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 ...
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1answer
56 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 ...
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45 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 ...
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77 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". ...
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3answers
556 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 tried ...
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26 views

Problem when integrating a discontinuous function

I have this simple code: ...
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2answers
80 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 ...
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50 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 ...
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21 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. ...
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0answers
79 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: ...
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1answer
43 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 ...
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56 views

Combined probability function

I have two PDFs given by: ...
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0answers
53 views

How to reduce the probability density function of binary normal distribution to the form of textbook

The probability density function of binary normal distribution in textbooks is in the following form: ...
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1answer
68 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 ...
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1answer
84 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 ...
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0answers
43 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 ...
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2answers
137 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. ...
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65 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] = ...
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22 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 ...
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58 views

Strange behavior with Conditioned[]

I am using Mathematica 12.0 on Windows and I recently tried to evaluate a conditional expectation, namely ...
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119 views

Kolmogorov backward PDE with boundary conditions

I am trying to solve numerically Kolmogorov backward PDE with boundary conditions: ...
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1answer
32 views
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1answer
50 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 ...
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1answer
104 views

Find PDF of a stochastic process

I consider the following Ito process ...
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38 views
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81 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 ...
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60 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 ...
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37 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)}{\...
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1answer
136 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 ...
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0answers
42 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 ...
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2answers
103 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
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2answers
319 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 ...
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2answers
540 views

How does BoxWhiskerChart detect outliers?

BoxWhiskerChart can detect and show outliers: ...
7
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1answer
157 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 ...
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2answers
388 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 ...

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