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
50 views

'FindFit' ignoring certain data points to optimise r^2 value

As shown in the code below, ...
0
votes
0answers
28 views

Derivative of an expectation function

For a general function $g$, define $f=\mathbb{E}_{(x,y)\sim \mathcal{N}(0, \Sigma)}[g(x)g(y)]$, where $\Sigma=\begin{pmatrix}a & c \\c & b \end{pmatrix}$, and $a>0,b>0,ab>c^2$. I am ...
0
votes
1answer
35 views

Confidence interval for variance in fit

When using (Non)LinearModelFit you can get estimates for all parameters and for the variance of the fit and confidence intervals for parameters, but what about a confidence interval for the variance? <...
1
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1answer
31 views

Values corresponding to SmoothDensityHistogram

I am looking for extracting the values associated with SmoothDensityHistogram. For example in ...
3
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0answers
21 views

Assessing your own classifier function with ClassifierMeasurements or NetMeasurements

The functions ClassifierMeasurements and NetMeasurements expect objects that are created through ...
4
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2answers
171 views

Why is the conditional probability not working for `CategoricalDistribution`?

Consider the following simple example for demonstration: ...
1
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1answer
42 views

Help with NIntegrate settings to evaluate integral [closed]

I am trying to evaluate this integral: \begin{align*} \alpha_{2}=\int_{-\infty}^{1.645}\left[1-\Phi\left(\frac{\sqrt{25}}{\sqrt{15}} 1.645-\frac{\sqrt{10}}{\sqrt{15}} z_{1}\right)\right] \phi\left(z_{...
2
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1answer
127 views

Entropy of a distribution

I need to calculate the entropy of a distribution from raw data. I found two approaches here and here. But it seems they don't work for my case. My data is: ...
1
vote
1answer
41 views

Moving average over time on data entering stochastically

The examples for using MovingAverage mostly refer to data evenly spaced in time,such as stock values. In typical physics data, events arrive random in time (e.g. radio active decay events, but also ...
0
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0answers
28 views

ARIMAProcess function: how can I use raw data sheet in ARIMAProcess?

I have a data column given by: $$0.0000093\\ 0.0000019\\ 0.0000003\\ 0.0000002\\ 0.0000032\\ 0.0000002\\\\$$ How can I use the ARIMAProcess function$[1]$ on this data sheet? $$ * * *$$ $[1]$ https://...
4
votes
2answers
96 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
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1answer
55 views

Skewness and central moment

I have distribution which I want to calculate the third order moment function of my distribution. I got confused what is different between Moment third order and ...
1
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0answers
36 views

Create CDF from a custom function

I have a complex function as follows (sorry for ugly script due to many parameters in the code!) which gives CDF of some data. I wonder whether there's any way to write it in CDF form in Mathematica, ...
2
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2answers
125 views
0
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0answers
40 views

How to go from a Pareto Distribution in Scipy to a Pareto Distribution in Mathematica?

Assume that I have fitted a Pareto distribution via Scipy and have gotten the following parameters: ...
0
votes
1answer
61 views

3D scatter plot combined with user-defined adjustable planes [closed]

I am trying to find some service/application/web-app or otherwise that allows for the following functionality: Plot points in 3d space. Insert plane in 3d space wherever I like. As in it must not be ...
0
votes
1answer
36 views

outcomes and payoff in probability games [closed]

I am reading probability from AI point of view from book Artificial Intellegence A Modern approach by Russel and Norving. Below is text snippet from chapter 13. One argument for the axioms of ...
0
votes
1answer
66 views

Evaluation points following a bivariate Gaussian distribution [closed]

I have a function of two variables, say $f(a, b)$, which I want to evaluate (and later average) in the neighborhood of $a=0$ and $b=0$, with density of points around $(a,\,b)$ following a Gaussian ...
0
votes
1answer
36 views

How to plot Log(P(x)) in a histogram?

I have been using SmoothHistogram to plot the probability density function $P(x)$ of some experimental data. On the y-axis, I would like to have $\log(P(x))$ ...
2
votes
1answer
91 views

Speeding up code doing random sampling

I have a particular probability distribution (that is a function of a parameter $\phi$), that I would like to sample from and then do a listplot for that function. Here is the code that I came up with:...
0
votes
0answers
39 views

Taylor expansion of expected value of a function with multiple random variables

The expected value of a function of multiple random variables can be approximated by a Taylor expansion. How this can be done in MMA is described in other posts (Link1, Link2). Let's assume we have a ...
0
votes
1answer
84 views

Problem with parameters from fitting

I am trying to fit the following data (called TflogqIND): ...
1
vote
1answer
64 views

Specifying statistical models / Equations between Random Variables [closed]

I'm new to Mathematica and confused about how random variables work. Say I have a standard normal random variable $X\sim \mathcal N(0,1)$ and set $Y := 2X$. Then $\operatorname{Cov}(X,Y) = 2$. Now if ...
0
votes
0answers
24 views

Computation of 1- and 2-sided p-values for Fisher's Exact test for 2x2 table based on Monte Carlo

I am looking for code to compute the 1- and 2-sided p-value for Fisher's Exact test for 2x2 tables based on Monte Carlo (bootstrap simulations). For larger 2x2 crosstabulation tables, the exact p-...
2
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0answers
44 views

Matrix regularization, how to pick $\lambda$

Since v12 FindFit[] now supports regularisation, such as Tikhonov regularization. Do there exist statistics to help guide the choice of the hyper-parameter $\...
4
votes
3answers
317 views

Calculate variance for a lottery?

I'm trying to calculate the variance for a lottery using the mathematica function "variance". In the following a simplified example with just a few values, and how I tried to solve it: ...
3
votes
1answer
88 views

Taking mean of a numerical function $f(t',x,y)$ [closed]

$f(t,x,y)$ is a solution from NDSolve, in a domain $\mathcal{D}$. If $f(t,x,y)$ was an analytical func I would $$\overline{f(t)}=\frac{ \int _{\mathcal{D}} f(t,x,y) dx dy}{\mathcal{D}}$$ Since $f(t,x,...
1
vote
2answers
104 views

Expectation with conditional random variable [closed]

Given an Exponentially Distributed Random Variable $X\sim \exp(1)$, I need to find $\mathbb{E}[P_v]$ in Mathematica, where $P_v$ is given as: ...
4
votes
3answers
156 views

Empirical mean excess plot of (μ, e(μ))

Say I generated n random variates from the standard cauchy distribution. I want to construct the empirical mean excess plot of (μ, e(μ)) , where e(μ)={Σ(xi-μ) *I {xi>=μ}}/Nμ . Nμ is the number of ...
0
votes
1answer
126 views

How to solve following equation with multiple random variables

How can I program the following problem into Mathematica? $X,Y$ are i.i.d. Exponentially distributed random variables. Such that $X\sim\exp(1), \ Y\sim\exp(1)$. All other variables are positive real-...
1
vote
2answers
61 views

Find intercept line and intercept point from data sets

If I have two set of data such as: ...
3
votes
1answer
135 views

Problem with fitting a given data with an equation

I want to fit a given data using the approach developed by @Bob Hanlon here: Fit and find fitting parameters of data given an equation I have tried this approach for several different data sets but I ...
0
votes
0answers
32 views

Moment generating function of Maxima $E[\exp(t \max(X,Y))]$

Let $X,Y$ be two standard normal random variables with correlation coefficient $r\in[-1,1]$. I'm trying to compute the moment generating function of the maxima using Mathematica: ...
0
votes
0answers
27 views

does Mma provide exact critical values of Mann Whitney U (small samples)

Does Mma provide exact critical values for the Mann Whitney U test, along the lines of haskell? Or just as good, for given two small samples, can I easily ask ...
0
votes
0answers
39 views

Problem with a BarChart

I have problems with a graph, First: I am using data from a list, before I used RamdomReal, but I can't get it to work. Second: the statistical data doesn't appear in the graph, I do not know why. ...
0
votes
1answer
87 views

Resources to learn probability with mathematica?

Can someone recommend me any resources to learn Probability with Mathematica. Hopefully a book that has mathematica exercises and code examples.
2
votes
2answers
155 views

Incorrect results in probability calculation [closed]

By my calculations ...
3
votes
0answers
57 views

How to reproduce SmoothKernelDistribution[] for the bivariate case

I am trying to reproduce the results of SmoothKernelDistribution[] for the bivariate case. ...
1
vote
2answers
97 views

Translating MATLAB code into WL code [closed]

I want to solve the following problem by simulation. There is a bus with 100 labelled seats (labelled from 1 to 100). There are 100 persons standing in a queue. Persons are also labelled from 1 to ...
6
votes
1answer
87 views

How to find individual probabilities of all numbers from a list? [closed]

I have the following list of random numbers: ...
3
votes
1answer
56 views

Probability Generating Function(s)?

I'm very new to Mathematica and I have started to use it since I have been tackling some Physics related problems(I'm an engineer by training). Specifically, I'm dealing with Master Equations and one ...
5
votes
3answers
209 views

Plotting a normal curve over a histogram

I am teaching a basic introduction to normal curves, and the textbook introduces the topic with the idea of rolling five dice and recording the sum. Do this many times and create a histogram of the ...
3
votes
2answers
103 views

Estimation of the expected Euclidean distance between two random points on a unit $n$-hemisphere

What is the best approach to estimate, with Wolfram Mathematica, the expected Euclidean distance (in a $(n+1)$-dimensional space) between two points selected uniformly at random on a unit $n$-...
1
vote
1answer
52 views

How to find the inverse of CDF of geometric function? [closed]

The cdf of geometric distribution is given by $ F(x)=1-(1-p)^x$. I want to calculate the inverse of it, for example, $F^{-1}(U)$ I am doing the following ...
2
votes
3answers
115 views

Estimate the expected distance between two random points on the unit $n$-sphere [duplicate]

What is the best approach to estimate, with Wolfram Mathematica, the expected Euclidean distance in a $(n+1)$-dimensional space between two points selected uniformly at random on the unit $n$-sphere? ...
1
vote
2answers
71 views

TransformedDistribution of normal and skew-normal distributions

I have the following distributions: distC =NormalDistribution[251.563, 0.317394] distS =SkewNormalDistribution[252.973, 0.503173, 5.59741] I want to analyse what ...
1
vote
1answer
44 views

Implementing Random process for exponential correlation function

I'm trying to simulate a random process for a variable $-1<X(t)<1$ with average 0, i.e., $\left\langle X(t)\right\rangle =0$ and correlation $\left\langle X(t)X(0) \right\rangle \propto e^{-t/\...
1
vote
0answers
20 views

Consistency of sample quantile to population quantile for discrete variables [closed]

Can I know if the sample quantile converges to the population quantile in probability for discrete variables? If we use Hoeffding (1963)'s results, is this true?
3
votes
1answer
72 views

Evaluating expected improvement in Mathematica

There is a concept in optimization called expected improvement where you sequentially search for the value of x that optimizes the problem. Here is a screen shot of the general idea of the derivation: ...

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