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# 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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### Wrong definition of auto-correlation fucntion (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 ...
26 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 ...
40 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: ...
31 views

### How to calculate the average from the probability distribution? [closed]

I create a plot from the formula that I have for the probability distribution,, a parameter (I do not have data point). How can I calculate the average for that distribution that I have? Best
69 views

My code is: ...
256 views

### Approximate 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 ...
524 views

### How does BoxWhiskerChart detect outliers?

BoxWhiskerChart can detect and show outliers: ...
122 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 ...
361 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 ...
75 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 ...
62 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 ...
57 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 ...
9 views

### Stationary measure of a not-explosive continuous time Markov chain [migrated]

Let $X_n$ be a non-explosive continuous time Markov chain with a stationary measure. Is it possible that its embedded discrete time Markov chain does not have a stationary measure?
65 views

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

I'm intending to add white noise to a simple periodic signal ...
66 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 ...
111 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 ...
82 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: ...
63 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: ...
186 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 $$T=\{(x,y)\mid0\le x\le1,0\le y\le1-x\}$$ ...
64 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 ...
21 views

### How to estimate parameters of TransformedProcess?

Let's say we have the following time-series. ...
19 views

### Estimate the Hidden Markov Parameter while keeping some of them are same

How can I estimate the hidden Markov model while using the same value for some of parameters? First, let's get test data (sorry, messy!) ...
32 views

### Finding the sum of two independent Normal Mixture Distributions using Mathematica

Suppose random variable $X_1$ is a mixture of two Normal distributions with means of $\mu_A$ and $\mu_B$ respectively, standard deviations of $\sigma_A$ and $\sigma_B$ respectively, and weights given ...
81 views

### How can I show multiple PDFs derived from my distribution in one plot

My question is related to the This question. I want to plot different PDFs for a given random variable in the same plot using f[x_NumericQ]. For example, I have ...
31 views

### LinearModelFit with predefined coefficients

I want to use an estimation procedure different from OLS (say, LAR or LASSO), but then use the LinearModelFit to produce all the diagnostic statistics. Can I make LinearModelFit or the FittedModel ...
2k views

### Is there a way to randomly distribute points within a circle on the surface of a sphere?

I'm attempting to set up a situation where on a 3D sphere, I choose a random point and construct a circle around this point with some radius. I then want to randomly distribute points within this ...
88 views

### SmoothHistrogram plot is not smooth [closed]

I used the following code to show a small hump near 5000. With R it's fine but for some reason Mathematica draws strange vertical lines. I tried several combinations of ranges. (Data from here or here....
63 views

### Generating random numbers from specified distribution under a constraint

I need to generate 500 numbers from a distribution specified. I used the well-known CDF method, but since I'm new to Mathematica, I don't know how to set a condition on the sum of these variables. <...
95 views

### Conditional expectation

Suppose I have a bivariate normal random vector $(Y,Z)'$ where $Y\sim N(μ1,\sigma_1^2)$, $Z\sim N(μ2,\sigma_2^2)$, and $Cov[Y,Z]=\sigma_{12}$. If I want Mathematica to compute the conditional ...
98 views

### Non linear fit data

I am trying to fit this data with this two models. In the first one, the solution is too far from the exact values. In the second one, there is an error. Could you please help? ...
46 views

### Single toss of two dice [closed]

Does any one knows answer for this question related to probability? A pair of fair dice is tossed once. If the sum of the two numbers is greater than 9, the probability that one of the numbers is a ...
57 views

### How do you calculate the expected value of the sum of random variables?

For instance, when trying to compute $\mathbb{E}[\sum_{i=1}^{10}X_i]$ where $X_i \sim N(0,1)$, I input into Mathematica: ...
138 views

### Moments of Multinormal in symbolic form

Gaussian expectations often simplify (20.5 of Seber's "A Matrix Handbook for Statisticians" gives many examples). I'm wondering if there's a way to use Mathematica to produce the formulas semi-...
84 views

### How can I generate a histogram for the largest strongly connected component of a directed graph?

With the help of several persons from this forum, I have written the following MMA Code using Manipulate to describe certain ...
75 views

### Is there an issue with the correlation function?

I am trying to find the correlation between Uniform R.V.s using the Correlation command in mathematica, but it seems that either I am implementing it wrong or the software cannot find the answer. My ...
46 views

### How would one 3d plot the CDF of a probability mass function in Mathematica?

I have attempted to plot the Cumulative Distribution Function of a simple piecewise probability mass function, but the code: ...
35 views

### Weird behavior of Quantile function

I found a very strange behavior of Quantile function when evaluating the following expression: ...
20 views

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42 views

### How can I generate a Poisson gap sampled list?

tstart = 0; tend = 3; num = 1024; tstep = (tend - tstart)/(num - 1); list = Table[i, {i, tstart, tend, tstep}] // N; Histogram[list] I have a list of 1024 points ...
32 views

### Expression with Boole

Let us have an expression for example, this: 2 (-1 + p) (3 - 4 p + 2 p^2) Boole[\[FormalX] == 1] - 9 (1 - 2 p + p^2) Boole[\[FormalX] == 2] ... For the whole ...
44 views

### One Function of Two Random Variable

I wonder how to implement below derivation in wolfram mathematica. I want to see integrate results like below picture. Can you help. I used "TransformedDistribution" but it shows only distribution ...
28 views

### Are these TransformedDistributions identical?

If A1 and A2 are independent random variables, and B1 and B2 are as well, then are the following TransformedDistributions the same? ...
29 views

### Need help with plotting a probability distribution

I looked through the Mathematica directory and could not find a solution that is right for me. I already solved the mathematics behind this problem, I just need to visualize it in a plot. I am ...
82 views

### Speeding up Probability using Monte Carlo

I have a recipe for generating custom distributions, which I want to use Probability[...] on, but am finding that with more than a few variables it very quickly becomes intractable (it runs for hours)....
61 views

### Slicing an n-dimensional ellipsoid

NonlinearModelFit has as one of its diagnostics a parameter estimate ellipsoid. This is hard to visualize, however, if there are more than 3 parameters being ...
60 views

### RandomVariate drawn from a custom distribution function takes forever to finish

I'm using the following custom-defined PDF: ...
34 views

### Moment-generating function of the log-normal distribution. A question about integration

Consider the probability density function $f(x)$ of the log-normal distribution with parameters $-0.1$ and $0.01$: ...
70 views

### How to find de Mean and Variance of a defined distribution

I would like to find the Mean and Variance expressions for a Poisson-Lognormal Distribution f(x;\mu,\sigma)=\frac{1}{x!\sigma\sqrt{2\pi}}\int_{0}^{\infty}\lambda^{x-1} e^{-\lambda} e^{\frac{(log(\...