# Tagged Questions

Questions on the statistical functions of Mathematica.

4k views

### Simultaneously fitting multiple datasets

What is the proposed approach if one wants to simultaneously fit multiple functions to multiple datasets with shared parameters? As an example consider the following case: We have to measurements of ...
2k views

### Histograms with pre-counted data

I've got some large data sets which have been counted but not binned already - essentially, a list of pairs of values (not bins) and counts.* (Or, equivalently, it's been binned into too-small bins.) ...
491 views

### How to augment the realm of functions Mathematica thinks it knows how to integrate symbolically

My question involves extending the functionality of Integrate over specific integrals in the most generic manner. Specifically, is it possible to "hack into" ...
3k views

### Showing the correlation of two variables using a plot

I have a list of $\{x_i,y_i\}$ pairs and I want to show that $x_i$'s and $y_i$'s have positive correlation. The result of ...
346 views

### Unexpected behavior of confidence bands for data presenting two regions with uneven noise

Let's generate some noisy data with uneven noise. ...
6k views

### Estimate error on slope of linear regression given data with associated uncertainty

Given a set of data, is it possible to create a linear regression which has a slope error that takes into account the uncertainty of the data? This is for a high school class, and so the normal ...
2k views

### Efficiently generating n-D Gaussian random fields

I am interested in an efficient code to generate an $n$-D Gaussian random field (sometimes called processes in other fields of research), which has applications in cosmology. I wrote the following ...
2k views

### Standard errors for maximum likelihood estimates in FindDistributionParameters

I am trying to fit a non-standard PDF to data and FindDistributionParameters works great, and gives me the parameters of the distribution back using maximum ...
267 views

### Polynomial expectations of generic distributions

Summary Polynomial expectations depend only moments and cross moments of a multivariate distribution. I would like to use Expectation to compute polynomial ...
819 views

### How can I tell mathematica to generate an histogram from nominal data?

If I write: Histogram[{1, 1, 1, 2, 2, 2}] I get a nice histogram chart but if I write ...
307 views

### Visualization: elliptical insights into data sets…

I was recently reading the following paper on visualization techniques using ellipses to gain statistical insights. Elliptical visualization for looking at correlations has briefly been touched on ...
527 views

### Detecting and counting signals in list data: checking pulse rate

Hope this isn't too much of a basic question: I'm looking for some Mathematica functions, but I don't know which ones. Background I recently read about a simple technique for reading your body's ...
579 views

### Measure a DensityHistogram[] pair similarity

I study human vision and more specifically eye-movements. "If we display 2 symmetrical patterns (20 min one after the other), will our gaze distribution be symmetric is my research question." The 2 ...
973 views

### Obtaining joint distributions and conditional distributions using Mathematica

I have two multivariate Gaussian distributions $p(x)$ and $p(z)$ with mean vectors $m_x$ and $m_z$, and covariance matrices $\Sigma_x$ and $\Sigma_z$. my model is a simple linear model $x = W z+n$ ...
307 views

### Interfacing Mathematica with MINE using JLink

In last December's Science David N. Reshef, et al. proposed an interesting method to detect associations in data (Detecting Novel Associations in Large Data Sets, Science 334, 1518, 2011). Contrary to ...
442 views

### Which Distributions can be Compiled using RandomVariate

Recently, Oleksandr kindly showed a list of Mathematica commands that can be compiled. RandomVariate was part of that list. However, whether this can be compiled depends upon the distribution that is ...
168 views

### NExpectation behaves oddly with EmpiricalDistribution

Note: this is fixed in version 9. My question concerns the usage of NExpectation and Expectation and why I see the behavior I ...
219 views

### Randomness test suites that can be invoked from Mathematica

There are several test suites referenced at csrc.nist.gov designed to test a (pseudo-)random byte sequence for randomness, and discover possible skews, correlations, patterns, or other hidden ...
187 views

### How to efficiently find moments of a multinormal distribution?

I have a multinormal distribution with covariance matrix $\sigma$ and zero mean. I want to find moment $$E[x_1^{r_1}x_2^{r_2}\cdots x_n^{r_n}] =\,?$$ Of course, there is a build-in function ...
446 views

### Using ANOVA with a “Repeated measures” / “Within-subjects” design

Repeated measures designs or "Within-Subjects" designs are very important in live sciences and social sciences. Unfortunately, Mathematica's ANOVA package is not able to analyze those designs. It only ...
1k views

### Finding distribution parameters of a gaussian mixture distribution

Short version: how to estimate the parameters of a mixture of multivariate normal distributions (i.e.: Gaussian mixture model)? Long version. I am trying to estimate the parameters of a mixture of ...
182 views

### How does bandwidth selection work for low-variance dimensions with KernelMixtureDistribution?

I am puzzled because this toy example (in Mathematica 8) ...
1k views

### Persistence length of a polymer chain

I'm trying to calculate the persistence length (Lp) of a polymer chain using Mathematica. The first and simplest method is to compare the EuclideanDistance between ...
316 views

### What do the options of SmoothKernelDistribution do?

The function SmoothKernelDistribution has three options that are not described in too much detail in the Mathematica's help window. InterpolationPoints: What is ...
2k views

### Performing a chi-square goodness of fit test

How would I perform a chi-square goodness of fit test? I have tried the following, where my data consists of the observed values whilst the data pair contains the correct values. Then I use the ...
198 views

### Probability of the sum of the largest n samples

15 numbers are randomly chosen from U(0,1), what is the probability that the sum of largest four numbers is greater than 3.5? ...
292 views

### Incorrect means of order statistics for the standard normal distribution

Table[Mean[OrderDistribution[{NormalDistribution[], 4}, i]], {i, 1, 4}] // N (* {-1.02938, -6.47326, 0.297011, 1.02938} *) Above are the means of order statistics ...
380 views

### Cluster analysis returns questionable results

A few weeks ago I ran a cluster analysis on some economic data and (unfortunately only) now I found out that some results do not make sense. For instance I analyzed the development of unemployment ...
451 views

### Different calculation of median and quartiles, bug in BoxWhiskerChart?

When you plot a dataset with BoxWhiskerChart passing over the box in the plot with your mouse pointer shows some specifics about the dataset (min and max values, ...
187 views

### How to find synchronization offset?

I have 2 sets of data containing delays (audio / video). ...
223 views

### What default theoretical distribution does Mathematica use in PearsonChiSquareTest?

I used Mathematica's function PearsonChiSquareTest to test whether the data were drawn from a normal distribution. As in the reference, I expected Mathematica to compare the result to a normal ...
329 views

### BUGS-type calculations in Mathematica

Recently I have been teaching myself how to Bayesian calculations with the BUGS language (JAGS, in particular). However, I find myself wondering how one might use Mathematica to do similar ...
649 views

### What is the Mathematica equivalent for the Excel function tinv()?

TINV() returns the t-value of the Student's t-distribution as a function of the probability and the degrees of freedom. For example ...
636 views

### Forest plot with Mathematica 9

Does anyone have experience with or a package for the creation of forest plots in Mathematica 9? For instance for subgroup analyses of cox model or meta-analysis (e.g rmeta package in R)?
194 views

### CorrelationTest small bug?

Consider two Normally distributed random variables: x1 = RandomVariate[NormalDistribution[], {1000}]; x2 = RandomVariate[NormalDistribution[], {1000}]; I want to ...
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### Bayesian Inference with Continuous prior distribution

Assume that we have a prior distribution for the probability of success as follows. p = BetaDistribution[6, 14] which we can graph as this ...
484 views

### Most efficient way to obtain samples from high-dimensional multivariate distributions?

Is MultinormalDistribution[] efficient and easy to use for high dimensions? I have a variable $n$ representing the dimension of a Monte Carlo integration I do on a ...
419 views

### The default bandwidth of the SmoothKernelDistribution function

I am researching the Silverman rule of thumb for bandwidth selection. Below is a sample of my code, from which it seems that BW=63 is close to the default parameter given by Mathematica (2 images are ...
382 views

### Random variables with transformed discrete distributions cannot be applied to Probability[] function?

I have two discrete uniform distributions over same support: Dx = DiscreteUniformDistribution[{-8, 8}]; Dy = DiscreteUniformDistribution[{-8, 8}]; I use ...
142 views

### Inconsistent DistributionFitTest results?

In pondering this question, I used Mariana's function to generate the following data. ...
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### How to define a new copula distribution family

The function CopulaDistribution can be used with the most well known kernels. I was wondering how I can add a new family of kernels in a way that it works in the ...
536 views

### Recommended book on random processes to understand new functionality in Mathematica 9?

I am interested in exploring the new functionality on random processes available in Mathematica 9, but I am not familiar with all of the underlying mathematics. Could you recommend a book that ...
241 views

### How does LocationTest choose its “AutomaticTest”?

Is there a way of determining how LocationTest chooses its "AutomaticTest"? Sometimes it's clear from the ...
2k views

### Doing a chi-square independence test in Mathematica

I have a matrix consisting of the following data: Needs["HypothesisTesting`"] data = {{11, 206}, {32, 1374}} How would I make a chi-square independence test ...
832 views

### Plot Ellipse based on EigenSystem

Please consider the following : ...
827 views

### Probability and distribution from actual data

Let's say I have some data from a real world system: ...
811 views

### Wald–Wolfowitz Runs Test

Does Mathematica 8 implement Wald–Wolfowitz runs test for randomness? I can't find it in the documentation. I would like to test some fit residuals.
225 views

### Overlay of pdf using PairedHistogram in Mathematica

With a standard 1D histogram, I can generate a pdf overlay using Show and Plot. I'd like to do something similar with ...
Nature has provided me with a random variable $Z$ taking on the values $0, 1, 2, \ldots$, with probabilities $z_0, z_1, \cdots$. I can sample from the distribution of $Z$ reasonably efficiently (I ...