# Tagged Questions

Questions on the statistical functions of Mathematica.

9k 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 ...
6k 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

### 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 ...
3k 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 ...
831 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 ...
4k 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 ...
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.) ...
2k 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 ...
4k views

### How to use a 3×3 covariance matrix to plot an error ellipsoid?

I have a 3×3 error covariance in Mathematica, but I don't know how to use it for plotting the error ellipsoid. It would be great if you can show me how I can do that for the below covariance matrix: ...
4k 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 ...
633 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" ...
712 views

### How does Mma compute Confidence Intervals?

I am trying to understand how Mma computes the Confidence Intervals after a NonlinearModelFit. Consider the following example: ...
1k 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 ...
1k views

### Plot Ellipse based on EigenSystem

Please consider the following : ...
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### 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 ...
1k 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 $x = W z+n$ ...
258 views

### Inconsistent DistributionFitTest results?

In pondering this question, I used Mariana's function to generate the following data. ...
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### Testing for OLS Heteroscedasticity White's General Test

I've done my best to search the help and google White's test (http://en.wikipedia.org/wiki/White_test) in Mathematica. Can anyone point me to a function or Mathematica reference for this or do you ...
236 views

### How do I display the plane of best fit in 3D?

I'm trying to display the plane of best fit in the same 3D-box. Currently, I have the following code which spits out a plot of the points in 3D. I want to have a plane of best fit, can Mathematica do ...
318 views

### Representative Smooth Kernel Distribution from Truncated Distribution

I am trying to produce a better distribution from a dataset that is bounded to be greater than 0. Here is an example distribution from the documentation that mimics the behavior of the actual dataset: ...
3k views

### Filtering Lists in Mathematica [duplicate]

Possible Duplicate: Select/Delete with Sublist elements? I need help in filtering long lists of x,y coordinates.Lets use the following list as an ...
292 views

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

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

### Grain(Particle) Size Distribution (PSD) Analysis with Mathematica

I would like to do an analysis of the grain size distribution of a Monte Carlo Grain Growth simulation I implemented based on the nice example by Rituraj Nandan (see Link). The result of this ...
251 views

### How to draw confidence ellipse from a covariance matrix?

I am studying a two-dimensional dataset, whose mean vector and covariance matrix are the following: ...
256 views

### How to partition a list into sublists in a similar way to Histogram

I have a list of list as below (I show part of it) ...
108 views

### Estimating Parameters of a Custom Distribution

The problem is I can not get estimation of parameters of any custom probability distribution (distributions are not built in Mathematica), here is an example: First: I entered random numbers of ...
405 views

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

Let's generate some noisy data with uneven noise. ...
3k 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 ...
1k views

### Hodrick–Prescott filter (one-sided version)

I am interested in implementing Hodrick–Prescott filter (HP filter) on my time series data in Mathematica. I know that there is already a version of two-sided original filter for Mathematica (see ...
597 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 ...
340 views

### Summer Solstice Spurious Correlations Challenge

I came across this hilarious web site that has charts of bizarre "correlations" between disparate categories. Results like this: In the spirit of my summer solstice shedding spuriously earned rep. ...
646 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 ...
254 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 ...
147 views

### How to derive SinglePredictionBands from a NonlinearModelFit model

I have found NonlinearModelFit to be extremely useful in my work. Here I have fit 4 points to a function and am being asked to explain how the 95% SinglePredictionBands associated with the plot below ...
588 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, ...
380 views

### what is The Formula behind the Kolmogorov-Smirnov test statistics?

I calculate the Kolmogrov-samirnov test statistic for the following data: ...
735 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)?
143 views

### Best way to represent a joint distribution

The motivation for this question is producing a distribution that produces the gender and age of an individual when the distribution of ages depends on gender. Suppose I want a distribution which, ...
608 views

### Fitting data to an ARProcess using FindProcessParameters

I have 50 data points that I would like to represent as an AR(4) process. I'd like to over-plot the behaivor of the estimated process model with that of the original (raw) data before I use the model ...
3k views

### Function for Autocorrelation

Is there a built in function to compute the autocorrelation of a signal ?
1k views

### BoxWhiskerPlot - how to specify boxes position on the horizontal axis

Let's say I have a folowing set of data: k = 1 : list of values k = 3 : list of values k = 10 : list of values I know that to make a BoxWhiskerChart I have to ...
591 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 ...
792 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 ...
514 views

### BoxWhiskerChart with logarithmic axes

I would like to make a following chart Ideally I would also like to control the boxes position on a logarithmic x-axis. Some inspiration how to do the latter may be found in the answer to my ...
293 views

### How to plot an implicit value funtion

Previous question has been solved (Gap in a continuous plot). Here is a new related question. ...
126 views

### Given two samples, how does LocationTest select its AutomaticTest?

How does LocationTest select its "AutomaticTest" when testing two samples? Background: A previous post poses a similar question ...
968 views

### stationary distribution of a transition matrix

How can I solve the stationary distribution of a finite Markov Chain? In other words, how can I estimate the eigenvectors of a transition matrix?
166 views

### Compute symbolic Expectation of a summation

I am required to computed following Expectations : $E[\displaystyle\sum\limits_{i=1}^N \frac{X_{i}}{N}] = \bar{x}_{0}$ & \$E[\displaystyle(\sum\limits_{i=1}^N \frac{X_{i}}{N})^2] = ...