# 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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5answers
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### 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 ...
7answers
7k views

### Efficient way to generate random points with a predefined lower bound on their pairwise Euclidean distance

Using Mathematica what is an efficient way to generate a list of $n$ random two dimensional points $\{x_i,y_i\}$ where $i=1,...,n$ so that no two points $p_1$ and $p_2$ in the list has an Euclidean ...
6answers
17k 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 ...
3answers
5k views

### RandomVariate from 2-dimensional probability distribution

A probability distribution can be created in Mathematica (I am using 8.0.1) with e.g. ...
5answers
6k 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. Attempt I wrote the ...
3answers
12k views

### How to generate a RandomVariate of a custom distribution?

I'm trying to generate a pseudorandom variate out of a custom distribution. Suppose I want define a custom distribution, and for the sake of simplicity I define a Poisson distribution (the ...
4answers
2k 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 ...
3answers
5k 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 ...
2answers
11k 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 ...
3answers
3k views

### Ηow to create an interpolated CDF from its samples?

I want to use a distribution I have only aggregate statistics on, namely its CDF sampled at certain points. I would like to keep it "nonparametric" (remain noncommittal on the parametric form), but I ...
3answers
354 views

### Evaluate a certain three-dimensional constrained integral

The result of the three-dimensional integration ...
6answers
3k views

### Generate two random numbers with constraints

I want to generate two random numbers, $p$ and $q$, between $0.5$ and $1$. They are connected by the constraint $1/(2q) > p$. How do I generate $p$ and $q$?
1answer
1k views

### How can we create a histogram distribution from binning data?

HistogramDistribution takes a list of data points, creates a histogram from them, and returns this histogram in a form that can be used as a distribution. I ...
3answers
4k 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.) ...
1answer
924 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" ...
3answers
6k views

### How to remove outliers from data

I have a data with noise which some times includes significant outliers. The position of the outliers are random. For example: ...
2answers
9k 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: ...
3answers
3k views

### How can I calculate the correlation dimension and/or the Lyapunov exponent of a time series using Mathematica

I have a pretty long time series (4000 data points). How can I calculate the Correlation dimension and/or Lyapunov exponent for such data? Please also advise on how to import the data as well.
3answers
2k views

### Contour lines over SmoothDensityHistogram

I am using SmoothDensityHistogram on a data set of the form {{x1, y1}, {x2, y2}, …, {x_n, y_n}}, and I would like to also show ...
2answers
684 views