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

I am puzzled because this toy example (in Mathematica 8) ...
5k views

### Creating Optimal "Smoothed" Contour-Type Plots (X,Y,Z) Using Mathematica 8.04 [closed]

Update: data here Here is a contour plot produced in the SAS program: In this plot, variable 23405 forms the X axis, variable 20201 forms the Y axis, and outcome variable 50502 forms a pseudo Z ...
979 views

### Sensitivity Analysis: Global Sensitivity and Screening

I have a model which accepts several input parameters and now I want to study the sensitivity to certain parameters as described in here: Cross Validated Answer and in Wikipedia. There is also a link ...
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### WinBUGS Interface

Has anyone created on WinBUGS (Bayesian inference Using Gibbs Sampling) interface with Mathematica similar to BugsXLA for Excel? I'd like to setup the model, define the evidence in a notebook and then ...
1 vote
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### Expectation over a list with nested-mapped expressions

I need expected values of a list where the random variable to take expectations over should be an input into expressions defined earlier. I suspect Set[] and SetDelayed[] tripped me. (Or Map and Table?...
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### How to Compute Aggregate Best and Worst Cases for a Large Number of Estimates?

I need to aggregate multiple estimations, but I haven't been able to find a built-in function in Mathematica that aggregates multiple probablity estimations (I am specially interested in estimations ...
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### Using ANOVA with a "Repeated measures" / "Within-subjects" design

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

### Support for Multidimensional Scaling (MDS)?

Does Mathematica support MDS? Or, are there any libraries that support it? Basically, I have points and a distance function defined between them, and I want to plot them in 2D space, trying to ...
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### 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, 1/...
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### 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 ...
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### 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 ...
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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 ...
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### 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" ...
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### 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 ...
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### 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 ...
791 views

### Some questions about random numbers

How can I get non-repeating random numbers from Mathematica 8? How can I know which distribution the numbers I get are? Can I choose the distribution I want together with the non-repeating random ...
2k 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.
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### 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 ...
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### 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 ...
2k views

### How to plot CDF of a Poisson distribution in Mathematica

How to plot the following in Mathematica: $$P = \sum_{k=C+1}^{\infty}\frac{e^{-C^\gamma} (C^\gamma)^k}{k!}$$ I want to plot $P$ versus $C \log{C}$ for a given $\gamma$ with logarithmic scale on Y-...
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### Non-linear trend reduction with missing data

How can I reduce a non-linear trend of some data series if there are parts of "no data", represented by the value 99999? For example: ...
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### 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 ...
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### Creating word histograms from lists of strings

Consider the following: ...
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### 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 ...
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### Just what kind of transformations can TransformedDistribution handle?

Why does the following command return an empty plot? ...
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### How can an InverseQuantile or an interval valued Quantile function be implemented in Mathematica?

Quantile[] is the workhorse method in robust data analysis and statistics (see, eg Koenker's Quantile Regression). However, it should be complemented by an ...
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### Identifying subsets with minimal standard deviation

Consider the following: ...
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### 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 ...
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### 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 ...
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### Is there a function to calculate studentized range?

Is there a built-in function for studentized range or do I have to build it myself? Is there a test of normality for the studentized range?
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### 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.) ...
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### Extracting equations from Piecewise expressions

Say I have a PDF: PDF[LogNormalDistribution[1.75, 0.65], x] Calculating it, Mathematica gives me an expression that looks like this: I want to extract the ...
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### How do I calculate the probability of reaching mean residual life

I need to understand the Survival Analysis concept of "mean residual life (MRL)" and calculating probabilities for reaching it. From another discussion: The MRL at time t is the mean additional ...
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### 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 ...
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### Function to compute the probability of exactly one event occurring out of N independent events

Is there a built in function (or a function in one of the standard packages) that allows you to compute the probability of exactly one event occurring out of some known set of probabilities for N ...
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### RandomVariate with a Discrete Distribution

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 ...
1k 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 ...
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### RandomVariate from 2-dimensional probability distribution

A probability distribution can be created in Mathematica (I am using 8.0.1) with e.g. ...
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### 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 ...
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### How to solve for an Z-Score of a T-Distribution?

I'm looking for the Z-Score for a distribution, where the integrated area sums up to 0.90. Unfortunately I always get an error from Mathematica, "nonnumerical value"...
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### 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 ...
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### Function for Autocorrelation

Is there a built in function to compute the autocorrelation of a signal ?
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### 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 ...
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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 ... 845 views

### Probability problem -- Rube Goldberg solution?

A user posted this question on StackOverflow which was closed as off topic: 3 people are playing a game with a standard 52 card deck. Each player is given 2 cards each, possible cards and their ...
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### Conditional T distribution

Suppose $(X,Y)$ has a bivariate t distribution. I want to plot the density of the conditional density of $Y$ given $X$, i.e. $Y|X$. I wonder why the following does not work: ... 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 ...
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### 2D Gaussian distribution of squares coordinates

I would like to imitate the structure of this great painting from Ellsworth Kelly in Mathematica. Yet with all the colored squares in Black and the beige one in white. Below is what I have wrote to ...
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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 ...
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