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.
1,801
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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)
...
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2
answers
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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 ...
6
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0
answers
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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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7
votes
1
answer
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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 ...
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1
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2
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258
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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?...
- 345
2
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3
answers
375
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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 ...
- 866
16
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1
answer
1k
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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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2
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922
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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 ...
- 221
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3
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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/...
- 9,758
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2
answers
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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 ...
- 1,987
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votes
4
answers
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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 ...
- 301
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4
answers
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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
...
- 9,218
39
votes
1
answer
990
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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" ...
- 22.2k
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3
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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 ...
- 345
16
votes
2
answers
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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 ...
2
votes
3
answers
791
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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 ...
- 31
9
votes
1
answer
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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.
- 539
13
votes
1
answer
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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 ...
- 14.1k
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votes
4
answers
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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 ...
2
votes
3
answers
2k
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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-...
- 131
2
votes
2
answers
323
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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:
...
- 1,543
13
votes
2
answers
870
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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 ...
- 477
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4
answers
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40
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5
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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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13
votes
1
answer
462
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Just what kind of transformations can TransformedDistribution handle?
Why does the following command return an empty plot?
...
- 1,700
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1
answer
646
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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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4
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8
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1
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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 ...
- 1,533
9
votes
1
answer
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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 ...
- 1,287
3
votes
2
answers
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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?
- 1,287
32
votes
3
answers
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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.) ...
- 427
10
votes
4
answers
821
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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 ...
- 14.1k
7
votes
1
answer
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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 ...
- 14.1k
12
votes
1
answer
647
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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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votes
2
answers
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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 ...
- 471
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votes
1
answer
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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 ...
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2
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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 ...
- 1,533
51
votes
3
answers
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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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7
answers
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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 ...
- 14.5k
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2
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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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votes
5
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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 ...
- 4,039
6
votes
4
answers
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Function for Autocorrelation
Is there a built in function to compute the autocorrelation of a signal ?
- 5,479
16
votes
3
answers
893
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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 ...
- 5,479
12
votes
2
answers
1k
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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 ...
user371
13
votes
5
answers
845
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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 ...
- 267k
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votes
2
answers
536
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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:
...
user371
35
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4
answers
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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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6
answers
2k
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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 ...
- 5,479
52
votes
5
answers
14k
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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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4
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