For questions about distributions built-in in Mathematica, and functions that operate on them. Also includes questions about defining your own distributions.

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How to pass a custom method to a particular option?

In an answer to my question More efficient method to compute moments of the Johnson $S_B$ distribution, J. M. has come up with a method to compute the moments of the Johnson $S_B$ distribution, which ...
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540 views

When are `If`, `Piecewise`, `Switch`, and `Which` interchangeable and when are they not?

Experimenting with joint dependent distributions via the TransformedDistribution function, I used the following to derive a distribution where the second variate is ...
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45 views

Gaps in CDF produced from HistogramDistribution

I have about 200 real numbers spread over the range 0-400. I use HistogramDistribution to bin them and PDF to create the ...
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0answers
152 views

Goodness of Fit of Copula Distribution

I am trying to find out goodness of fit of copula distribution, but Mathematica 10 gives me the same answer for each copula type. e.g ...
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88 views

How to define a bivariate skew normal distribution?

There is BinormalDistribution that handles easily bivariate normal distribution and its mixtures. There is also ...
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35 views

How to generate an arbitrary discrete distribution? (EmpiricalDistribution vs ProbabilityDistribution)

I've just started using Mma's distributions. Suppose I want to generate an arbitrary discrete distribution by matching probabilities to outcomes. ...
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68 views

Detecting discontinuities in derivatives in images

Considering an grey-scale image as a function $z=f(x,y)$. (Specifically, I'm interested in $f=h*h*...*h$, where $h$ is the indicator function of a regular hexagon.) I am interested in finding places ...
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51 views

Marginal distribution with weight

Given a multi-variate distribution $P(\mathbf{x},\mathbf{y})$, I would like to obtain the marginal distribution $$P_m(\mathbf{x})=\sum\int_{\mathbf{y}}P(\mathbf{x},\mathbf{y})W(\mathbf{y})$$ In my ...
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44 views

Custom graph distribution

I am working with random graphs a lot. It's quite easy to describe random graph using, adjacency matrix or just a list of edges. However I am thinking that I might benefit from describing random ...
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116 views

Copula - Correlation or Covariance

Can someone explain to me why the CopulaDistribution function with a "Multinormal" kernal asks for the covariance matrix instead of the correlation matrix. Just by looking at the formula for copula, ...
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98 views

Why do EstimatedDistribution and DistributionFitTest work this way

I am fitting some time-series data to both a stable distribution and a normal distribution in order to assess the goodness of fit of each. Along the way I encountered the following confusing result. ...
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187 views

Partial convolution of random variables in random vectors

Suppose $(X_1,Y_1)$ is a bivariate random vector with a given distribution and let $X_2$ be a univariate random variable with the same distribution as $X_1$ but independent of $(X_1,Y_1)$. I want to ...
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774 views

Calculate variance of random walk?

How can I symbolically calculate the variance of the following random walk in Mathematica? Given several discrete random variables such that $p(Z_i=1-2k)=p$, where $k$ is a small real number, and ...
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101 views

Fitting data to an Normal Inverse Gaussian distribution

I am using data which I suspect is distributed according to the Normal Inverse Gaussian distribution (NIG). The literature says that the 4 parameters of the NIG can be estimated from the sample mean, ...
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92 views

Question about Mann-Whitney implementation in Mma

So, I've been doing some statistics using Mma. Typically, the Mann-Whitney U test is used to compare non-normally distributed samples, whose medians are compared if both distributions exhibit similar ...
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45 views

Mixture of a bivariate distribution defined as a copula

I define a bivariate distribution: ...
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99 views

Extrapolation of area for a 2D integration

I have a set of points distributed almost uniformly in a certain area of a 2D plane as follow: An example of data points (orange) data = {{0.919443, 1.68921*10^-22}, {0.262277, ...
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48 views

Fit a custom process to a data: inhomogeneous 2-state Markov chain

I would like to fit a custom process - a time inhomogeneous 2-state Markov chain, to data. The time inhomogeneity is a result of the transition probabilities varying sinusoidally through time with a ...
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0answers
127 views

Von Neumann's method to generate points uniformly distributed on a region of a n-sphere surface

I am trying to generate points uniformly distributed on a region of a single n-sphere surface (all angles in hyperspheric coordinates are between 0 and Pi/2). I decided to use von Neumann's method ...
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55 views

Why is Plot3D applied to TransformedDistribution in 2 random variables so slow?

I am trying to plot 3D, the pdf of a TransformedDistribution made up of random variables. So I can see the pdf in 3D, similar to this answer here Visualizing a 2-dimensional PDF But it seems to take ...
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107 views

Summing the probability distribution to 1 to convince myself

I have worked out a probability distribution and want to check its sum which is necessarily 1. First we write $$ r \triangleq \frac{(2 \lambda + \mu)^2}{2(\mu + \lambda)^2}, \quad s \triangleq ...
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38 views

FisherHypergeometricDistribution and WalleniusHypergeometricDistribution, how to specify boundary conditions

I'm trying to write a function that consists of a noncentral hypergeometric distribution. When I'm passing a set of parameters to the function, the following boundary problems occur: ...
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0answers
45 views

Why does integration of a radical times HeavisideTheta give a conditional expression?

If I want to compute an integral over x^p HeavisideTheta[y-x] where p is some fraction, I do not get the desired result, but ...
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0answers
178 views

Manahalobis distance between two vectors

I want to calculate the Mahalanobis distance between two vectors that represent two points. For example: ...
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175 views

Is this the correct method in using bootstrapping to determine a lower confidence bound?

Quite often in industry, due to cost and schedule constraints, decisions must be made on small sample size data. I have 4 cycles-to-failure values resulting from running samples to failure in a ...
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57 views

Moments Ratio Plot using “ProbabilityDistribution”

I am trying to plot moments ratio plot with the following code: ...
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274 views

Developing easy code to apply Delta Method to generate prediction bands for custom distributions

I think that this is an interesting issue for all those who when to not only adjust one prediction function, but also to obtain the prediction bands to asses the graphical or tabular error I'm trying ...
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41 views

Exploring contours plots of two Binormal distributions

I am facing a little interesting problem. Let´s suppose two binormal distributions, as follows: ...
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36 views

Non-existent PDF for combined MixtureDistribution and TransformedDistribution?

I am trying to mix two discrete distributions, one of them shifted by an integer amount by means of TransformedDistribution. When I then try to access the mix, it responds to CDF but not PDF. This ...
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60 views

Multinormal Distribution with an affine transformation

The affine property of Gaussians says: if $x \sim N_x(\mu_x, \Sigma_x)$, one can apply an affine transformation to $x$, $y = Ax + b$, which gives the distribution --> $y \sim N_y(A\mu_x+b, A\Sigma_x ...
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107 views

Creating a Distribution

Say I want to create a multivariate distribution that perhaps, as an example, looks something like this. ...
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117 views

How to perform a distribution fit test to censored data

With following code I will get an error: ...
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0answers
45 views

Comparing NIntegrate with definite integration

I want to calculate without error a sum of double integrals with the following definitions for the functions within them: ...
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228 views

Function not recognized by Mathematica?

I'm trying to do triple integration on a bivariate function where one of the upper integration limits is the variable of the outer-most integration. When I execute the following lines, Mathematica ...