# Tagged Questions

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 generate random points in a region?

The Mathematica 10 documentation was updated for FindInstance adding support for regions. In my use case, I'm trying to sample points in a set of disks: ...
3k views

### 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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### 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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### Visualization of Bivariate Distributions

I know it is perfectly possible to show the bivariate probability distributions in MMA. But my question is can we show each dimension of distribution in 2D dimension while we are showing the 3D plot? ...
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### Efficient Generation of Random Variates from a Copula Distribution

I have a 7-asset portfolio for which I want to simulate daily log-deltas using a Student T copula. The marginal distributions are all either Stable or TsallisQGaussian. Using NMaximize, I have ...
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### Given an exact formula, how can Mathematica find a probability distribution whose PDF matches it?

So, given some data, Mathematica 10.2 can now attempt to figure out what probability distribution might have produced it. Cool! But suppose that, instead of having data, we have something that is in ...
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### 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 ...
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### More efficient method to compute moments of the Johnson $S_B$ distribution

Here is a very specific feature request. I need Mean[JohnsonDistribution["SB", γ, δ, 0, 1]] When I issue e.g. ...
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### Speed up adding Poisson noise to an image

I'm simulating some images corrupted with Poisson noise, but I'm encountering a few problems with performance. According to the documentation on ImageEffect, one ...
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### 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 $x = W z+n$ ...
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### How to compute the inverse CDF of HyperbolicDistribution properly?

Fixed in version 9. I want to compute the CDF and inverse CDF of the hyperbolic distribution: ...
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### RandomVariate returns values outside the support of a PDF

Bug introduced in 8.0.1 and fixed in 10.2.0 Let $X$ be a random variable with pdf: dist = ProbabilityDistribution[1/(Abs[x]*Log[Abs[x]]^2), {x, -E^-2, E^-2}] ...
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Observe: ...
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### 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 ...
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### What is the best distribution for my histogram?

I defined a security bound for a random walk (cube with 15 length) and I have this code to obtain a sample of the random times at which the random walk crosses the boundary for the first time: ...
336 views

### Frequency of punctuation characters used in Mathematica languages

I would like to determine the computer language character frequency in Mathematica code. I want to remap my keyboard to the most used character such as [], {}, -, +. There are the frequency of ...
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### Probability and distribution from actual data

Let's say I have some data from a real world system: ...
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### Sampling a phase space uniformly for a given energy?

The energy for a 1D harmonic oscillator can be written: $$E = \frac{1}{2 m} p^2 + \frac{m \omega^2}{2} x^2$$ where x is position and p is the momentum. I would like to sample phase space $(x,p)$ ...
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### Generating uniform random points over a binary image

So I recently read this excellent post about generating random points over arbitrary regions. I hope Wolfram eventually builds that functionality into Mathematica's Random functions. I want to do this ...
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### Trying to fit an unknown extreme distribution

First up, I'm quite new to Mathematica so any hints on better code would be greatly appreciated. I have some histogram frequency data from an unknown distribution that I'm trying to fit. Here's the ...
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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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### 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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### Probability: MultivariateHypergeometricDistribution broken with more than five categories?

2016-04-09: This bug is indeed fixed (thank you, Stefan R.!) in 10.4. It may have been fixed in 10.3 or 10.3.1, but I haven't tried these versions. ...
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### Possible bug in VonMisesDistribution?

Bug introduced in 10.2 or earlier and fixed in 10.3 Observe: ...
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### Compiling the VoigtDistribution PDF

According to List of compilable functions, Erf and Erfc are compilable functions. However, I want to make a compiled version ...
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### How does LocationTest choose its “AutomaticTest”?

Is there a way of determining how LocationTest chooses its "AutomaticTest"? Sometimes it's clear from the ...
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### FullSimplify on TransformedDistribution

Bug introduced in 8.0.0 and fixed in 10.3.0 Could someone check that I haven't gone mad? I would like to take the maximum of two $[0, 2 \pi]$ independent uniform random variables. ...
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### Deriving a PDF for an annulus distribution

I would like to derive the PDF for an ''annulus'' type distribution, defined by the parameters $\theta\sim U(0,2 \pi)$ and $d\sim N(0,\sigma)$; where $\theta$ is the angle round a circle of radius $r$,...
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### Linear fit with conditional noise distribution

I need to fit a linear model of the form $y_i = a · x_i + b + e_i$. The $e_i$ are independent noise from a distribution that depends on $x$ as well as on global parameters of the data; however, the ...
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### Finding skewness and kurtosis numerically in Mathematica

I have a function given by ...
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### The default bandwidth of the SmoothKernelDistribution function

I am researching the Silverman rule of thumb for bandwidth selection. Below is a sample of my code, from which it seems that BW=63 is close to the default parameter given by Mathematica (2 images are ...
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### Why are Binormal and Multinormal giving me different results when I use NExpectation?

fixed in 10.1 (windows) Binormal and Multinormal can both be used to represent normal random variables: ...
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### How to evaluate if a list obeys the Normal distribution?

I am processing a data when I encountered this problem. I use the way of plotting the "normal probability plot" to show the result The list I have is: ...
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### Inconsistent DistributionFitTest results?

In pondering this question, I used Mariana's function to generate the following data. ...
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### AndersonDarlingTest and DistributionFitTest Leaking Memory

I believe AndersonDarlingTest and probably all other tests are keeping a copy of data somewhere and not freeing it: ...
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### How to randomly erode a 3D distribution of points with Mma 7.0?

Suppose we have a 3D distribution of points, like the spherical ball example below : ...
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### Is there any function that compares distributions of two populations?

Imagine I have two populations that I want to test whether they exhibit similar shape distributions. Is there such a function that does this sort of testing already implemented? I am asking this ...
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### Distribution over the product of three, or n, independent Beta random variables

I would like to calculate the PDF for the product of three independent Beta random variables. Specifically, I would like to find the distribution of the product of the following: $X_1\sim Beta(1,3/2)$,...
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### RandomVariate does not fill range of PDF of distribution

I've declared my own probability distribution as follows dist[a_, b_] := ProbabilityDistribution[Cos[(b x)/2]^2 Sinc[a x]^2, {x, -400, 400}]; When I try to ...
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### How to generate two group of $n$ random numbers in $U(0,1)$ such that sum of these two groups equal? [closed]

I want to have two groups of $n$ random numbers $u_i$ and $v_i$ in $U(0,1)$, such that $\sum u_i = \sum v_i$ What I tried is: I can firstly get $u_i$ by ...
351 views

### How to create a spliced survival statistical distribution?

I am trying to use Mathematica for more of my reliability engineering work and am having trouble using SplicedDistribution. I have a Weibull distribution (dist1) associated with a low stress ...
360 views

### DistributionFitTest with WeightedData?

My problem is related to statistical testing with weighted data. I have a data sample and I assume that a part of the data follows a specific distribution (Pareto). So I fit my data to a distribution ...
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Observe: ...
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### Nearest neighbor distribution

I need to construct nearest neighbor distribution for a given finite set of real numbers. I have no clue how this can be realized. Any suggestion would be very much appreciated.
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### How to measure accuracy of prediction distribution?

I have been trying to come op with a way to test if my dataset follows a Poisson distribution. Normally one would use the DistributionFitTest function, but here is ...
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### Is there a free version of the Springer book “Mathematical Statistics with Mathematica”?

Is there a free version of the Springer book: $$\text{Mathematical Statistics with Mathematica}$$ by Rose and Smith ... available on the internet?
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### Creating a custom distribution with specified skew and kurtosis

Let's say I want to create a simulated sample of returns for a given investing/trading strategy. I know that my strategy is profitable on 64% of trades, that the ratio of mean win / mean loss is 0.72, ...
160 views

### Scale SmoothHistogram curve to Histogram

Like in this question, I would like to display a histogram and a smooth histogram in the same plot. I believe the default “bin height specification” (or $\textit{hspec}$) for ...
I am trying to calculate the following probability $$\mathbb{P} \big(\sum_{i=1}^{m} (A_i + S_i) \le L < \sum_{i=1}^{m+1} (A_i + S_i) \big)$$ where, A_i \sim \exp(\lambda), \quad S_i \sim \exp(...