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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1
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2answers
45 views

Random Variate from a transformed Distribution

I would like to simulate random variates from a transformed distribution of a joint distribution and a constant. i.e. ...
1
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1answer
51 views

Joint Distribution with a Constant

I would like to simulate from a joint distribution multiplied by a constant. e.g. 3*NormalDistribution[0,1]*NormalDistribution[1,1] I tried using something like ProductDistribution but that doesn't ...
9
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2answers
178 views

Sampling phase space uniformly for a given energy

For example, for the 1D harmonic oscillator, the energy is given by: $$ E = \frac{1}{2 m} p^2 + \frac{m \omega^2}{2} x^2 $$ where x is position and p is the momentum. I would like to sample phase ...
1
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1answer
49 views

eigenvalues distribution

How does one plot eigenvalues distribution of a large matrix? I want to plot the distribution to show that the set of eigenvalues of the matrix of current interest is symmetric with respect to the ...
1
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1answer
78 views

multivariate lognormal distribution in mathematica

Is the LogMultinormalDistribution function really the multivariate lognormal distribution? Because I get different results with the same parameters in ...
1
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0answers
37 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 ...
0
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0answers
64 views

Creating a Distribution

Say I want to create a multivariate distribution that perhaps, as an example, looks something like this. f(x1,x2,x3)=f1(x1)*f2(x2)*f3(x3)InverseStandardNormal[F1(x1)]... Obviously the function I am ...
1
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1answer
44 views

Mixture coefficients and Parameter estimation for moving Normal distributions

I am searching for a way to do the following steps below. I am stumped and I have stumped a few profs too. Any help would be appreciated. I would like to import data from, say, excel or a .txt file ...
2
votes
1answer
100 views

How to get a more compact form of this probability calculation?

Inspired by the probability calculation here, I am trying to solve a little general one: $$\mathbb{P} (\sum_{i=1}^{m-1} A_i + \sum_{i=1}^{m} S_i < L < \sum_{i=1}^{m} A_i + \sum_{i=1}^{m+1} ...
4
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2answers
146 views

what is The Formula behind the Kolmogorov-Smirnov test statistics?

I calculate the Kolmogrov-samirnov test statistic for the following data: ...
5
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1answer
277 views

How to solve this probability symbolically or numerically?

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 ...
1
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1answer
113 views

Country density plot of lines (highways)

I love solution from question (histogram as well as distrubution) http://mathematica.stackexchange.com/questions/31948/show-density-plot-on-us-map#=. But both cases are a bit more difficult in my ...
2
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1answer
38 views

TransformedDistribution using n iid random variables

How do I create a TransformedDistribution that uses $n$ independent identically distributed (i.i.d.) random variables? For example, I can derive a chi-squared ...
0
votes
0answers
37 views

Using List/Histogram Data As A Weighted Function?

I have a list of data points that I would like to use as a weighted fucntion. The data represents the number of particles within a bin of a particle distribution. Ultimately I would like to multiply ...
2
votes
1answer
116 views

on Kolmogorov-Smirnov test

I found a problem to calculate Kolmogorov-Smirnov test statistic or p-value the data is ...
1
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1answer
100 views

In there a way to derive the inverse value of CDF format MultinormalDistribution?

Is there a way to produce the inverse value of multinormal distribution function in CDF format with 0.05 significance level? I found the function called ...
2
votes
0answers
81 views

Distance between vectors does not match distance between probability distribution [closed]

I have vectors that describe shapes. I am doing Euclidian distance between vectors to get the similar shapes and I get a good results of all classes. Theoretically, two similar shapes (shapes in a ...
0
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0answers
40 views
1
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0answers
27 views

Dependent probabilities distributions?

What's the best way to model situations with dependencies--I pick a world state, then pick a distribution to draw samples from based on that state. Here's a concrete version: If I choose a 6-sided ...
2
votes
1answer
54 views

Statistical Analyzis of Observed Data (Queuing Process)

Basically I have a process that belongs to a certain state at any point of time. However, the time intervals are not fixed (in fact they are exponentially distributed). Essentially, the data points ...
0
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1answer
38 views

Understanding `TransformedDistribution` behavior on two similar lines of code

The two following lines of code does not give the same output. Mathematica manages to calculate the first one but fails to calculate the second one. ...
0
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0answers
18 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: ...
1
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0answers
38 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 ...
1
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1answer
95 views

Where can I find a good tutorial for stochastic modeling using Mathematica?

I am a newbie in Mathematica and I aim to use Mathematica mostly for stochastic modeling (to develop and analyze models in evolutionary biology). Note that I am not necessarily a great mathematician ...
1
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1answer
129 views

What is the PDF of a variable where a parameter is itself a random variable?

Question How do we analyze in Mathematica cases where a parameter in a Probability Density Function (PDF) varies according to another PDF? Consider the following example... Example The text below ...
-1
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1answer
114 views

Uniform distribution on unit circle

I need a uniform distribution on the unit circle (x; y) : x^2 + y^2 <= 1 with the density f(x) = (2/Pi) Sqrt[1-x^2] ...
4
votes
2answers
108 views

Why doesn't FullSimplify simplify expressions with DiracDelta?

I want to simplify a complicated expression with some Dirac delta distributions, but FullSimplify does not do what I want. Specifically, I want ...
14
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2answers
1k views

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 $x = W z+n$ ...
5
votes
2answers
135 views

Getting the Cumulative Distribution Function of f(x) from a dataset of x

I've a data set $\mathcal{X}$ which consists of randomly generated numbers. Let's say for example data = RandomVariate[ExponentialDistribution[1], 10^4]; My aim ...
1
vote
3answers
157 views

Plotting a frequency function

I have a list of numbers and I want to plot the fraction of numbers >= k against k which will naturally be a decreasing curve. How do I do that?
1
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0answers
72 views

Manahalobis distance between two vectors

I want to calculate the Mahalanobis distance between two vectors that represent two points. For example: ...
0
votes
1answer
93 views

On plotting the Weibull distribution

First: How can I plot the Weibull distribution with parameters a = 2 and b = 3.5 on the range of ...
2
votes
1answer
93 views

Structure of KernelMixtureDistribution and SmoothKernelDistribution

I would like to know more about the structure behind the KernelMixtureDistribution and SmoothKernelDistribution in Mathematica. ...
2
votes
1answer
94 views

Choosing The Best Fitted Probability Distribution Model

The following Example 20 Obs and i used Goodness of fit test with Exponential distribution, another time with Weibull distribution and third time with Pareto distribution .All of them are significant ...
1
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1answer
96 views

Estimating Confidence Interval Variance covariance matrix from weibull distribution

In The following Example 50 obs . I estimated distribution parameters (by point) but *i want to estimate parameters by confidence interval and calculate covariance matrix i need help * ...
5
votes
1answer
261 views

Areas of Voronoi cells from image file

I have an binary image with non-point objects. Does anyone have any suggestions how to determine area of each Voronoi cell in Voronoi diagram (goal is area distribution)? Thank you in advance.
3
votes
1answer
91 views

How to measure cross-covariance in mathematica

In matlab cross-covariance is given by [c,lags] = xcov(x,maxlags,'coeff'); How can I measure in Mathematica?
0
votes
1answer
76 views

Estimating Parameters of a Custom Distribution

The problem is I can not get estimation of parameters of any custom probability distribution (distributions are not built in Mathematica), here is an example: First: I entered random numbers of ...
0
votes
1answer
574 views

PDF of binomial distribution and mixed binomial distribution

I want to plot the PDF of binomial distributed function and a mixed binomial distributed function, therefore I entered for the binomial distribution function the following: ...
0
votes
1answer
65 views

Moment generating function for custom distribution [closed]

For some reason the following fails. I tried everything I could, and I don't know what else to try. ...
0
votes
1answer
34 views

Calculate deviation of sum of several equal normal distribution [closed]

I have a normal distribution with mean m and standard deviation d. How can I calculate what will be the deviation if I add N such distributions? As I understand, mean will be m*N. Will standard ...
6
votes
1answer
135 views

How can I create a Distribution from its probability density function?

I have a probability density function. Is there a mechanism to create a Distribution object from it, such that normal Mathematica commands that usually work on ...
15
votes
1answer
318 views

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 ...
8
votes
2answers
827 views

What is the best distribution for my histogram?

I defined a security bound for a random walk (cube with 15 lengh) 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: ...
3
votes
2answers
175 views

How to extract the probability density function from SmoothHistogram? [duplicate]

I have some data.I plot the histogram with SmoothHistogram in Mathematica. If the y-axis of the histogram is my p(x) function, I want to plot f(x)=(1/n)ln(p(x)) ...
1
vote
1answer
104 views

Parameter Estimation of a mixture of sums of Lognormals

Let $X$ be a random variable that is of a mixture distribution of two lognormals (with the same sigma), so $X \approx p\cdot \mathcal L (\mu_1, \sigma) + (1-p)\cdot \mathcal L (\mu_2,\sigma)$. Now ...