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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2
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0answers
169 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 ...
2
votes
1answer
161 views

Time inhomogeneous Markov Chain in Mathematica

I would like to create a discrete 2-state Markov process, where the switching probabilities in the transition matrix vary with time. I can currently do the following, which creates a process with ...
1
vote
1answer
67 views

Using Inner to calculate a log likelihood

I am trying to use the function Inner to calculate the sum of log likelihoods of a custom probability distribution 'custom' applied to a vector of data 'vData'. The custom distribution changes ...
4
votes
2answers
356 views

Calculate PDF and CDF of a product of independent exponentially distributed random variables

Let x[1], x[2], ..., x[n] be independent random variables each of which is distributed exponentially, i.e. with the PDF ...
0
votes
1answer
105 views

Sketch Probability density function [closed]

My question is : Suppose that the PDF of a random variable X is as follows: \begin{equation*} f(x) = \begin{cases} ce^{-2x} & \text {$x > 0$}\\ 0 & \text {otherwise}\\ ...
0
votes
1answer
136 views

Custom distribution [closed]

I am trying to define a custom distribution using the code below. Unfortunately, it did not produce a satisfactory result ...
1
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1answer
113 views

Mean Preserving PDF Spreading

I have a histogram representing the PDF (probability density function) of an unknown discrete RV. The histogram is asymmetrical. Is there a known way in Mathematica to increase/decrease the variance ...
6
votes
2answers
250 views

When analytical and numerical methods do not agree - Case study with Maximum Likelihoods methods

Here is the probability distribution I am interested in: $$P(q)=C e^{4 n s q} q^{4 n \nu - 1} (1 - q)^{4 n \mu - 1}$$ , where $e$ is the constant of Euler and $C$ is constant so that the whole thing ...
2
votes
2answers
109 views

RandomVariate from Dirichlet into Multinomial Not Summing to 1

I have a draw from a Dirichlet distribution that I would like to use as input into a MultinomialDistribution. For instance: ...
-6
votes
1answer
105 views

Plot 2 student T distributions with different center values

Plot 2 student T distributions with different center values µ, but same DOF. The center values,µ has to be 45 and 48, DOF shall be 9.
4
votes
2answers
318 views

How to plot an implicit value funtion

Previous question has been solved (Gap in a continuous plot). Here is a new related question. ...
2
votes
2answers
120 views

Interpretation of CopulaDistribution [closed]

I was just wondering, when I call the CopulaDistribution function in Mathematica, am I calling its cumulative function or its density function? I have looked up ...
1
vote
2answers
85 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. ...
2
votes
1answer
88 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 ...
0
votes
1answer
79 views

Product Distribution with Copula

I am trying to create a joint probability function that is of the form: f(a,b,c)=f1(a).f2(b).f3(c).copula where ...
1
vote
1answer
67 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 ...
12
votes
2answers
303 views

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 $(x,p)$ ...
2
votes
1answer
349 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 ...
2
votes
0answers
130 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, ...
0
votes
0answers
111 views

Creating a Distribution

Say I want to create a multivariate distribution that perhaps, as an example, looks something like this. ...
1
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0answers
113 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 \...
1
vote
1answer
202 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 ...
3
votes
1answer
129 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} S_i)$...
3
votes
1answer
158 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 ...
5
votes
2answers
1k views

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

I calculate the Kolmogrov-samirnov test statistic for the following data: ...
1
vote
1answer
106 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 function. The data represents the number of particles within a bin of a particle distribution. Ultimately I would like to multiply ...
0
votes
0answers
137 views

Comparing heavy tailed and non-heavy tailed distribution using Mathematica

I have data from a heavy tailed distribution (see picture 1) and a non-heavy tailed distribution (see picture 2) and want to compare it using a histogram on log-scale. However the picture 3 does not ...
6
votes
1answer
379 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 \exp(...
1
vote
1answer
144 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
votes
1answer
284 views

on Kolmogorov-Smirnov test

I found a problem to calculate Kolmogorov-Smirnov test statistic or p-value the data is ...
1
vote
1answer
185 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 ...
0
votes
0answers
143 views

How to perform a distribution fit test to censored data

With following code I will get an error: ...
4
votes
2answers
98 views

Dependent probabilities distributions?

What's the best way to model situations with dependencies? What I mean is well-defined arrangements like: If I choose a 6-sided die with probability $p$ and a 20-sided one otherwise, and then roll ...
2
votes
1answer
96 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
votes
1answer
47 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. ...
1
vote
0answers
39 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
vote
0answers
47 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 ...
2
votes
1answer
311 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
vote
1answer
182 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
votes
1answer
346 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
441 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 ...
5
votes
2answers
423 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
0answers
227 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
238 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
166 views

Structure of KernelMixtureDistribution and SmoothKernelDistribution

I would like to know more about the structure behind the KernelMixtureDistribution and SmoothKernelDistribution in Mathematica. ...
1
vote
1answer
249 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 * ...
2
votes
1answer
316 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 ...
5
votes
1answer
390 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.
2
votes
1answer
178 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 ...