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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0answers
13 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 ...
-1
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1answer
47 views

How to generate normally distributed random number [on hold]

I want to sample or return random number from a distribution which is normally distributed with mean of zero and standard deviation of 1. I am using RandomReal[NormalDistribution[0, 1]] I s this ...
0
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1answer
53 views

to find limiting value of function at large N i.e. N->infinity

Is it possible to find the limiting value of function at large N ...
0
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0answers
48 views

to determine asymptotic value of function when N->infinity [closed]

To determine the asymptotic value of function for large value of N, given 'm' is much less than N i.e. in the limit N->infinity and m/N->0 $f(m,N)=\sum_{a=1}^{\lfloor N/2 \rfloor} \binom{N}{S} ...
1
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1answer
34 views

Is this behavior of DistributionFitTest together with StableDistribution a bug?

I have been using DistributionFitTest to fit the following data: ...
3
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2answers
96 views

Iterating distributions

I want to calculate the distribution that comes from summing up random numbers between -0.5 and 0.5. A computationally intensive version of doing this is to simply do the following: ...
5
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2answers
161 views

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.
1
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1answer
61 views

calculate variance of conditional sum of Normals

Let $\quad W \sim N(\mu_0, \sigma_0^2), \quad X_1 \sim N(\mu_1, \sigma_1^2), \quad X_2 \sim N(\mu_2, \sigma_2^2)$ denote independent random variables, and let $c$ denote a constant. I want to find ...
4
votes
2answers
135 views

Deriving a Rayleigh distribution

When I tried to find this Rayleigh distribution Mathematica couldn't come with an answer: ...
1
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1answer
93 views

Accumulating elements of lists taking the criteria out of another list

In order to find the critical values for the significance of a discrete distribution, for example BinomialDistribution[20,0.6], i need a function which works on the ...
0
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2answers
69 views

Plot Bivariate Data with Marginals

I would like to plot bivariate data along with the marginal distributions. I've arranged the plots in a GraphicsGrid as below but the marginals are centered away from the bivariate plot and I wonder ...
1
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1answer
37 views

Generate a sample from a multivariate Cauchy distribution

I want to generate a random sample from a multivariate Cauchy distribution, however I couldn't find a function for the multivariate Cauchy in Mathematica. I know how to define a distribution in 1D and ...
4
votes
1answer
52 views

How to get probabilities for multinomial & hypergeometric distribution ranges more quickly?

I often need to calculate the probability of a result from a multinomial distribution falling within some range, e.g., the maximum of the categories having an upper bound, or a lower bound for the ...
9
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2answers
116 views

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: ...
2
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1answer
37 views

Cannot use the MultinormalDistribution code

I am trying to use the MultinormalDistribution code with the Quantile function to get the 0.01 quartile of the multinormal ...
1
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0answers
80 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, ...
1
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1answer
58 views

Find maximum Log likelihood for repeated random variates

I have the following code ...
0
votes
0answers
32 views

How to fix the PlotRange on LogPlot? [duplicate]

I'm plotting families of Boltzmann'esque distribution functions $\propto\exp\left(-{\dfrac{\varepsilon+{\mathcal O}(\varepsilon^2)}{k_\mathrm{B} T}}\right)$. But it won't let me fix the ...
2
votes
1answer
54 views

Why is RandomVariate of special probability distribution doesn't working in all cases

I would like to generate a random variates in Mathematica 9 with this distribution: ...
0
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1answer
29 views

Fit process parameters to a transformed AR(1) process

I would like to fit the parameters of an exponented AR(1) process using Mathematica's EstimatedProcess, however, the function does not seem to evaluate to anything. First of all I create the ...
1
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1answer
66 views

Cannot evaluate TransformedDistribution for vectorial sum

I'm trying to obtain the distribution of the magnitude (length) of the vectorial sum of two vectors under a random (uniformly distributed) angle $\phi$. The sum is $\sqrt{x^2+y^2+2xy\cos(\phi)}$, ...
1
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0answers
26 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 ...
0
votes
0answers
69 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
76 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
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1answer
49 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
192 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
62 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
73 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
90 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 ...
4
votes
2answers
173 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
63 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: ...
-5
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1answer
68 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
282 views

How to plot an implicit value funtion

Previous question has been solved (Gap in a continuous plot). Here is a new related question. ...
1
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2answers
70 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
62 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 ...
1
vote
1answer
55 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 ...
9
votes
2answers
211 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
128 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
45 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
votes
0answers
72 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
vote
1answer
76 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
106 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} ...
2
votes
1answer
64 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 ...
4
votes
2answers
262 views

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

I calculate the Kolmogrov-samirnov test statistic for the following data: ...
0
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0answers
44 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 ...
5
votes
1answer
311 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
vote
1answer
124 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
162 views

on Kolmogorov-Smirnov test

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