Questions about performing probabilistic calculations, especially those concerned with the Mathematica commands Probability, Expectation and the various functions related to distributions such as NormalDistribution, CDF, PDF etc.

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30
votes
6answers
2k views

Efficient way to generate random points with a predefined lower bound on their pairwise Euclidean distance

Using Mathematica what is an efficient way to generate a list of $n$ random two dimensional points $\{x_i,y_i\}$ where $i=1,...,n$ so that no two points $p_1$ and $p_2$ in the list has an Euclidean ...
11
votes
3answers
2k views

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 ...
27
votes
1answer
2k views

RandomVariate from 2-dimensional probability distribution

A probability distribution can be created in Mathematica (I am using 8.0.1) with e.g. ...
4
votes
3answers
339 views

Plotting the convolution of the same probability density function with itself

I would like to compute the integral $$q_n(x)=\int_{B}^A q_{n-1} (\omega)f(x-\omega)\mathrm{d} \omega,\quad q_1=f,\quad n\geq 1.$$ for a given density function $f$. Basically it is the convolution ...
7
votes
1answer
863 views

Mathematica Package for Bayesian Networks

Are there any packages that allow the simulation of Bayesian Networks with Mathematica? I found what seemed to be a promising package (Dynamics) on a Brown University URL, ...
4
votes
3answers
600 views

Graphical Plots of PDF and CDF

I have a joint density and distribution function that I want to plot in a meaningful way, (i.e., want to be able to see how the functions behaves as changes in x and y happen simultaneously. If ...
3
votes
1answer
147 views

Determining the dimension of a probability distribution

Functions like Mean and RandomVariate clearly infer the dimension of the distribution passed to them. One can also usually ...
3
votes
2answers
92 views

Expectation of a composite Markov-Gamma distribution

In a model I have a discrete two-state first order Markov process, defined by a (2x2) transition matrix with two free parameters. If the first state occurs then the process outputs zero for that ...
0
votes
1answer
62 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 ...
8
votes
1answer
804 views

Mathematica code for hidden Markov models (HMM)

I am looking for some simple Mathematica code to model an HMM with just a few states and an equal number of observable signals (emissions). I am hoping to generate sample paths and keep track of the ...
6
votes
0answers
201 views

Speeding up multilinear PRA branch-and-bound algorithm with worst-case exponential time scenario with respect to basic events

The algorithm is a branch-and-bound algorithm that calculates dominances for PRA, probalistic risk assessment. The task was to find faster ways to do it in numerical software such as Matlab but we ...
13
votes
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 $x = W z+n$ ...
4
votes
4answers
487 views

Generate random points in a region with higher probability in a sub-region

I am trying to generate random samples of points in the unit square in such a way that points inside a given circle are twice as likely to be selected as points outside of that circle. I tried to ...
10
votes
6answers
1k views

2D Gaussian distribution of squares coordinates

I would like to imitate the structure of this great painting from Ellsworth Kelly in Mathematica. Yet with all the colored squares in Black and the beige one in white. Below is what I have wrote to ...
1
vote
1answer
233 views

Detecting a nonlinear edge in a 2D point pattern

Following an earlier post here, I have generated a point pattern on the unit square $[0,1]\otimes[0,1]$, which is described by a piecewise constant intensity function constructed so that (in ...
10
votes
4answers
412 views

Extracting equations from Piecewise expressions

Say I have a PDF: PDF[LogNormalDistribution[1.75, 0.65], x] Calculating it, Mathematica gives me an expression that looks like this: I want to extract the ...
8
votes
2answers
522 views

Expected Value: Strange/unexpected result

Assume $X$ is an exponential random variable with unit mean ($f_X(x)=e^{-x}$, $x>0$). I want to calculate the expected value of $\frac{1}{X}$. Since $X>0$, I am expecting that ...
8
votes
1answer
404 views

Random variables with transformed discrete distributions cannot be applied to Probability[] function?

I have two discrete uniform distributions over same support: Dx = DiscreteUniformDistribution[{-8, 8}]; Dy = DiscreteUniformDistribution[{-8, 8}]; I use ...
5
votes
4answers
317 views

Probability: proportion of 1000 random lists for x that contain the same nrs

Give a function which calculates for each x a random list of birthdays (which can be x=1 to x=365) birthdays[x_] := RandomInteger[{1, 365}, x] is my answer. ...
4
votes
2answers
414 views

Why does this integral have a complex component?

I wanted to find the probability of my normally-distributed random variable being at least 15, so I set up this integral: ...