# Tagged Questions

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.

5answers
352 views

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

I want to estimate, for groups of x persons, the probability that at least two of them have the same birthday. I want to repeat this process 1000 times. So I'm looking for the number of 1000 random ...
0answers
39 views

### Better chances on a gambling game [closed]

I'm working on a program that I hope it will help me to get better chances on a gambling game. I have a very large database of numbers how occur in this game and my program pass through those numbers ...
0answers
40 views

### Half Normal Distribution [migrated]

I have a question about Half Normal Distribution. Suppose that $x$ is Normally Distributed with zero mean $(\mu=0)$ and variance $(0<\sigma^2 <1)$. I want to find the probability distribution ...
1answer
108 views

1answer
64 views

### Mean of inverse probability distribution does not agree with explicit integral

I tried to work with the inverse exponential distribution and encountered the following, which I think is an inconsistency in Mathematica (version 10.0.2): ...
1answer
188 views

### Integration of linked PDFs over probability simplex

I'm trying to integrate the following expression: f[a1,p1+p2+p3+p4]*f[a2,p2+p3+p4]*f[a3,p3+p4]*f[a4,p4] Where ...
1answer
96 views

### Find fit of an experimental PDF

After quite some struggle, I managed to put up a code that is syntaxically correct. The goal is to find the parameters for a gamma distribution that best match experimental data. The data is a set of ...
1answer
74 views

0answers
47 views

### Optimization of custom probability distibutions?

Consider the two tests: Timing[Do[RandomVariate[NormalDistribution[0.5, 0.3]], {200}]] {0.001188, Null} ...
2answers
138 views

### Plot contours for 3d histograms

I have a data set which is a list of pairs. From this I can easily make a 3d histogram with Histogram3D[data] or a smoothed ...
1answer
64 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 ...
2answers
142 views

### Deriving a Rayleigh distribution

When I tried to find this Rayleigh distribution Mathematica couldn't come with an answer: ...
2answers
117 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: ...
0answers
45 views

### How to Fit a Generalized Pareto Distribution to data in Mathematica

I'd like to know how to fit a Generalized Pareto distribution in Mathematica to implement the Peak Over Threshold method for tail estimation of operational risk losses. Does anybody have a toy example ...
1answer
70 views

### Find confidence interval for negative binomial using Mathematica

I would like to find the exact 95% confidence intervals on the mean of a negative binomial random variable using Mathematica. It is possible to approximate the distribution using a gamma/normal, but ...
1answer
58 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 ...
0answers
84 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, ...
5answers
630 views

### Probability problem — Rube Goldberg solution?

A user posted this question on StackOverflow which was closed as off topic: 3 people are playing a game with a standard 52 card deck. Each player is given 2 cards each, possible cards and their ...
2answers
37 views

### Simulate from an AR(1) process where the parameters vary over time

I would like to simulate from an AR(1) process, where the $\rho$ parameter in the process of the form: $X_t = \rho X_{t-1} + \epsilon_t$ varies over time. The path of $\rho$ and $var(\epsilon_t)$ ...
1answer
59 views

### Find maximum Log likelihood for repeated random variates

I have the following code ...
1answer
67 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 $\sqrt{x^2+y^2+2xy\cos(\phi)}$, ...
2answers
120 views

### How to plot points with error circles on map with latitude/longitude grid

I am currently working on a project to model the location of icebergs in the northwest atlantic. When an iceberg is sighted, an error circle is plotted around it (with a bivariate normal probability ...
1answer
56 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: ...
2answers
197 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 ...
0answers
94 views

### Computational Bayesian analysis in Mathematica: Any plans to develop MCMC?

Does anyone know if there are any plans to develop an MCMC capability in Mathematica? My reasoning for asking is that as it stands, I can't seem to find any 'out-of-the-box' functions/capabilities ...
0answers
76 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 ...
1answer
81 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 ...
1answer
105 views

### how to scale the plot of PDF (t-distribution)

The directions in my book say: "To sketch the t distribution in Figure 3.11, simply multiply the abscissa t value by the scale factor and plot this against the ordinate of t at that point." So ...
1answer
70 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}\\ ...
2answers
65 views

### Maximum likelihood estimation based on frequency table

I have a frequency table of grades, I'm trying to estimate the distribution as a truncated normal distribution (a grade below 65 is a failing grade and doesn't count). Since I don't have the actual ...
1answer
92 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 ...
3answers
183 views

### Find 2 points in a normal distribution with these given properties

I would like to find a and b. How should I code this in Mathematica? What I did wrong? ...
2answers
177 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 ...
7answers
3k 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 ...
1answer
74 views

...
0answers
48 views

### Help with Multivariate ProbabilityDistribution

I wish to obtain numbers from ...
3answers
371 views

### Negative probability?

Bug introduced in 9.0.1 and fixed in 10.0.2 I am trying to get the sum of the squares of seven random variables, all uniformly distributed. This is what I tried. ...
0answers
74 views

### Constrained Nonlinear Optimization with expectations functions in the constraints

I am modeling an optimal compensation contract with a CRRA utility function : ...
0answers
46 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 ...
1answer
39 views

0answers
12 views

### In Mathematica, how to calculate marginal probability of continuous conditional distributions? [duplicate]

I have random variables A and B, given by Beta distributions. This can be easily defined in Mathematica. I have a conditional probability P(C|A,B) which I custom-design as a function. The function ...
1answer
56 views

### There is an higher probability to win with 3 dices versus 2 or with 4 dices versus 3?

In Dice wars, you gain a territory rolling the dices you have in an adiacent territory (almost like Risk game). If I have more options to choose, there are more chances to win with 3 dices versus 2 ...