# Tagged Questions

For questions about distributions built-in in Mathematica, and functions that operate on them. Also includes questions about defining your own distributions.

1answer
3k views

### RandomVariate from 2-dimensional probability distribution

A probability distribution can be created in Mathematica (I am using 8.0.1) with e.g. ...
8answers
2k views

### How to generate random points in a region?

The Mathematica 10 documentation was updated for FindInstance adding support for regions. In my use case, I'm trying to sample points in a set of disks: ...
3answers
6k 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 ...
3answers
3k views

### Standard errors for maximum likelihood estimates in FindDistributionParameters

I am trying to fit a non-standard PDF to data and FindDistributionParameters works great, and gives me the parameters of the distribution back using maximum ...
4answers
2k views

### Visualization of Bivariate Distributions

I know it is perfectly possible to show the bivariate probability distributions in MMA. But my question is can we show each dimension of distribution in 2D dimension while we are showing the 3D plot? ...
1answer
676 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 ...
2answers
2k views

### Finding distribution parameters of a gaussian mixture distribution

Short version: how to estimate the parameters of a mixture of multivariate normal distributions (i.e.: Gaussian mixture model)? Long version. I am trying to estimate the parameters of a mixture of ...
3answers
392 views

### Random non-overlapping disks in a square

I've found a nice code snippet by @belisarius from this question, that I'll reproduce here for reference: ...
2answers
1k views

### Efficient Generation of Random Variates from a Copula Distribution

I have a 7-asset portfolio for which I want to simulate daily log-deltas using a Student T copula. The marginal distributions are all either Stable or TsallisQGaussian. Using NMaximize, I have ...
1answer
375 views

### Inconsistent DistributionFitTest results?

In pondering this question, I used Mariana's function to generate the following data. ...
1answer
333 views

### How does LocationTest choose its “AutomaticTest”?

Is there a way of determining how LocationTest chooses its "AutomaticTest"? Sometimes it's clear from the ...
1answer
191 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 ...
3answers
1k 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 ...
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 ...
1answer
185 views

### Confusion with SplineFit (Angle calculation)

This question is continuation to this other one I am creating polymers (where each monomer is of equal length) using this method: ...
1answer
64 views

### Efficient maximisation of log-likelihood

I would like to efficiently find the maximum $(\sigma,\lambda)$ for the log-likelihood of the derived distribution below. I only need $\sigma$ and $\lambda$ to one decimal place - so not very precise. ...
2answers
2k 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 $x = W z+n$ ...
2answers
3k views

### What is the best distribution for my histogram?

I defined a security bound for a random walk (cube with 15 length) 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: ...
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(...
2answers
1k views

### How to compute the inverse CDF of HyperbolicDistribution properly?

Fixed in version 9. I want to compute the CDF and inverse CDF of the hyperbolic distribution: ...
2answers
1k views

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

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

### Finding Distribution based on quantile data

I am trying to determine an approximate distribution based on quantile data. I have the following information regarding Profit/Loss from an investing strategy backtest, and I want to use the data to ...
1answer
233 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 ...
2answers
217 views

### Best way to represent a joint distribution

The motivation for this question is producing a distribution that produces the gender and age of an individual when the distribution of ages depends on gender. Suppose I want a distribution which, ...
1answer
155 views

### AndersonDarlingTest and DistributionFitTest Leaking Memory

I believe AndersonDarlingTest and probably all other tests are keeping a copy of data somewhere and not freeing it: ...
4answers
239 views

### How to generate two group of $n$ random numbers in $U(0,1)$ such that sum of these two groups equal? [closed]

I want to have two groups of $n$ random numbers $u_i$ and $v_i$ in $U(0,1)$, such that $\sum u_i = \sum v_i$ What I tried is: I can firstly get $u_i$ by ...
1answer
740 views

### How can we create a histogram distribution from binning data?

HistogramDistribution takes a list of data points, creates a histogram from them, and returns this histogram in a form that can be used as a distribution. I ...
2answers
316 views

### How to plot an implicit value funtion

Previous question has been solved (Gap in a continuous plot). Here is a new related question. ...
3answers
399 views

### TransformedDistribution doesn't work

I'm trying to obtain a sum distribution of two discrete random variables. The function TransformedDistribution doesn't work for me in such case: ...
1answer
360 views

### How to reject or repulse some points in a 3D cloud of particles?

I'm having an issue with a 3D distribution of points. The distribution is really nicely looking in Mathematica, but it is used in an OpenGL astronomy program (Celestia) to generate a nebula, with ...
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 ...
2answers
140 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 ...
2answers
305 views

### More efficient method to compute moments of the Johnson $S_B$ distribution

Here is a very specific feature request. I need Mean[JohnsonDistribution["SB", γ, δ, 0, 1]] When I issue e.g. ...
1answer
94 views

### Overriding a built-in function with custom coded procedures

Sometimes it might be useful to override Mathematica's built-in functions with custom code that is either more specific or more efficient (or even less "smart"), but at the same time keeping the same ...
0answers
65 views

### How to pass a custom method to a particular option?

In an answer to my question More efficient method to compute moments of the Johnson $S_B$ distribution, J. M. has come up with a method to compute the moments of the Johnson $S_B$ distribution, which ...
2answers
136 views

### Estimate parameters of a derived distribution

I would like to estimate the parameters of a derived distribution fSurvivalGompertzNoiseDist below. This distribution represents simulations from a probability ...
2answers
365 views

### Calculating the Mean of a Truncated Multinormal Distribution

First, I'm a little disappointed that Mathematica balks at: Mean[TruncatedDistribution[{{0, Infinity}},MultinormalDistribution[{0}, {{1}}]]] Second, is the ...
1answer
81 views

### Performance of a bootstrap - time of computation not linear with number of iterations

I'm doing a bootstrap based on this thread with the following code (file.txt here): ...
1answer
230 views

### Safe values of $\mu$ and $\sigma$ when randomly sampling from a Log-Normal Distribution?

I believe I'm obtaining overflow errors when randomly sampling from a log-normal distribution with the command: RandomVariate[LogNormalDistribution[μ, σ], 1] ...
2answers
160 views

### Why can't Mathematica integrate this PDF?

I'm trying to integrate a transformed Gumbel PDF in Mathematica. Integrate[E^(η*(-(x - q)) - E^((-η)*(x - q))), {x, t, ∞}] However, it doesn't compute. It's fine ...
1answer
132 views

### Reflecting the Polya-Aeppli distribution

How would I go about reflecting the Polya-Aeppli distribution in Mathematica about a y-axis (switching left and right) while keeping the command. The distribution will not allow negative parameters ...
1answer
162 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 ...
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 ...
2answers
184 views

### Fraction of fibers that have failed

I have the following to set into mathematica. Assume a stress(sigma) applied on a specimen which has a number of fibers within it. All fibers that have a strength less than the applied stress should ...
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 ...
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] ...