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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9
votes
3answers
598 views

The default bandwidth of the SmoothKernelDistribution function

I am researching the Silverman rule of thumb for bandwidth selection. Below is a sample of my code, from which it seems that BW=63 is close to the default parameter given by Mathematica (2 images are ...
1
vote
1answer
216 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] ...
2
votes
0answers
715 views

Calculate variance of random walk?

How can I symbolically calculate the variance of the following random walk in Mathematica? Given several discrete random variables such that $p(Z_i=1-2k)=p$, where $k$ is a small real number, and ...
0
votes
1answer
1k views

Solving derivative of cumulative normal distribution log likelihood

I am a newbie and I'm trying to use Mathematica to obtain the symbolic Maximum Likelihood Estimation for a cumulative normal distribution. So far I have reached the step where I have the derivative of ...
3
votes
2answers
350 views

Colors associated to parts of a 3D distribution of points

Suppose we have a long list of random points (cartesian coordinates) in 3D space. coords := ...; Until now, I was associating colors in a radial way, from the ...
3
votes
1answer
518 views

Radial Random Walk

I'm trying to generate a spherical distribution of radial random walk points in 3D space. The following code works, but the random walk lines aren't radial. Why ? Where is my mistake ? ...
0
votes
1answer
231 views

Fitting a theoretical density function with log-return sample

I am working on a exercise to fit a theoretical density function,presented below, with log-return series of a stock. $\frac{1}{2}a e^{a(x-\mu)} \quad \text{if x } < \mu $ or $ ...
4
votes
1answer
177 views

Closed form for convolutions of random variables

Is it possible to get Mathematica (9) to calculate PDF's for combined distributions? I can't seem to find the right notation, if this is possible at all. My attempts: ...
-1
votes
3answers
215 views

MixtureDistribution in Mathematica 7

Is it possible to use a mixture of several distributions in Mathematica 7.0? Consider for example the following code : ...
2
votes
1answer
327 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 ...
4
votes
3answers
852 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 ...
20
votes
2answers
886 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 ...
5
votes
1answer
178 views

Expectation of CauchyDistribution

I've noticed this strange behavior and I'm wondering if it's a bug. I define a Cauchy distribution: c = CauchyDistribution[0, 1]; If I evaluate ...
4
votes
1answer
462 views

Using DistributionFitTest on custom distributions in Mathematica 8

I originally posted this question on Stack Overflow, but I didn't get any answers, and I'm hoping to have better luck here. I'm trying to compute the goodness-of-fit of a bi-modal Gaussian ...
15
votes
1answer
388 views

RandomVariate returns values outside the support of a PDF

Bug introduced in 8.0.1 and fixed in 10.2.0 Let $X$ be a random variable with pdf: dist = ProbabilityDistribution[1/(Abs[x]*Log[Abs[x]]^2), {x, -E^-2, E^-2}] ...
5
votes
1answer
107 views

Can I store a DataDistribution in a database?

I have a DataDistribution data = KernelMixtureDistribution[RandomVariate[NormalDistribution[], 10^5]] that takes a long time ...
3
votes
2answers
351 views

Generating a range of numbers according to some rules

I'm pretty new to Mathematica, and I'm mainly a programmer so I don't have a lot of knowledge about maths. I want to generate a set of UNIQUE incremental numbers (series) according to the following ...
12
votes
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 ...
6
votes
1answer
412 views

Fix end point in smooth kernel distribution density

I am using some extreme value fitting method which results in a parametric distribution for values exceeding some threshold, all values $\geq 0$. For smaller values I'd like to use a smooth kernel ...
0
votes
1answer
265 views

Trying to plot this probability

Can anyone help me plot this? log P(X >= x) = alpha logx x=0.001 + k(0.001) k= 0, ..., 100 I can't figure out the coding for this.. I've been trying this for a while, and can't seem to figure it ...
15
votes
3answers
4k 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 ...
16
votes
2answers
974 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: ...
5
votes
2answers
562 views

How to fit one distribution to another?

I have a custom distribution created to model some experimental observations. While too complicated to include in this question, I can provide an example and some illustrations to convey a sense of ...
16
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 $x = W z+n$ ...
10
votes
1answer
1k views

Probability and distribution from actual data

Let's say I have some data from a real world system: ...
11
votes
2answers
1k views

Trying to fit an unknown extreme distribution

First up, I'm quite new to Mathematica so any hints on better code would be greatly appreciated. I have some histogram frequency data from an unknown distribution that I'm trying to fit. Here's the ...
3
votes
2answers
160 views

How to change type order in PearsonDistribution?

I need to estimate a Pearson distribution from a batch of tables tab: ...
11
votes
1answer
208 views
2
votes
3answers
270 views

How to Compute Aggregate Best and Worst Cases for a Large Number of Estimates?

I need to aggregate multiple estimations, but I haven't been able to find a built-in function in Mathematica that aggregates multiple probablity estimations (I am specially interested in estimations ...
24
votes
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 ...
10
votes
2answers
430 views

What do the options of SmoothKernelDistribution do?

The function SmoothKernelDistribution has three options that are not described in too much detail in the Mathematica's help window. InterpolationPoints: What is ...
30
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. ...