# Tagged Questions

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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### Smooth Kernel Distribution

Smooth Kernel Distribution Hi i am in the research of 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 ...
2answers
226 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 ...
1answer
98 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] ...
1answer
204 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 ...
0answers
53 views

### integral of inverse distribution function

Can Mathematica solve the following problem? The parameter of interests is $\alpha$. Let $G(y)$ be the distribution function of $y$. (e.g. $G$ is a lognormal distribution function with given ...
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73 views

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1answer
143 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 ...
0answers
49 views

### Is there a common name for OrderDistribution? [closed]

I can't seem to find any reference material on what Mathematica calls OrderDistribution via Google or Wolfram|Alpha or the ASA. I can read what the Documentation ...
1answer
218 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 ...
2answers
138 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 ...
1answer
166 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 ? ...
0answers
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### 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 \$ ...
1answer
243 views

### Distribution of random points in 3D space to simulate an Orion-like Nebula [closed]

I'm creating 3D nebulae models for Celestia, a free OpenGL astronomy software. The following question is in part related to another one I already asked on this forum (see this question, for which I ...
1answer
80 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: ...
3answers
146 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 : ...
1answer
151 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
118 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 ...
2answers
392 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 ...
1answer
288 views

### RandomVariate returns values outside the support of a PDF

Let $X$ be a random variable with pdf: dist = ProbabilityDistribution[1/(Abs[x]*Log[Abs[x]]^2), {x, -E^-2, E^-2}] Here are some pseudo-random drawings from it: ...
1answer
187 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 ...
1answer
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### Can I store a DataDistribution in a database?

I have a DataDistribution data = KernelMixtureDistribution[RandomVariate[NormalDistribution[], 10^5]] that takes a long time ...
2answers
167 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 ...
1answer
155 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 ...
3answers
614 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 ...
1answer
386 views

### How to compute the inverse CDF properly?

I want to compute the CDF and inverse CDF of the hyperbolic distribution: α = 2; β = 3/2; x = -3; u = N[CDF[HyperbolicDistribution[α, β, 1, 0], x], 30] The ...
2answers
506 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
246 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 ...
1answer
302 views

### Probability and distribution from actual data

Let's say I have some data from a real world system: ...
2answers
403 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 ...
2answers
130 views

### How to change type order in PearsonDistribution?

I need to estimate a Pearson distribution from a batch of tables tab: ...
1answer
138 views

### How does bandwidth selection work for low-variance dimensions with KernelMixtureDistribution?

I am puzzled because this toy example (in Mathematica 8) ...
3answers
180 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 ...
2answers
757 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 ...
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