For questions about distributions built-in in Mathematica, and functions that operate on them. Also includes questions about defining your own distributions.
6
votes
3answers
189 views
Smooth Kernel Distribution
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
101 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]
...
1
vote
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 ...
1
vote
2answers
73 views
2
votes
1answer
145 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 ...
4
votes
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 ...
0
votes
1answer
229 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
142 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 ...
1
vote
1answer
168 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
0answers
128 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
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:
...
-1
votes
3answers
148 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 :
...
-4
votes
1answer
244 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 ...
1
vote
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 ...
3
votes
1answer
120 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
205 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 ...
13
votes
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:
...
5
votes
1answer
77 views
Can I store a DataDistribution in a database?
I have a DataDistribution
data = KernelMixtureDistribution[RandomVariate[NormalDistribution[], 10^5]]
that takes a long time ...
2
votes
2answers
168 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 ...
8
votes
2answers
398 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
193 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
157 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 ...
8
votes
3answers
629 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 ...
12
votes
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 ...
4
votes
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 ...
12
votes
2answers
510 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 $x = W z+n$ ...
7
votes
1answer
305 views
Probability and distribution from actual data
Let's say I have some data from a real world system:
...
11
votes
2answers
409 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
130 views
How to change type order in PearsonDistribution?
I need to estimate a Pearson distribution from a batch of tables tab:
...
11
votes
1answer
139 views
How does bandwidth selection work for low-variance dimensions with KernelMixtureDistribution?
I am puzzled because this toy example (in Mathematica 8)
...
2
votes
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 ...
11
votes
2answers
765 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
229 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 ...
