For questions about distributions built-in in Mathematica, and functions that operate on them. Also includes questions about defining your own distributions.
0
votes
1answer
76 views
How to simulate with a user specified bivariate continuous probability distribution [duplicate]
I am very new to Mathematica set up and I have the following question: I have a bivariate probability distribution which is a little complicated and of the form:
$$f(x,y)=(a_0+a_1+a_2)\frac{a_1 ...
11
votes
4answers
307 views
Visualization of Bivariate Distributions
I know it is perfectly possible to show the bivariate probability distributions in MMA. But my question is can we show each dimension of distribution in 2D dimension while we are showing the 3D plot? ...
0
votes
0answers
83 views
Coefficient of determination (R squared) of EstimatedDistribution
I have estimated the distribution for a set of data as LogisticDistribution[3.5, 1.037]. How can I calculate and plot the coefficient of determination (R squared) ...
1
vote
0answers
76 views
Numerical integration involving Inverse Normal CDF
I'd like to evaluate the following numerical integration using Mathematica
$$
\ \int_0^T\int_0^\infty xe^{-0.04 s}g(x,s) dxds\
$$
where g(x,s) is a Gaussian copula function with say, marginal ...
2
votes
3answers
110 views
Covariance of transformed random variables
I am trying to solve the following:
$\begin{align*}
&X \sim N(1,1)\\
&\mathrm{cov}(X, X^3) = \text{?}
\end{align*}$
where $\mathrm{cov}$ is the covariance.
How would you do this in ...
0
votes
0answers
40 views
Plotting a mixture CDF with a truncated distribution in version 7
I'd like to plot the CDF of the following pdf in Mathematica 7:
$$f(x)=0.1 g(x)+0.85 m(x)+0.05 h(x)$$
where
$$
\begin{array}{ccl}
g(x)&:&P(0)=1,\ P(x\neq 0)=0\\
...
8
votes
3answers
228 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
108 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
59 views
integral of inverse distribution function [closed]
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
74 views
2
votes
0answers
157 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
53 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
275 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
152 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
185 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
130 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
85 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
155 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
251 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
167 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
341 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 ...
3
votes
1answer
125 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
212 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
295 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
175 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
434 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
199 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
160 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
688 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
389 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
258 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
529 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
331 views
Probability and distribution from actual data
Let's say I have some data from a real world system:
...
11
votes
2answers
438 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
131 views
How to change type order in PearsonDistribution?
I need to estimate a Pearson distribution from a batch of tables tab:
...
11
votes
1answer
142 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
181 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
801 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
232 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 ...
