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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12
votes
2answers
297 views

Sampling a phase space uniformly for a given energy?

The energy for a 1D harmonic oscillator can be written: $$ E = \frac{1}{2 m} p^2 + \frac{m \omega^2}{2} x^2 $$ where x is position and p is the momentum. I would like to sample phase space $(x,p)$ ...
2
votes
1answer
323 views

multivariate lognormal distribution in mathematica

Is the LogMultinormalDistribution function really the multivariate lognormal distribution? Because I get different results with the same parameters in ...
1
vote
0answers
62 views

Why is Plot3D applied to TransformedDistribution in 2 random variables so slow? [closed]

I am trying to plot 3D, the pdf of a TransformedDistribution made up of random variables. So I can see the pdf in 3D, similar to this answer here Visualizing a 2-dimensional PDF But it seems to take ...
2
votes
0answers
124 views

Copula - Correlation or Covariance

Can someone explain to me why the CopulaDistribution function with a "Multinormal" kernal asks for the covariance matrix instead of the correlation matrix. Just by looking at the formula for copula, ...
0
votes
0answers
110 views

Creating a Distribution

Say I want to create a multivariate distribution that perhaps, as an example, looks something like this. ...
1
vote
0answers
110 views

Summing the probability distribution to 1 to convince myself

I have worked out a probability distribution and want to check its sum which is necessarily 1. First we write $$ r \triangleq \frac{(2 \lambda + \mu)^2}{2(\mu + \lambda)^2}, \quad s \triangleq ...
1
vote
1answer
184 views

Mixture coefficients and Parameter estimation for moving Normal distributions

I am searching for a way to do the following steps below. I am stumped and I have stumped a few profs too. Any help would be appreciated. I would like to import data from, say, excel or a .txt file ...
3
votes
1answer
127 views

How to get a more compact form of this probability calculation?

Inspired by the probability calculation here, I am trying to solve a little general one: $$\mathbb{P} (\sum_{i=1}^{m-1} A_i + \sum_{i=1}^{m} S_i < L < \sum_{i=1}^{m} A_i + \sum_{i=1}^{m+1} ...
3
votes
1answer
143 views

TransformedDistribution using n iid random variables

How do I create a TransformedDistribution that uses $n$ independent identically distributed (i.i.d.) random variables? For example, I can derive a chi-squared ...
5
votes
2answers
1k views

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

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

Using List/Histogram Data As A Weighted Function?

I have a list of data points that I would like to use as a weighted function. The data represents the number of particles within a bin of a particle distribution. Ultimately I would like to multiply ...
6
votes
1answer
370 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 ...
1
vote
1answer
141 views

Country density plot of lines (highways)

I love solution from question (histogram as well as distrubution) http://mathematica.stackexchange.com/questions/31948/show-density-plot-on-us-map#=. But both cases are a bit more difficult in my ...
2
votes
1answer
271 views

on Kolmogorov-Smirnov test

I found a problem to calculate Kolmogorov-Smirnov test statistic or p-value the data is ...
1
vote
1answer
175 views

In there a way to derive the inverse value of CDF format MultinormalDistribution?

Is there a way to produce the inverse value of multinormal distribution function in CDF format with 0.05 significance level? I found the function called ...
0
votes
0answers
127 views

How to perform a distribution fit test to censored data

With following code I will get an error: ...
4
votes
2answers
94 views

Dependent probabilities distributions?

What's the best way to model situations with dependencies? What I mean is well-defined arrangements like: If I choose a 6-sided die with probability $p$ and a 20-sided one otherwise, and then roll ...
2
votes
1answer
92 views

Statistical Analyzis of Observed Data (Queuing Process)

Basically I have a process that belongs to a certain state at any point of time. However, the time intervals are not fixed (in fact they are exponentially distributed). Essentially, the data points ...
0
votes
1answer
47 views

Understanding `TransformedDistribution` behavior on two similar lines of code

The two following lines of code does not give the same output. Mathematica manages to calculate the first one but fails to calculate the second one. ...
1
vote
0answers
38 views

FisherHypergeometricDistribution and WalleniusHypergeometricDistribution, how to specify boundary conditions

I'm trying to write a function that consists of a noncentral hypergeometric distribution. When I'm passing a set of parameters to the function, the following boundary problems occur: ...
1
vote
0answers
46 views

Why does integration of a radical times HeavisideTheta give a conditional expression?

If I want to compute an integral over x^p HeavisideTheta[y-x] where p is some fraction, I do not get the desired result, but ...
2
votes
1answer
281 views

Where can I find a good tutorial for stochastic modeling using Mathematica?

I am a newbie in Mathematica and I aim to use Mathematica mostly for stochastic modeling (to develop and analyze models in evolutionary biology). Note that I am not necessarily a great mathematician ...
1
vote
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 ...
-1
votes
1answer
334 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] ...
4
votes
2answers
394 views

Why doesn't FullSimplify simplify expressions with DiracDelta?

I want to simplify a complicated expression with some Dirac delta distributions, but FullSimplify does not do what I want. Specifically, I want ...
5
votes
2answers
384 views

Getting the Cumulative Distribution Function of f(x) from a dataset of x

I've a data set $\mathcal{X}$ which consists of randomly generated numbers. Let's say for example data = RandomVariate[ExponentialDistribution[1], 10^4]; My aim ...
1
vote
0answers
214 views

Manahalobis distance between two vectors

I want to calculate the Mahalanobis distance between two vectors that represent two points. For example: ...
0
votes
1answer
220 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 ...
2
votes
1answer
155 views

Structure of KernelMixtureDistribution and SmoothKernelDistribution

I would like to know more about the structure behind the KernelMixtureDistribution and SmoothKernelDistribution in Mathematica. ...
1
vote
1answer
228 views

Estimating Confidence Interval Variance covariance matrix from weibull distribution

In The following Example 50 obs . I estimated distribution parameters (by point) but *i want to estimate parameters by confidence interval and calculate covariance matrix i need help * ...
2
votes
1answer
289 views

Choosing The Best Fitted Probability Distribution Model

The following Example 20 Obs and i used Goodness of fit test with Exponential distribution, another time with Weibull distribution and third time with Pareto distribution .All of them are significant ...
5
votes
1answer
375 views

Areas of Voronoi cells from image file

I have an binary image with non-point objects. Does anyone have any suggestions how to determine area of each Voronoi cell in Voronoi diagram (goal is area distribution)? Thank you in advance.
2
votes
1answer
167 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 ...
3
votes
1answer
221 views

How to measure cross-covariance in mathematica

In matlab cross-covariance is given by [c,lags] = xcov(x,maxlags,'coeff'); How can I measure in Mathematica?
6
votes
1answer
464 views

How can I create a Distribution from its probability density function?

I have a probability density function. Is there a mechanism to create a Distribution object from it, such that normal Mathematica commands that usually work on ...
3
votes
2answers
934 views

How to extract the probability density function from SmoothHistogram? [duplicate]

I have some data.I plot the histogram with SmoothHistogram in Mathematica. If the y-axis of the histogram is my p(x) function, I want to plot f(x)=(1/n)ln(p(x)) ...
3
votes
1answer
98 views

What ProcessEstimator Options can I use with FractionalBrownianMotionProcess

I can generate an fBm process: ...
1
vote
0answers
197 views

Is this the correct method in using bootstrapping to determine a lower confidence bound?

Quite often in industry, due to cost and schedule constraints, decisions must be made on small sample size data. I have 4 cycles-to-failure values resulting from running samples to failure in a ...
34
votes
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: ...
1
vote
0answers
58 views

Moments Ratio Plot using “ProbabilityDistribution”

I am trying to plot moments ratio plot with the following code: ...
1
vote
1answer
154 views

Parameter Estimation of a mixture of sums of Lognormals

Let $X$ be a random variable that is of a mixture distribution of two lognormals (with the same sigma), so $X \approx p\cdot \mathcal L (\mu_1, \sigma) + (1-p)\cdot \mathcal L (\mu_2,\sigma)$. Now ...
0
votes
1answer
87 views

Using ImplicitRegion to define an ellipse around Multinormal distribution for integration

I have both a 2D 'MultinormalDistribution', and also a single xy point, and I would like to be able to calculate the probability of this point (given the multinormal distribution) and also plot an ...
16
votes
1answer
633 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 ...
2
votes
1answer
220 views

FindDistributionParameters of a sum of a mixture distribution

I have this Mixture Distribution of two Normal Distributions: ...
1
vote
0answers
300 views

Developing easy code to apply Delta Method to generate prediction bands for custom distributions

I think that this is an interesting issue for all those who when to not only adjust one prediction function, but also to obtain the prediction bands to asses the graphical or tabular error I'm trying ...
1
vote
1answer
180 views
2
votes
2answers
122 views

Transforming a CopulaDistribution only works with the Product Copula

What I want to do: 1) Define a joint distribution function using CopulaDistribution 2) then transform it with TransformedDistribution 3) to get the new Culmulative Distribution Function (CDF). The ...
2
votes
0answers
112 views

Why do EstimatedDistribution and DistributionFitTest work this way

I am fitting some time-series data to both a stable distribution and a normal distribution in order to assess the goodness of fit of each. Along the way I encountered the following confusing result. ...
0
votes
1answer
742 views

Fitting data to a Poisson distribution

I'm trying to fit a Poisson Distribution to data produced in a lab. I've successfully made a Histogram of the data, which looks like: However, when I try to fit the Poisson Distribution using: ...
3
votes
2answers
553 views

Multiple histograms grouped in a chart

I have this problem: I have three distributions and the relative histograms. But I would like to create an histogram in which the three columns of each single histogram for the same bin are put ...