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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3
votes
1answer
97 views

What ProcessEstimator Options can I use with FractionalBrownianMotionProcess

I can generate an fBm process: ...
1
vote
0answers
175 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 ...
32
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
57 views

Moments Ratio Plot using “ProbabilityDistribution”

I am trying to plot moments ratio plot with the following code: ...
1
vote
1answer
145 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
85 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
586 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
205 views

FindDistributionParameters of a sum of a mixture distribution

I have this Mixture Distribution of two Normal Distributions: ...
1
vote
0answers
274 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
178 views
2
votes
2answers
107 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
97 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
615 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
500 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 ...
0
votes
0answers
45 views

Comparing NIntegrate with definite integration

I want to calculate without error a sum of double integrals with the following definitions for the functions within them: ...
6
votes
1answer
987 views

Is there a free version of the Springer book “Mathematical Statistics with Mathematica”?

Is there a free version of the Springer book: $$\text{Mathematical Statistics with Mathematica}$$ by Rose and Smith ... available on the internet?
2
votes
1answer
217 views

Compute symbolic Expectation of a summation

I am required to computed following Expectations : $E[\displaystyle\sum\limits_{i=1}^N \frac{X_{i}}{N}] = \bar{x}_{0}$ & $E[\displaystyle(\sum\limits_{i=1}^N \frac{X_{i}}{N})^2] = ...
5
votes
1answer
667 views

How can we create a histogram distribution from binning data?

HistogramDistribution takes a list of data points, creates a histogram from them, and returns this histogram in a form that can be used as a distribution. I ...
2
votes
1answer
135 views

Contourplot of Binomial Distribution

Ok, so before anything else, I have no idea what I'm doing. Not in mathematica and maybe not in the maths either. My question is basically if I can contour-plot ...
5
votes
1answer
183 views

SmoothHistogram with sharp boundary [duplicate]

When using SmoothHistogram (to plot probability distribution function), I noticed that the edge of the figure is automatically smoothed towards zero probability. ...
5
votes
1answer
144 views

MarginalDistribution with Symbolic range in ProbabilityDistribution

Given the following joint density: for 10 < x < 20, x/2 < y < x. To find the marginal density for X we do: ...
0
votes
2answers
178 views

Fraction of fibers that have failed

I have the following to set into mathematica. Assume a stress(sigma) applied on a specimen which has a number of fibers within it. All fibers that have a strength less than the applied stress should ...
1
vote
1answer
238 views

Expressing a joint distribution for use in ContourPlot

I have $$X_1=T + W$$ $$X_2=2 T + 3 W$$ where $$W \sim N(3,5) \,\text{;}\,\, T \sim N(1,2)$$ and $$P(X=X_1)=P(X=X_2)=\tfrac{1}{2}$$ which I have awkwardly expressed as ...
4
votes
1answer
72 views

RandomVariate does not evaluate a Hyperbolic Distribution

Any Idea why I can't get a result from this expression: ...
0
votes
2answers
133 views

SplicedDistribution - different definition across Mathematica 9?

I am having troubles with my notebook. I succesfully defined Asymmetric Laplace Distribution at school using SplicedDistribution function, and Mathematica was able ...
4
votes
1answer
186 views

Determining the dimension of a probability distribution

Functions like Mean and RandomVariate clearly infer the dimension of the distribution passed to them. One can also usually ...
0
votes
1answer
87 views

Pattern matching with PDF, Distributed and multivariate distributions

I have defined a function to compute the Shannon entropy of a probability distribution: ent[p_] := Expectation[-Log[PDF[p, x]], x \[Distributed] p] This works ...
1
vote
3answers
203 views

Plotting a frequency function

I have a list of numbers and I want to plot the fraction of numbers >= k against k which will naturally be a decreasing curve. How do I do that?
2
votes
1answer
125 views

Determining sample size with no replacement for a given confidence and reliability when there are x failures observed during sampling?

I am trying to follow the procedure of a Sandia Labs report found here to determine the required sample size, for various population sizes, with no replacement for a given confidence and reliability. ...
2
votes
0answers
187 views

Partial convolution of random variables in random vectors

Suppose $(X_1,Y_1)$ is a bivariate random vector with a given distribution and let $X_2$ be a univariate random variable with the same distribution as $X_1$ but independent of $(X_1,Y_1)$. I want to ...
8
votes
1answer
338 views

Inconsistent DistributionFitTest results?

In pondering this question, I used Mariana's function to generate the following data. ...
9
votes
2answers
2k views

What is the best distribution for my histogram?

I defined a security bound for a random walk (cube with 15 lengh) and i have this code to obtain a sample of the random times at which the random walk crosses the boundary for the first time: ...
1
vote
2answers
80 views

CDF of TransformedDistribution Not Returned And No Error Message Produced

I am unable to get Mathematica to return the CDF of a distribution produced by TransformedDistribution. It "executes" for 6 hours on my machine and then returns a blank plot. Could someone execute the ...
0
votes
1answer
101 views

Summing Multinormal Distributions

So, I'll explain the problem first. I have two populations that have values for two different channels (c1,c2). I've modeled these using MultinormalDistribution[]. I would like to add some noise to ...
3
votes
3answers
393 views

Colorize a 3D distribution of points according to density

Suppose we have some random 3D distribution of points. I'll use the spherical ball defined below as an example and a starting point for the discussion here : ...
4
votes
1answer
631 views

Categorical Distribution

Suppose I want to do calculations with a random variable $X$ that has a simple categorical distribution (a.k.a generalised Bernoulli distribution or discrete distribution). I was expecting to be able ...
0
votes
1answer
225 views

PDF for Gamma Distribution not what I expect

I have plotted the the PDF for a Gamma Distribution with various parameters (e.g. 3 and 5) using Manipulate: ...
2
votes
1answer
157 views

Expectation of GeometricBrownianMotionProcess

I am trying to compute $$\mathbb E\left[\max\left(\frac{S_{1/2}+S_1}{2}-K,0\right)\right]$$ where $K=100$ and $S_t$ is a geometric brownian motion (with $S_0=100$, drift $r=0.05$ and volatility ...
5
votes
1answer
164 views
0
votes
0answers
47 views

Using an Interpolating Function as a probability density function [duplicate]

I have seen a couple of similar questions but have not been able to figure out a solution for my particular problem. I have a probability density function of two variables ...
7
votes
3answers
574 views

How to randomly erode a 3D distribution of points with Mma 7.0?

Suppose we have a 3D distribution of points, like the spherical ball example below : ...
-4
votes
1answer
606 views

How to generate this fractal-like 3D distribution of points in Mma 7.0?

I would like to produce some 3D distributions of points using Mathematica 7.0, that look like the picture below : How could I do that ? What are your suggestions ? What Mma 7 codes could do a ...
5
votes
0answers
538 views

When are `If`, `Piecewise`, `Switch`, and `Which` interchangeable and when are they not?

Experimenting with joint dependent distributions via the TransformedDistribution function, I used the following to derive a distribution where the second variate is ...
6
votes
2answers
174 views

Best way to represent a joint distribution

The motivation for this question is producing a distribution that produces the gender and age of an individual when the distribution of ages depends on gender. Suppose I want a distribution which, ...
0
votes
1answer
207 views

Better way to plot multiple discrete PDFs?

I often find myself trying to plot multiple PDFs for my courses. I find the default tools available to me are lacking and/or cumbersome. After readings some suggestions here, I have come up with the ...
8
votes
1answer
153 views

AndersonDarlingTest and DistributionFitTest Leaking Memory

I believe AndersonDarlingTest and probably all other tests are keeping a copy of data somewhere and not freeing it: ...
-1
votes
2answers
459 views

Fitting a beta distribution to a probability density curve

If I have a spectral data set showing measured energy on the y-axis and frequency on the x-axis, how would I go about fitting this to a beta distribution? For example, lets say I had the data for the ...
1
vote
1answer
128 views

Reflecting the Polya-Aeppli distribution

How would I go about reflecting the Polya-Aeppli distribution in Mathematica about a y-axis (switching left and right) while keeping the command. The distribution will not allow negative parameters ...
10
votes
1answer
324 views

How does LocationTest choose its “AutomaticTest”?

Is there a way of determining how LocationTest chooses its "AutomaticTest"? Sometimes it's clear from the ...
7
votes
1answer
295 views

How to create a spliced survival statistical distribution?

I am trying to use Mathematica for more of my reliability engineering work and am having trouble using SplicedDistribution. I have a Weibull distribution (dist1) associated with a low stress ...