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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2
votes
0answers
39 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
78 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
172 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
36 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: ...
0
votes
0answers
49 views

Computing integrals with differential operator

I've to compute this expression $$ \hat{H} = \frac{1}{4}g_2\int d^3R\int d^3r\ \bar{\Psi}(\vec{R}+\frac{\vec{r}}{2})\bar{\Psi}(\vec{R}-\frac{\vec{r}}{2})\left[ \delta(\vec{r})\nabla_{\vec{r}}^2 ...
5
votes
1answer
288 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?
1
vote
1answer
103 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] = ...
1
vote
2answers
93 views

Assign a Distribution to a group of symbolic variable [closed]

I'm looking to compute this Expectation : "i" represent a individual and h(i) is value. I would like the compute the Expected value of his value times the mean of the groups. Everything is unknown ...
5
votes
1answer
172 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
92 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 ...
4
votes
1answer
118 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
91 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
170 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
83 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 ...
3
votes
1answer
54 views

RandomVariate does not evaluate a Hyperbolic Distribution

Any Idea why I can't get a result from this expression: ...
0
votes
1answer
89 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 ...
3
votes
1answer
137 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
62 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
117 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
59 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
104 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
142 views

Inconsistent DistributionFitTest results?

In pondering this question, I used Mariana's function to generate the following data. ...
5
votes
2answers
528 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
61 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
72 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
199 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 : ...
3
votes
1answer
188 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
108 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
106 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 ...
4
votes
1answer
77 views

Define customised distribution with discontinuous CDF

I have the following CDF: ...
0
votes
0answers
43 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 ...
6
votes
3answers
452 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
278 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 ...
1
vote
0answers
199 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 ...
0
votes
1answer
162 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
139 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
181 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
105 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 ...
7
votes
1answer
122 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 ...
0
votes
1answer
184 views

Solve Probability of Distribution

Why does this work: Solve[Probability[x <= t, x \[Distributed] NormalDistribution[]] == 0.95 ,t] But this doesn't: ...
4
votes
2answers
123 views

NMaximize the Likelihood

I am still pretty new to Mathematica, but have to solve a quite complex problem. The function ...
4
votes
2answers
130 views

Finding the characteristic function of a TransformedDistribution[]

I am trying to find the characteristic function of a sum of "named" distributions, though I am interested in how to use Mathematica to find the characteristic function of $$f(X_1,\ldots, X_n),$$ where ...
2
votes
1answer
86 views

Defining and evaluating new continuous distributions based on Mathematica's distributions

A number of functions operate with Mathematica's set of distributions e.g. Through[{Mean, StandardDeviation, Variance}[UniformDistribution[{umin,umax}]]] which ...
1
vote
1answer
107 views

Defining a function of a distribution

I have a discrete- time and space markov process that I want to evolve given an initial distribution. To that, I defined ...
0
votes
1answer
114 views

Understanding distribution chart

How to explain DistributionChart function in mathematica, For example: if I have ...
2
votes
1answer
158 views

Judging the quality of fitting an EventData object to a distribution using LogRankTest

I have $389$ data points defined in an EventData object and want to judge the quality of fit of this data to a fitted $3$-parameter Weibull distribution. This ...
6
votes
1answer
141 views

RandomVariate does not fill range of PDF of distribution

I've declared my own probability distribution as follows dist[a_, b_] := ProbabilityDistribution[Cos[(b x)/2]^2 Sinc[a x]^2, {x, -400, 400}]; When I try to ...
4
votes
4answers
129 views

How do I emulate DiscreteUniformDistribution in Mathematica?

How do I define a function from scratch that emulates DiscreteUniformDistribution? As shown below, attempting to use ...
0
votes
1answer
453 views

PDF of binomial distribution and mixed binomial distribution

I want to plot the PDF of binomial distributed function and a mixed binomial distributed function, therefore I entered for the binomial distribution function the following: ...
4
votes
3answers
163 views

TransformedDistribution doesn't work

I'm trying to obtain a sum distribution of two discrete random variables. The function TransformedDistribution doesn't work for me in such case: ...