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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0
votes
1answer
55 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 ...
2
votes
1answer
96 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
40 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
97 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
40 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. ...
0
votes
2answers
365 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: ...
2
votes
0answers
83 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 ...
7
votes
1answer
102 views

Inconsistent DistributionFitTest results?

In pondering this question, I used Mariana's function to generate the following data. ...
5
votes
2answers
465 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: ...
16
votes
2answers
647 views

How to compute the inverse CDF properly?

Note: this has been fixed in version 9. I want to compute the CDF and inverse CDF of the hyperbolic distribution: ...
1
vote
2answers
52 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
65 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
158 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
116 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
92 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
91 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 ...
16
votes
2answers
2k 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 ...
4
votes
1answer
68 views
0
votes
0answers
41 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
423 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
226 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
131 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 ...
1
vote
1answer
95 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 ...
0
votes
1answer
144 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
132 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
152 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 ...
0
votes
1answer
159 views

Solve Probability of Distribution

Why does this work: Solve[Probability[x <= t, x \[Distributed] NormalDistribution[]] == 0.95 ,t] But this doesn't: ...
2
votes
1answer
140 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 ...
7
votes
1answer
100 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 ...
4
votes
2answers
109 views

NMaximize the Likelihood

I am still pretty new to Mathematica, but have to solve a quite complex problem. The function ...
4
votes
2answers
110 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
73 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
103 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
100 views

Understanding distribution chart

How to explain DistributionChart function in mathematica, For example: if I have ...
6
votes
1answer
129 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 ...
2
votes
1answer
128 views

DistributionFitTest with WeightedData?

My problem is related to statistical testing with weighted data. I have a data sample and I assume that a part of the data follows a specific distribution (Pareto). So I fit my data to a distribution ...
4
votes
4answers
122 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 ...
15
votes
4answers
737 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? ...
4
votes
1answer
316 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 ...
3
votes
3answers
147 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: ...
1
vote
1answer
100 views

How to find best MLE using `FindDistributionParameters`

This question is an extension of this question, if we change the initial values ...
0
votes
0answers
89 views

Binomial Distribution (binomial model inspired by Merton)

Binomial Distribution (binomial model inspired by Merton) Hi I want to do the following and I hope that anyone of you can help me out. In short, I have a portfolio consisting of 10 companies, ...
0
votes
1answer
149 views

Fast integration of 2D distribution across lines parallel to y-axis

I'm struggling with a small data set and a slow calculation. I have hundreds of small 2D data arrays and need to integrate across several lines parallel to the y-axis. Let me start with the data ...
0
votes
1answer
127 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 ...
8
votes
3answers
377 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
0answers
225 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 ...
0
votes
0answers
352 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) ...
4
votes
3answers
505 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 ...
2
votes
3answers
230 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
111 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\\ ...