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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Question about Mann-Whitney implementation in Mma

So, I've been doing some statistics using Mma. Typically, the Mann-Whitney U test is used to compare non-normally distributed samples, whose medians are compared if both distributions exhibit similar ...
7
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2answers
263 views

Is there any function that compares distributions of two populations?

Imagine I have two populations that I want to test whether they exhibit similar shape distributions. Is there such a function that does this sort of testing already implemented? I am asking this ...
1
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1answer
68 views

Calculate mean and variance of conditional sum of Gammas

Find $Mean(Z)$ and $Var(Z)$, where: $Z = \begin{cases}W + X_1 & \text{if } W \leq c \\ W + X_2 & \text{if } W > c \end{cases}$ where $\quad W \sim \Gamma(k_0, \theta_0), \quad X_1 \sim ...
5
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1answer
195 views

Mathematica function to calculate equivalent NormalDistribution from a WeibullDistribution

I have a WeibullDistribution with mean 12.0 and standard deviation 3.2. Is there any built-in Mathematica function that calculates an equivalent ...
4
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1answer
86 views

Overriding a built-in function with custom coded procedures

Sometimes it might be useful to override Mathematica's built-in functions with custom code that is either more specific or more efficient (or even less "smart"), but at the same time keeping the same ...
2
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0answers
39 views

How to generate an arbitrary discrete distribution? (EmpiricalDistribution vs ProbabilityDistribution)

I've just started using Mma's distributions. Suppose I want to generate an arbitrary discrete distribution by matching probabilities to outcomes. ...
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3answers
190 views

Fit dataset with customized discontinuous distribution

I have the following parametric CDF: F[x_, λ_, β_, γ_] = Piecewise[{ {0, x < 0}, {1 - (1 - β) E^(-x λ), 0 <= x < γ }, {1, x >= γ} }]; ...
6
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1answer
95 views

RandomVariate of a custom distribution gives only negative points

I don't understand why the following code ...
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1answer
51 views

Custom kernel in CopulaDistribution

Note: I recognize that my question is strongly related to How to define a new copula distribution family, but it seems that there was no clear answer there, and the suggestions given were to simply ...
10
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2answers
136 views

Probability: MultivariateHypergeometricDistribution broken with more than five categories?

2016-04-09: This bug is indeed fixed (thank you, Stefan R.!) in 10.4. It may have been fixed in 10.3 or 10.3.1, but I haven't tried these versions. ...
3
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3answers
269 views

What is a good way to display many discrete probability distributions on the same plot in Mathematica?

For something like 2 to 30 distributions each with 2 to 30 values. If we assume the distributions have unique values, a standard stacked bar chart is insufficient, but maybe something similar would ...
5
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2answers
133 views

Calculate the mean of ordered distribution of the defined distribution

I am trying to evaluate the mean of the following: Let $a\sim Binom(10,1/2)$ and consider the random variable $\quad \quad d=\left|\frac{2}{\sqrt{10}}a-\sqrt{10}\right|$ Let $d_1,\dots,d_{20}$ be ...
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1answer
170 views

How to create a vertical (smooth) Histogram on the y-axis of a function graph for an uncertain x?

This is my first time posting a question in StackExchange. I have encountered a certain problem and I can't seem too find a solution. Just a word of caution, I am kind of an amateur when it comes to ...
3
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3answers
182 views

How to Plot the PDF of Product of two Normals

I've been looking to plot the distribution of the product of two normally distributed variables, x and y, that are uncorrelated. I've tried symbolically calculating the PDF using the ...
2
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0answers
73 views

Detecting discontinuities in derivatives in images [closed]

Considering an grey-scale image as a function $z=f(x,y)$. (Specifically, I'm interested in $f=h*h*...*h$, where $h$ is the indicator function of a regular hexagon.) I am interested in finding places ...
4
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1answer
115 views

Why doesn't NSolve work for this equality? Wildly incorrect solutions are given in certain cases

I am trying to write a function that solves for p in the following equation: PDF[BinomialDistribution[n, p], x] == op The ...
10
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1answer
105 views

FullSimplify on TransformedDistribution

Bug introduced in 8.0.0 and fixed in 10.3.0 Could someone check that I haven't gone mad? I would like to take the maximum of two $[0, 2 \pi]$ independent uniform random variables. ...
13
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3answers
170 views
2
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2answers
205 views

Can not generate graph using smooth kernel distribution

I am a newbie to Mathematica so this question might looks silly. I want to generate a smooth kernel distribution graph for this set of data. The data I uploaded has two columns, the first column is ...
1
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2answers
73 views

Custom multivariate discrete distribution [closed]

This is related to How to define an n-variate empirical distribution function probability for any n? and RandomVariate from 2-dimensional probability distribution but I don't think neither questions ...
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0answers
167 views

Goodness of Fit of Copula Distribution

I am trying to find out goodness of fit of copula distribution, but Mathematica 10 gives me the same answer for each copula type. e.g ...
3
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2answers
148 views

Estimate parameters of AR1 process

I am trying to estimate the parameters of a series $Z_t=W_t^\beta$, where W_t follows an AR1 process with mean 2, $\rho=0.9$ and $\sigma=0.1$: $W_t = \rho W_{t-1} + (1-\rho) \bar{W} + \epsilon_t$ ...
1
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1answer
74 views

Defining Probability Distribution with parameters

I have a family of probability distributions, indexed by elements in $\mathcal I =\mathbb N \times [0,1] \times [0,1]$. For each $(A,B,C) \in \mathcal I$ I know how to define the corresponding ...
4
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1answer
220 views

How to transform an image into a probability density function?

I'd like to use the Metropolis algorithm to randomly generate points with density according to the brightness of an image. I just need to transform a binary image into a pdf function to use this ...
21
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2answers
676 views

Given an exact formula, how can Mathematica find a probability distribution whose PDF matches it?

So, given some data, Mathematica 10.2 can now attempt to figure out what probability distribution might have produced it. Cool! But suppose that, instead of having data, we have something that is in ...
7
votes
3answers
243 views

Distribution over the product of three, or n, independent Beta random variables

I would like to calculate the PDF for the product of three independent Beta random variables. Specifically, I would like to find the distribution of the product of the following: $X_1\sim ...
2
votes
1answer
69 views

Plot a product of Beta distributions

I would like to plot the PDF of the product of a $Beta(1,1)$ and $Beta(3/2,1/2)$ random variables. I can use the following to calculate the PDF at a point $x$: ...
10
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2answers
164 views

Possible bug in VonMisesDistribution?

Bug introduced in 10.2 or earlier and fixed in 10.3 Observe: ...
4
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0answers
101 views

How to define a bivariate skew normal distribution?

There is BinormalDistribution that handles easily bivariate normal distribution and its mixtures. There is also ...
1
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0answers
49 views

Mixture of a bivariate distribution defined as a copula

I define a bivariate distribution: ...
0
votes
1answer
47 views

Error message when exporting plot as XLS file

I imported data from excel which has 300 data (which are change in CDS spread). I want to compute corresponding CDF for the data using kernel density estimation. I get the CDF plot but cannt get the ...
0
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1answer
92 views

kernel density estimation

I am trying to compute CDF of historical data ( weekly change in CDS spread) using kernel density estimation. The original data has 300 observation. I uploaded data from excel ...
3
votes
1answer
71 views

How should I iteratively refine a MixtureDistribution?

I am trying to find a stopping time for a randomized simulation such that say 95% of trials that will be successful will have already finished. I would like to do this by creating and then refining ...
2
votes
1answer
48 views

Documentation for the Bounded option of SmoothKernelDistribution

I have found the Bounded option useful in the SmoothKernelDistribution function, but I can't find any documentation for exactly ...
3
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1answer
106 views

How does Matematica compute the CDF of the binomial distribution?

I want to know, how Mathematica actually implements the cumulative distribution function of the binomial distribution. Which algorithm does Mathematica use to compute ...
2
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3answers
344 views

Fitting and plotting Weibull distribution

How can I find the best fitted 2-parameter Weibull's distribution (PDF) to describe my data? How can i plot my data and estimated distribution all in one graph? How can I show/compare results of ...
5
votes
2answers
107 views

Dirichlet marginals - why does Mathematica not give the *Kth* marginal?

Observe: MarginalDistribution[DirichletDistribution[{a, b, c, d}], #] & /@ Range@4 {BetaDistribution[a, b + c + d], BetaDistribution[b, a + c + d], ...
1
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3answers
324 views

Random non-overlapping disks in a square

I've found a nice code snippet by @belisarius from this question, that I'll reproduce here for reference: ...
0
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1answer
58 views

How to get DistributionChart to show normalised densities?

I am having some issue getting DistributionChart to show bin widths as expected, or perhaps it is in my interpretation of the plots. I have four data sets, all of the same length, and plot them in ...
1
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2answers
102 views

TargetFunctions option in FindDistribution yields error

I have some data set that I am trying to find the maximums . I figured I could do this by fitting the many peaks of the dataset to Gaussian distributions and then finding the peaks of this data from ...
9
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1answer
248 views
1
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1answer
195 views

How can I draw a box with moving particles inside and a hole in one side? [closed]

The idea is to create a simulation for ideal gas motion in a container that have a hole and then find the speed distribution for the gas particles that leave the box through the hole. I have a ...
2
votes
1answer
182 views

Confusion with SplineFit (Angle calculation)

This question is continuation to this other one I am creating polymers (where each monomer is of equal length) using this method: ...
3
votes
2answers
120 views

Efficient Sampling of A (Countable) Discrete Distribution

I have a sequence of positive terms $(a_n)$, for which $\sum_{n=1}^\infty a_n = A <\infty$, and wish to take a psuedo-random sample from the discrete probability distribution \begin{equation} ...
2
votes
1answer
114 views

P-Values are inconsistent when using DistributionFitTest repeatedly

I am attempting to become more familiar with the DistributionFitTest, specifically the distributions it yields and their fittedness. What I have found is that when I generate random data, fit it, and ...
2
votes
2answers
130 views

How to simplify and evaluate Integral with lots of DiracDelta dists

I have a question about an Integrals which I can do by hand but I want to implement this Integral in Mathematica. Actually it is the definition of a 2 Particle Phase Space. The Expression is the ...
2
votes
1answer
199 views

Mathematica equivalent of `qnorm` or `invNorm`

In R and TI-89 you can do qnorm(prob, mu, sigma) or invNorm(prob, mu, sigma) to get a value of ...
0
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1answer
206 views

Prime number The Ulam spiral [closed]

I want a simple method of visualizing the prime numbers that reveals the apparent tendency of certain quadratic polynomials to generate unusually large numbers of primes. I was able to display the ...