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
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0answers
40 views

Key mapping an association applied to a distribution

I am attempting to import data from a database, group it according to a given identification parameter, get it's statistically relevant information, and then export it as a JSON object for ...
3
votes
3answers
104 views

How do I define a two point random variable?

How do I define a random variable $X$ such that $Pr[X=x_1]=p_1$ and $Pr[X=x_2]=p_2$ where the values $x_i$, $i=1,\,2$ are just symbols and the probabilities $p_i$, $i=1,\,2$ are symbolic expressions ...
0
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0answers
24 views

How to get the numerical result of inverse CDF?

This is my code. And I want to solve the function which contains both Q and L. But Mathematica only gives me a result with "InverseCDF" function, but not a number? I'm not sure whether I use the code ...
1
vote
3answers
239 views

How to fit a Distribution to data that already looks like a distribution?

I have a set of data that is already ordered as a distribution. Here is a picture worth 999 words: I tried FindDistributionParameters, and ...
7
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3answers
103 views
2
votes
0answers
62 views

Why does Expectation function compute, while explicit integration does not?

The code: Expectation[1 + 1/y, {y \[Distributed] ExponentialDistribution[1]}] outputs 1 - EulerGamma While, ...
1
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1answer
46 views

Using distribution of data instead of data in `EstimatedDistribution`

Because of huge amount of data, the data saved in their frequency. for example {1,1,1,1,1,1,2,2,1,2,2,1,1,2,1,2,1,3,24} saved as ...
1
vote
1answer
90 views

package for calculating exponent of power law distribution

There are some packages to fitting power law to empirical date in "R", "matlab", "python" Here with maximum likelihood method As it said here. Does it exist similar package in Mathematica?
1
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1answer
116 views

How to draw a certain PDF

Here Dist is the PDF. I need to draw it. Can someone suggest me a way to do it? ...
3
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1answer
52 views

TransformedDistribution using integration with parameter doesn't work

I would like to ask for kind help with a following problem using TransformedDistribution in Mathematica. First here is the beginning of the code, that works: ...
1
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2answers
73 views

Modeling Gaussian Distribution for 4 Variables

I have 4 random variables A,B,C,D, that all have the same variance $\sigma^2$, but they are independent of each other. What I am trying to find, or to at least approximate, is the standard deviation ...
1
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3answers
79 views

API for defining parametric probability distributions

Mathematica has a lot of machinery for working with predefined probability distributions. It is not clear how to make that machinery work with a new distribution. Suppose I want to define a brand new ...
6
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2answers
204 views

How to measure accuracy of prediction distribution?

I have been trying to come op with a way to test if my dataset follows a Poisson distribution. Normally one would use the DistributionFitTest function, but here is ...
-1
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1answer
192 views

Can Mathematica solve this integral numerically?

I need to evaluate numerically the following $$\int_0^{\infty}\exp\left(-\pi\lambda\mathbb{E}_H\left(\int_r^\infty\left(1-\exp\left(-sP_{\text{M}}Hr^{-1/\delta}\right)\right){\rm{d}}r\right)\right)2\...
3
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0answers
53 views

PearsonChiSquareTest for count/frequency data?

I read with interest a previous question on the PearsonChiSquareTest from a few years ago, and one answer was very helpful: Performing a chi-square goodness of fit ...
6
votes
3answers
244 views

Creating a custom distribution with specified skew and kurtosis

Let's say I want to create a simulated sample of returns for a given investing/trading strategy. I know that my strategy is profitable on 64% of trades, that the ratio of mean win / mean loss is 0.72, ...
2
votes
1answer
85 views

Sampling a Dirichlet Distribution efficiently

I'm sampling a DirichletDistribution like so: ...
0
votes
0answers
32 views

Evaluating the cumulative multivariate hypergeometric distribution

Suppose there are 5 black, 10 white, and 15 red marbles in an urn for a total of $N=5+10+15$ marbles. You randomly draw $n=6$ marbles without replacement. The probability that you pick exactly two of ...
0
votes
1answer
39 views

Is it the correct syntax with TransformedDistribution?

I define a function as f[x_] := ...;which is in fact the PDF of a random variable $X$. The PDF if given by $f_X(x)$. Let $Y$ is a random variable, which is the ...
1
vote
1answer
154 views

How can I evaluate a certain probability density function?

The PDF of a random variable $X$ is given by Note that $H(t)$ is also a function of $x$. Here $-\infty<\mu<\infty$, $\lambda>=0$ and $m>=1/2$ Let $I$ be a function of random variable $Y$....
9
votes
3answers
247 views

Deriving a PDF for an annulus distribution

I would like to derive the PDF for an ''annulus'' type distribution, defined by the parameters $\theta\sim U(0,2 \pi)$ and $d\sim N(0,\sigma)$; where $\theta$ is the angle round a circle of radius $r$,...
1
vote
2answers
65 views

MMA gives error when a different PDF expression is used for the same distribution

I have the following MMA code. Note that the function I declared at the very beginning is the PDF of square of a Nakagami Distributed random variable. With $m=1$ and $P=1$, $f(h)$ becomes Exponential ...
0
votes
1answer
60 views

How to find this probability with PDF from TransformedDistribution?

I need to find the expression for the following equation, where $m>0$ ...
2
votes
0answers
74 views

The correct assignment of probability distribution to generate random variables

I'm asking you for a help to solve a difficult (for myself) task. Now I will tell you what and why I'm trying to implement. The task is to simulate the passage of elementary particles through a ...
1
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2answers
86 views

ContourPlot of HistogramDistribution

I am trying to create a density plot of a 2-dimensional HistogramDistribution. ...
1
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1answer
59 views

How to generate a histogram distribution with height function

According to the Mathematica documentation the HistogramList command allows to specify a height function fh, as third argument, ...
1
vote
2answers
160 views

Why can't Mathematica integrate this PDF?

I'm trying to integrate a transformed Gumbel PDF in Mathematica. Integrate[E^(η*(-(x - q)) - E^((-η)*(x - q))), {x, t, ∞}] However, it doesn't compute. It's fine ...
0
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0answers
37 views

Stable numeric integration of multidimensional step function

I am trying to integrate numerically a two-dimensional function (a SmoothKernelDistribution) with a step. I tried a few different settings for the parameters of <...
0
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1answer
66 views

Poisson point distribution

The probability of n telephone calls received at an exchange in a time frame (t_i, t_f ) is given by the Poisson point distribution: ...
0
votes
1answer
70 views

How to generate samples from an arbitrary continuous pdf?

If I define an arbitrary pdf p[x_] for a arbitrary-dimensional continuous variable x, how can I use Mathematica to create a function that will return a set of n random samples of x with distribution p?...
6
votes
1answer
71 views

Bug (or missed opportunity) in MarginalDistribution?

Observe: dist = MultivariateHypergeometricDistribution[k, Range@5]; Tr@Range@5 MarginalDistribution[dist, {1}] MarginalDistribution[dist, {1, 2}] First@% 15 ...
1
vote
1answer
42 views

Difference between two usages of TransformedDistribution

I am modeling the distribution of the sum of two dice throws as a TransformedDistribution ...
4
votes
1answer
121 views

PDF of product of two random variable with PDFs involving Dirac-delta function

I am trying to find the PDF of product of two random variables with the following distributions, ...
3
votes
2answers
145 views

Fast way to evaluate the PDF of a multivariable distribution

I'm trying to evaluate the PDF of a truncated multi-normal distribution. My distribution has 8 dimensions and each value must be ≥ 0. ...
-1
votes
1answer
85 views

Draw independent samples from conditional distribution at a fast rate

I would like to draw samples from the following conditional distribution of the following (don't ask why): ...
0
votes
0answers
83 views

Maximum Likelihood Estimation of Gamma-distribution Scale parameter

I have the following tasks: Generate random sample with given parameters shape = 2, scale = 0.001 and shape = 2, scale = 1/1200 for the right censored sample; Using Maximum Likelihood Method ...
0
votes
1answer
45 views

Dependency of parameter to find maximum vanishes after simplification

EDIT: It turns out I just made a dumb mistake: Simplify[Exp[x^2]*2^n*Pi*D[maxdist[n,x]/n*(1+Erf[x/Sqrt[2]])^(2-n),x]] A portion of my "factor" is actually inside ...
4
votes
4answers
201 views

Fitting Coxian distribution to some data

I'm trying to fit a transformed (actually shifted to the right) Coxian distribution to some data ( if needed an example set is here Sim data ). I've tried a number of ways for this: ...
1
vote
2answers
169 views

Speed up RandomVariate on a custom probability distribution

I have created a custom probability distribution: ...
0
votes
1answer
66 views

PDF for square of Rician random variable? [closed]

Let the random variable $X$ has Rician distribution (unit power in direct and scattered paths), whose PDF is given by $$f_X(x)=\frac{2x}{\alpha}\text{exp}\left(\frac{-(x^2+v^2)}{\alpha}\right)I_0\...
1
vote
1answer
91 views

Using ListDeconvolve to find velocity distrbution

Consider a Distribution of Particles correspondent with the NormalDistribution: PDF[NormalDistribution[], x] The Particles also have a velocity distribution: <...
0
votes
1answer
63 views

InverseFourierTransform very slow

I determined a distribution dist = SmoothKernelDistribution[ListOfValues];. Then I determined the FT of the PDF, which is the ...
4
votes
2answers
136 views

Estimate parameters of a derived distribution

I would like to estimate the parameters of a derived distribution fSurvivalGompertzNoiseDist below. This distribution represents simulations from a probability ...
0
votes
2answers
57 views

Estimate parameters from distribution created with ProbabilityDistribution

I would like to estimate the parameters of the following distribution: ...
0
votes
2answers
63 views

generate “dynamic” random variables?

I have the following problem: I generated two random numbers ...
4
votes
3answers
92 views

FindDistributionParameters failing for a TransformedDistribution

I would like to estimate the parameters of a distribution that I obtain via TransformedDistribution: ...
1
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1answer
64 views

Efficient maximisation of log-likelihood

I would like to efficiently find the maximum $(\sigma,\lambda)$ for the log-likelihood of the derived distribution below. I only need $\sigma$ and $\lambda$ to one decimal place - so not very precise. ...
0
votes
1answer
44 views

Integrating Poisson distributions [closed]

I'm trying to do the following Integrate[Exp[-λ] λ^k/k!, {k, 0, ∞}] The answer should be 1 but Mathematica is unable to do it. Same story when I try the ...
0
votes
1answer
47 views

How is the DistributionFitTest[data, dist] function actually using the dist parameter?

The first "Applications" example given for the DistributionFitTest of the Wolfram Language & System Documentation Center is: Analyze whether a dataset is drawn from a normal distribution: <...
6
votes
1answer
149 views

P-values differ in tests for normality between Mathematica and SAS

I am testing the following data for normality, in Mathematica and SAS: ...