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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0answers
23 views

Expectation of Rician Distributed Data [on hold]

As you can see in the attached file, I'm trying to obtain the expectation of some Rician distributed symbolic data. However output and input are the same. I guess that happens because Mathematica is ...
6
votes
3answers
90 views
0
votes
0answers
51 views

Adding a random shock to a sine wave [on hold]

I have the following sine wave generated: Plot[Sin[2 Pi*x], {x, 0, 1}] How can I add a random value to this function generated from the Guassian distribution?
2
votes
0answers
61 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
vote
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
89 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
vote
1answer
115 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
votes
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
vote
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
vote
3answers
77 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
votes
2answers
199 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
votes
1answer
187 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
votes
0answers
48 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
237 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
81 views

Sampling a Dirichlet Distribution efficiently

I'm sampling a DirichletDistribution like so: ...
0
votes
0answers
31 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
38 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
152 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
245 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
64 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
58 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
vote
2answers
85 views

ContourPlot of HistogramDistribution

I am trying to create a density plot of a 2-dimensional HistogramDistribution. ...
1
vote
1answer
58 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
159 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
votes
0answers
36 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
votes
1answer
65 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
41 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
110 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
84 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
80 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
196 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
166 views

Speed up RandomVariate on a custom probability distribution

I have created a custom probability distribution: ...
0
votes
1answer
63 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
89 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
127 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
54 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
90 views

FindDistributionParameters failing for a TransformedDistribution

I would like to estimate the parameters of a distribution that I obtain via TransformedDistribution: ...
1
vote
1answer
63 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
131 views

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

I am testing the following data for normality, in Mathematica and SAS: ...
7
votes
4answers
239 views

How to generate two group of $n$ random numbers in $U(0,1)$ such that sum of these two groups equal? [closed]

I want to have two groups of $n$ random numbers $u_i$ and $v_i$ in $U(0,1)$, such that $\sum u_i = \sum v_i$ What I tried is: I can firstly get $u_i$ by ...
1
vote
1answer
44 views

Limit involving DiracDelta gives zero [closed]

Why is the following limit zero? In[147]:= Limit[DiracDelta[ϵ], ϵ -> 0] Out[147]= 0 It does not matter if the limit is taken from either sides (+/-), since ...