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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21 views

Getting Random Integers from the set {-1,1} quickly [on hold]

I was wondering if in Mathematica there is a quick way to get a random integer from the set {-1,1} with equal probability (i.e. getting -1 or 1 with equal probability). Usually I deal with Normal ...
1
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2answers
67 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
74 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
188 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
153 views

Can Mathematica solve this integral numerically?

I need to evaluate numerically the following ...
3
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0answers
44 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
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3answers
231 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
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1answer
81 views

Sampling a Dirichlet Distribution efficiently

I'm sampling a DirichletDistribution like so: ...
0
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0answers
26 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 ...
1
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1answer
133 views

How can I evaluate a certain probability density function?

The PDF of a random variable $X$ is given by $$f_X(x)=\frac{2m^mx^{2m-1}}{\sqrt{\pi}\Gamma(m)}\sum_{i=1}^{N}W_iH(T_i)$$ with $$H(t)=\exp\left(-m\left(\sqrt{2}\lambda ...
8
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3answers
240 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 ...
1
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2answers
54 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
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1answer
53 views

How to find this probability with PDF from TransformedDistribution?

I need to find the expression for the following equation, where $m>0$ ...
2
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0answers
71 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
81 views

ContourPlot of HistogramDistribution

I am trying to create a density plot of a 2-dimensional HistogramDistribution. ...
1
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1answer
56 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
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2answers
157 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 ...
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0answers
32 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
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
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1answer
67 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 ...
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
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1answer
39 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
103 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
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2answers
140 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
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1answer
83 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
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0answers
74 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
44 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
187 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
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2answers
142 views

Speed up RandomVariate on a custom probability distribution

I have created a custom probability distribution: ...
0
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1answer
54 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 ...
1
vote
1answer
85 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
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1answer
62 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
119 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
62 views

generate “dynamic” random variables?

I have the following problem: I generated two random numbers ...
4
votes
3answers
88 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
43 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
123 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
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4answers
234 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
43 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 ...
9
votes
3answers
169 views

Linear fit with conditional noise distribution

I need to fit a linear model of the form $y_i = a · x_i + b + e_i$. The $e_i$ are independent noise from a distribution that depends on $x$ as well as on global parameters of the data; however, the ...
4
votes
2answers
108 views

Gaps in the plot of a cumulative distribution function produced from HistogramDistribution [duplicate]

I have about 200 real numbers spread over the range 0-400. I use HistogramDistribution to bin them and PDF to create the ...
3
votes
3answers
91 views

Working with $X^2$, where $X$ has the uniform distribution in $[-b,b]$

Consider $b>0$ and let $X \sim U[-b,b]$ (the continuous uniform distribution in $[-b,b]$ ). I want to do two computations in Mathematica. First is to compute the density function of $X^2$, which I ...
3
votes
1answer
138 views

Random Variate generating strange results when using ProbabilityDistribution

I have created a probability distribution that follows a general normal distribution, given by: $$ \frac{b *e^{-\left(\frac{\sqrt{(x-u )^2}}{a }\right)^{b }}}{2 a \Gamma \left(\frac{1}{b }\right)} ...
1
vote
1answer
50 views

Mean of a half-Cauchy distribution

I am trying to calculate the mean (if it exists) of a half-Cauchy distribution. I know that the mean of the a Cauchy is undefined, but I was wondering whether the same is true of a half-Cauchy? (A ...
1
vote
0answers
153 views

Fitting data to an Normal Inverse Gaussian distribution

I am using data which I suspect is distributed according to the Normal Inverse Gaussian distribution (NIG). The literature says that the 4 parameters of the NIG distribution can be estimated from the ...
8
votes
3answers
318 views

How to evaluate if a list obeys the Normal distribution?

I am processing a data when I encountered this problem. I use the way of plotting the "normal probability plot" to show the result The list I have is: ...
1
vote
1answer
73 views

Boundary parameter in Beta Distribution

I use EasyFit to find the probability distribution of my data. It turns out the data follows BetaDistribution with 0.54022,0.70601 shape parameters and 1.33,6.83 continuous boundary parameters I am ...