All Questions
Tagged with copulas or distributions
851 questions
1
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2
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130
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TransformedDistribution not returning a function
I'm trying to use TransformedDistribution to find the distribution of a function of two variables that have Normal distributions.
The function is $h(x, y)=x^2+y^2$.
I tried to do this two ways, first ...
- 37
0
votes
1
answer
40
views
Probability in a given distribution
I have the following distribution:
a=0.215775;
b=1.76885;
c=2.28023;
edistT=StudentTDistribution[a,b,c]
I would like to calculate, numerically, the value, ...
- 1,303
2
votes
3
answers
206
views
Chen weibull distribution
I write the density function of cw distribution and add data to calculate parameters maximum likelihood but the results of Mathematica no like the research
...
- 59
6
votes
2
answers
253
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Why is the conditional probability not working for `CategoricalDistribution`?
Bug introduced in 12.1 and fixed in 12.3
Consider the following simple example for demonstration:
...
- 9,751
2
votes
1
answer
415
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Entropy of a distribution
I need to calculate the entropy of a distribution from raw data. I found two approaches here and here.
But it seems they don't work for my case.
My data is:
...
user77316
1
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1
answer
265
views
0
votes
1
answer
93
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Skewness and central moment
I have distribution which I want to calculate the third order moment function of my distribution. I got confused what is different between Moment third order and ...
- 3
1
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0
answers
63
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Create CDF from a custom function
I have a complex function as follows (sorry for ugly script due to many parameters in the code!) which gives CDF of some data. I wonder whether there's any way to write it in CDF form in Mathematica, ...
- 11
2
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2
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246
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0
votes
0
answers
117
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How to go from a Pareto Distribution in Scipy to a Pareto Distribution in Mathematica?
Assume that I have fitted a Pareto distribution via Scipy and have gotten the following parameters:
...
- 1
0
votes
1
answer
112
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Evaluation points following a bivariate Gaussian distribution [closed]
I have a function of two variables, say $f(a, b)$, which I want to evaluate (and later average) in the neighborhood of $a=0$ and $b=0$, with density of points around $(a,\,b)$ following a Gaussian ...
- 1,225
1
vote
2
answers
120
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Expectation with conditional random variable [closed]
Given an Exponentially Distributed Random Variable $X\sim \exp(1)$, I need to find $\mathbb{E}[P_v]$ in Mathematica, where $P_v$ is given as:
...
- 113
2
votes
1
answer
238
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Integral for Bhattacharyya distance between two Cauchy distributions
I need to perform the following integral to calculate the Bhattacharyya distance between two Cauchy distributions:
$$
I = \frac{\sqrt{b_+ b_-}}{\pi}\int_{-\infty}^{\infty}dx\,\frac{1}{\sqrt{\left[(x-1)...
- 323
1
vote
1
answer
70
views
distribution implement for RandomVariate
I have a scalar function of two random matrices of dimension $n$ which are in the Gaussian Unitary Ensemble
$$f(x,y) \in \mathbb R, \quad x^{\dagger}=x \: \operatorname{and} \: y^{\dagger} = y, \:\...
- 13
2
votes
2
answers
167
views
4
votes
2
answers
190
views
Maximum of all distances between any pairs of vertices of a random triangle
Given a set $S_n$ of $n$ points selected uniformly at random in a $d$-ball, I want to estimate the average length of the longest side of a triangle having as vertices any three distinct points of $S_n$...
3
votes
2
answers
280
views
Estimation of the expected Euclidean distance between two random points on a unit $n$-hemisphere
What is the best approach to estimate, with Wolfram Mathematica, the expected Euclidean distance (in a $(n+1)$-dimensional space) between two points selected uniformly at random on a unit $n$-...
1
vote
1
answer
376
views
How to find the inverse of CDF of geometric function? [closed]
The cdf of geometric distribution is given by $ F(x)=1-(1-p)^x$.
I want to calculate the inverse of it, for example, $F^{-1}(U)$
I am doing the following
...
- 565
2
votes
3
answers
523
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Estimate the expected distance between two random points on the unit $n$-sphere [duplicate]
What is the best approach to estimate, with Wolfram Mathematica, the expected Euclidean distance in a $(n+1)$-dimensional space between two points selected uniformly at random on the unit $n$-sphere? ...
3
votes
1
answer
190
views
Does mathematica have support for mixture models?
Does Mathematica have support mixture models? Similar to the R language libraries mclust or ...
- 2,530
1
vote
2
answers
293
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Extracting the component distribution parameters from a mixed-normal distribution (for n > 2 normal)
I'm trying to extract the distribution parameters of the sub-distributions which comprise a mixed normal distribution.
I'll give my attempts so far.
First the simulated data:
...
- 2,530
2
votes
1
answer
270
views
Raising the normal distribution curve to a specified height on the $y$-axis
I'd like to know how to fit the normal distribution curve between $x$ and $y$ values so that the curve maintains its bell shape. I guessed the sigma is the scale ratio, but it doesn't work as I ...
- 123
3
votes
1
answer
87
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Failure in MultinormalDistribution
My RandomVariate fails to evaluate when sampling from a multinormal distribution, any idea what's happening here?
This is Mathematica 12.1 on Mac:
...
- 6,697
1
vote
0
answers
41
views
Speed up exact distribution of the sum of the top $k$ statistics on a bounded discrete uniform distribution?
I came across a nice answer by Sasha (I believe a Wolfram engineer) on mathematics stack exchange regarding the distribution of the sum of the top $k$ order statistics. (This was an answer to an RPG ...
- 26k
2
votes
1
answer
136
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Intepreting the results of DistributionFitTest, and other alternatives in Mathematica 12.1
I have been playing with DistributionFitTest as a means of testing how normal some data sets I have. I've been working with some simulated data sets so I can try ...
- 2,530
0
votes
2
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566
views
How to plot this pdf?
Let $x\sim N(\mu,\sigma^2)$ and $y=\max\{e^{x-1}-\kappa,0\}$. How to get and plot the pdf of y? In particular, there will be a probability mass at $y=0$, which is a nondifferentiable point. I tried
<...
- 213
1
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1
answer
95
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Probability distribution with random paremeters
Is it possible to set something like this? A probability distribution with random parameters
...
- 33
2
votes
2
answers
741
views
Normalized functions
I'm looking for a smart way to define normalized functions. I usually write
f[x_] := f[x] = A Sin[x]/x;
Then I integrate the function
...
- 294
5
votes
2
answers
837
views
Numerical solution to an integro-differential equation
I would like to solve numerically the following integro-differential equation
$$ \partial_t \rho(t,x) \,=\, \partial_x\big(f'(x)\,\rho(t,x)\big) \int_0^\infty f(\xi)\,\rho(t,\xi)\,d\xi \;+\\ +\; \...
- 183
2
votes
1
answer
136
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Concatenation of Distributions
I would like to calculate mean, variance, ... of a concatenation of distributions (is this the correct technical term?). For an easy example I am trying to calculate the mean of a PoissonDistribution ...
- 123
4
votes
5
answers
360
views
Expressions for moments of sample cumulants?
I sample $n$ points from standard normal and need the mean and variance of 3rd and 4th sample cumulants.
@JimB suggested that variance of 4th sample cumulant is given by the expression below. This ...
- 6,697
-1
votes
1
answer
105
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Can the WishartMatrixDistribution command be used for generating random density matrices?
I am interested in generating random members of two classes of $n \times n$ positive-definite matrices $A$ and $B$--the former symmetric in nature, the latter, Hermitian.
The standard (Ginibre-matrix-...
- 2,385
0
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1
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112
views
Integrate over a set or over the domain of a distribution
If Z is a distribution, how do I express “integrate over its domain”?
i.e. in handling symbolic calculation of an expectation of an unknown distribution, you'd normally put a Z under the the integral ...
- 161
4
votes
2
answers
76
views
EstimatdDistribution returns evaluated expression, not function name/
Ok, this takes a little bit o preparation. I'd like to estimate a distribution for some data. I have a distribution function that is not part of the canonical Mathematica set so I define it via ...
- 1,194
0
votes
0
answers
21
views
Defining the support of a random variable in Mathematica [duplicate]
I wish to create a Mathematica module that would take as input a Mathematica-defined probability distribution D and will perform an integration over the support of its density f, $supp(f)$ (where $f:X\...
- 11
-3
votes
1
answer
400
views
How to calculate the expectation and variance of a complex probability distribution
Assuming that the continuous random variables X1 and X2 are independent of each other, and the variances exist, the probability ...
0
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0
answers
30
views
Getting MatrixPropertyDistribution::sclrvctr: error from documentation example
I'm new to StackExchange, but I am having a strange error using just downloaded Mathematica 12.1.1.0 (Student version). I'm trying to use the MatrixPropertyDistribution function, but Mathematica gives ...
- 43
1
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1
answer
69
views
How to deal with more complex transformation distributions
Assume that X1, X2,..., Xn ($n\ge 2$) are simple random samples from a normal distribution $\mathrm{N}(\mu, 1)$, let $\overline{\mathbf{X}}=\frac{1}{\mathrm{n}} \sum_{i=1}^{\mathrm{n}} \mathrm{X}_{i}$....
0
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0
answers
50
views
Why are these expressions with shifted delta functions not equal?
I have the following equation
Exp[a-t]*DiracDelta[t-a] == DiracDelta[t-a]
which cannot be evaluated. However, if I plug in 0 for a:
...
- 343
1
vote
1
answer
124
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Problem plotting expression involving Generalized hypergeometric functions $_2F_2 \left(.,.,. \right)$
I'm trying to plot a graph for the following expectation
$$\mathbb{E}\left[ a \mathcal{Q} \left( \sqrt{b } \gamma \right) \right]=a 2^{-\frac{\kappa }{2}-1} b^{-\frac{\kappa }{2}} \theta ^{-\kappa } \...
2
votes
1
answer
137
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How to find the expectation $\mathbb{E}\left[ a \mathcal{Q} \left( \sqrt{b } \gamma \right) \right]$?
I'm trying to find the following expectation
$$\mathbb{E}\left[ a \mathcal{Q} \left( \sqrt{b } \gamma \right) \right],$$
where $a$ and $b$ are constant values, $\mathcal{Q}$ is the Gaussian Q-function,...
1
vote
1
answer
74
views
How to compute summary statistics and quantiles of user defined discrete distribution? [closed]
I am interested to find out the mean, median, Variance, Skewness, Kurtosis and Quantiles of the following discrete distribution with pmf (E^((1 - E^[Nu]) n) [Nu]^x BellB[n, x])/x! with x=0,1,2......
...
1
vote
0
answers
128
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Computing expected value of multinomial variables
We consider a two-dimensional dicrete probability distribution on $\mathcal{X} \times \mathcal{Y}$ with $|\mathcal{X}|\cdot |\mathcal{Y}| = r \cdot q$ distinct values with corresponding probabilities $...
- 11
7
votes
1
answer
393
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How to distribute points on a Sphere[] cap from a normal distribution?
I was wondering if one could distribute points on a "cap" of a sphere, following a normal distribution of the points instead of a uniform distribution. This normal could be centered at the ...
- 1,643
0
votes
2
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82
views
How to get a list of exponentially distributed points sampled in a range
I want to get 256 points exponentially sampled in a range, and then get its histogram.
If I plot PDF, I get the following:
...
- 157
3
votes
1
answer
164
views
FindDistribution[] with error bars? (And a ChiSquared Question)
I've got some data defined as follows:
...
- 31
1
vote
1
answer
226
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Problem with DiracDelta evaluating to zero
I am having an issue (in Mathematica 11.2.0.0) where the following integral evaluates to zero:
...
- 119
1
vote
1
answer
64
views
Using NIntegrate to reproduce NProbability over joint Gaussian distribution
Consider a random vector {s,c} with a bivariate normal distribution. For a vector of positive scalars {a, ß, σz}, I'm interested ...
- 335
4
votes
1
answer
121
views
Domain of ProbabilityDistributions
I am trying to do some symbolic statistics.
Is there a way to get the Domain of a distribution?
Like this
...
- 520
4
votes
0
answers
137
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Integration involving DiracDelta
I tried the following integration
Integrate[DiracDelta[Tan[x]], {x, -4, 4}]
I got 1 as the result. However, between -4 and 4 ...
- 49