All Questions
Tagged with distributions probability-or-statistics
63 questions with no upvoted or accepted answers
6
votes
0
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264
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Does DegreeGraphDistribution sample uniformly?
Bug introduced in 10.0 or earlier and persisting through 12.1
The first symptom (histogram below) is gone in 12.0. The second (fraction of connected graphs) persists, showing that the sampling is ...
- 236k
6
votes
0
answers
73
views
5
votes
0
answers
403
views
Histogram (automatic binning)
There are different methods for choosing widths of bins for a histogram, like Freedman-Diaconis rule. In Mathematica, without choosing a specific method, with the command ...
user79703
5
votes
0
answers
75
views
How to pass a custom method to a particular option?
In an answer to my question More efficient method to compute moments of the Johnson $S_B$ distribution, J. M. has come up with a method to compute the moments of the Johnson $S_B$ distribution, which ...
- 2,182
4
votes
0
answers
76
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Why is ProbabilityDistribution 100x slower than ExtremeValueDistribution?
The two distributions are the same, except the ProbabilityDistribution cuts out below x=0. The wolfram documentation on ProbabilityDistribution says nothing about speed. A search of this site gave no ...
- 1,637
4
votes
0
answers
426
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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
...
- 627
3
votes
0
answers
88
views
How can I calculate P-Value for a custom distribution?
I used DistributionFitTest but it works only with a defined distribution.
This is the distribution that I used:
...
- 59
3
votes
0
answers
180
views
Piecewise and ProbabilityDistribution malfunction when used together
Yesterday I opened this question, what had a happy end after all.
But when I tried to model more complex discrete random variables using Piecewise instead of ...
user44169
3
votes
0
answers
88
views
Evaluating an expectation expressed by a difficult expression
Background
I have a 2-dimensional space. The receiver is at the center. The locations of transmitters are given by the PPP $\Phi$ with density $\lambda$. The serving transmitter is the one that is ...
3
votes
0
answers
171
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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 ...
- 43
2
votes
0
answers
137
views
Insights on using the HypergeometricDistribution functions in Mathematica
I'm trying to calculate the upper confidence interval for the hypergeometric distribution in mathematica and I came up with this very simple code.
...
- 580
2
votes
0
answers
71
views
Mathematica unable to realize simple distributional relationship
I was trying to find the CDF for the following problem:
...
- 513
2
votes
0
answers
83
views
Creating a distribution of random sample means
The following is taken from Chapter 19: Distribution of Random Sample Means from the book: Illuminating Statistical Analysis Using Scenarios and Simulations.
Fifty random monkeys, each randomly pick ...
- 251
2
votes
0
answers
151
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Is Mathematica computing the conditional expectation correctly?
Given a simple case of say 2 independent trials each with probability of success 1/3. Consider a random variable that is gives the 3 times the total successes.
We can define this random variable in ...
- 9,751
2
votes
0
answers
188
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DistributionChart and kernel smoothing: preventing negative numbers
I am visualising rather scarce data about size distribution of certain objects (here - oil basin areas on continents, to be specific). There is no raw data, but some already processed quantities, for ...
- 93
2
votes
0
answers
193
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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 ...
- 255
2
votes
0
answers
320
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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 ...
- 2,188
2
votes
0
answers
217
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Mixture of a bivariate distribution defined as a copula
I define a bivariate distribution:
...
- 24.3k
2
votes
0
answers
182
views
Marginal distribution with weight
Given a multi-variate distribution $P(\mathbf{x},\mathbf{y})$, I would like to obtain the marginal distribution
$$P_m(\mathbf{x})=\sum\int_{\mathbf{y}}P(\mathbf{x},\mathbf{y})W(\mathbf{y})$$
In my ...
- 1,700
2
votes
0
answers
115
views
Optimization of custom probability distibutions?
Consider the two tests:
Timing[Do[RandomVariate[NormalDistribution[0.5, 0.3]], {200}]]
{0.001188, Null}
...
- 1,890
2
votes
0
answers
403
views
Von Neumann's method to generate points uniformly distributed on a region of a n-sphere surface
I am trying to generate points uniformly distributed on a region of a single n-sphere surface (all angles in hyperspheric coordinates are between 0 and Pi/2).
I decided to use von Neumann's method ...
- 195
2
votes
0
answers
367
views
Why do EstimatedDistribution and DistributionFitTest work this way
I am fitting some time-series data to both a stable distribution and a normal distribution in order to assess the goodness of fit of each. Along the way I encountered the following confusing result. ...
- 701
2
votes
0
answers
1k
views
Calculate variance of random walk?
How can I symbolically calculate the variance of the following random walk in Mathematica?
Given several discrete random variables such that $p(Z_i=1-2k)=p$, where $k$ is a small real number, and $p(...
- 839
1
vote
0
answers
39
views
Cannot recover Marginal Distribution from Product Distribution
In this simple example MarginalDistribution is unable to recover the marginal distribution from a Product Distribution. Why does it fail?
Start with a simple empirical distribution (It is a discrete ...
- 663
1
vote
0
answers
62
views
How to measure a LearnedDistribution?
I would like to measure the qualities of a LearnedDistribution in general and with regard to test sets. The docs say that it takes an option ValidationSet, but ...
- 3,790
1
vote
0
answers
62
views
Implementing approximatePDF function
Sometimes distribution is too complicated for built-in PDF command, so it would be useful to have approximatePDF[dist,x,n] which ...
- 6,697
1
vote
0
answers
63
views
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
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
1
vote
0
answers
128
views
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
1
vote
0
answers
184
views
Deriving the maximum likelihood estimates for a multivariate Gaussian
I am new to Mathematica and wonder if anyone can give me skeleton of a solution to a simple problem that I will then modify for my purposes as so far I have not managed to properly grasp the syntax.
...
- 11
1
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0
answers
65
views
1
vote
0
answers
2k
views
A simple/fast way to estimate distribution modality?
Is there a simple and performant way to estimate whether an empirical distribution generated from a list of data is unimodal and if not (or is reasonably uniform and doesn't have modality at all), to ...
- 1,370
1
vote
0
answers
115
views
Calculating mass density using kernel density estimation
I have a data set comprising of three columns:
Column A: Position in $x$ direction ($x_p$)
Column B: Position in $y$ direction ($y_p$)
Column C: Mass ($m_p$) at position $(x_p,y_p)$
I am trying to ...
- 71
1
vote
0
answers
70
views
Finding parameters of custom distribution with no analytical function
I need to shift one distribution to another using a simple positional correction parameter. For illustrative purposes, I will create a "double hump" or "twin peaks" distribution here, but my actual ...
- 185
1
vote
0
answers
287
views
Inverse Fourier Transform of Poisson Characteristic Function?
The follow line is returning without evaluation:
InverseFourierTransform[
CharacteristicFunction[PoissonDistribution[1], t], t, w]
It is meant to output ...
- 2,223
1
vote
0
answers
101
views
Mathematica cannot generate the random variables for a given Probability Distribution
I need to generate a large number of random variables from the distribution generated by the following code. Distribution is given by DistributionF. The code is ...
1
vote
0
answers
78
views
Efficient computation of density of ratio of two normal random variables
I want to manipulate the density of the ratio of two normal random variables. One way to do this is:
...
- 335
1
vote
0
answers
138
views
Extrapolation of area for a 2D integration
I have a set of points distributed almost uniformly in a certain area of a 2D plane as follow:
An example of data points (orange)
data = {{0.919443, 1.68921*10^-22}, {0.262277, 1.46747*10^-22}, {...
- 23
1
vote
0
answers
259
views
Comparing heavy tailed and non-heavy tailed distribution using Mathematica
I have data from a heavy tailed distribution (see picture 1) and a non-heavy tailed distribution (see picture 2) and want to compare it using a histogram on log-scale. However the picture 3 does not ...
- 551
1
vote
0
answers
457
views
Is this the correct method in using bootstrapping to determine a lower confidence bound?
Quite often in industry, due to cost and schedule constraints, decisions must be made on small sample size data. I have 4 cycles-to-failure values resulting from running samples to failure in a ...
- 1,417
0
votes
0
answers
41
views
The "StandardGaussian" bandwidth selection method in the SmoothKernelDistribution function
I have a list of points which follow the Gaussian distribution:
...
- 71
0
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0
answers
92
views
0
votes
0
answers
74
views
How does Mathematica work with multivariate distributions?
I recently found the AEP algorithm. Curious how Mathematica would handle the situation, I made an experiment:
...
- 203
0
votes
0
answers
33
views
how i write this custom distribution power function distribution i want to write in family distribution?
this is basic pareto distriibution
...
- 369
0
votes
0
answers
49
views
I have found out CDFs of 2 data and listed them. I need to find out the composition of such 2 CDFs
x= RandomVariate[ExponentialDistribution[2], 10]
y = RandomVariate[ExponentialDistribution[3], 10]
f = EmpiricalDistribution[x]
...
0
votes
0
answers
78
views
How to find the appropriate fit?
Imagine we are given this set of data:
data = {{0, 1}, {1, 0}, {3, 2}, {5, 4}, {6, 4}, {7, 5}};
We fit the data with:
...
user80433
0
votes
0
answers
117
views
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
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
0
votes
0
answers
52
views
Derivative for conditional expectation of non-independent gaussian variables is increasing
Consider two non-independent gaussian random variables:
$$(t,c)∼\text{BiNormal}[(𝜇𝑡,𝜇𝑐),(𝜎𝑡,𝜎𝑐),𝜌]$$
I'm interested in understanding when (i.e. for which values of the distribution ...
- 335
0
votes
0
answers
55
views
Kernel Unexpectedly Quits in evaluating NExpectation
I have defined a function (EVR) that is the expectation of a term with an integral inside. I'm trying the expression when using a uniform distribution with min = 0 and max = 2*b (a random parameter). ...
- 1