# Tag Info

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### Huge bug involving MultinormalDistribution?

I almost believe the precision argument. But not quite. ...
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### Backtesting a Probability of Default (PD) model

This kind of backtest is often performed using approximations, for instance with normal distributions, which may not be always valid. An exact test would be very nice to have. The probability ...
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### Sisyphus Random Walk

We can iterate with FoldList: data = {0, 1, 1, 0, 1, 0, 1, 1, 1, 1}; FoldList[#2 * (#1 + #2)&, data] ...

### More efficient method to compute moments of the Johnson $S_B$ distribution

I'll preface this answer first with a complaint: NExpectation[] and NProbability[] are not sufficiently resilient obviously ...
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### How to implement Kullback-Leibler divergence using Mathematica's probability and distribution functions?

In the continuous case the Kullback-Leibler-Divergence from distribution $Q$ to distribution $P$ is defined as \begin{equation} D_{KL}( P ||Q) = \int \limits_{-\infty}^{+\infty} p(x)\cdot \log \...
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### Does Mathematica have an implementation of the Poisson binomial distribution?

Mathematica does not know about the PoissonBinomialDistribution, but you can use the formula given for the PDF on Wikipedia: ...

### More efficient method to compute moments of the Johnson $S_B$ distribution

As a minor addition to J.M.'s excellent answer, If something breaks while evaluating NExpectation[] or NProbability[], a ...
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### How to plot paired smooth histogram/distribution plots?

Here is something using a custom ChartElementFunction ...
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### Update: Combining DistributionChart and BoxWhiskerChart

Final Update: Adding Callouts to special points ...
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### Define a simple discrete probability distribution

You can first define a piecewise function piece[x_] := Piecewise[{{0.3, x == 0}, {0.4, x == 1}, {0.3, x == 2}}] and feed it to ...
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### How to replace $x$ and $x^2$ with different value?

Give the replacement rules in a list: expr /. {x^2 -> k p + k (k - 1) p^2, x -> k p} 2 k p + (-1 + k) k p^2
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### Histogram "PDF" vs "Probability"

I believe that when you specify "PDF", the value on the ordinate is the average probability density within a given bin. And to get the "within-this-bin" ...

### Uniform distribution on z = 1 − √( x ^2 + y ^2) , z ≥ 0

If you set up your region S as a region in Mathematica you can use RandomPoint to generate uniformly distributed points over it. ...
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### Why does FindDistribution give nonrepeatable results for fit parameters?

I don't know what FindDistribution is doing because it doesn't produce estimates that match any of those produced by ...

### Is there any function that compares distributions of two populations?

SeedRandom; data1 = RandomVariate[NormalDistribution[2, 3], 10^3]; data2 = RandomVariate[LaplaceDistribution[1, 2], 10^3]; Use ...
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### Is there any function that compares distributions of two populations?

Data data1 = RandomVariate[NormalDistribution[2, 3], 10^3]; data2 = RandomVariate[LaplaceDistribution[1, 2], 10^3]; Visual comparison ...
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### Scale SmoothHistogram curve to Histogram

If you really want to, you can scale up from the "PDF". The "scaling" factor depends on how the Histogram was binned, but we can use HistogramDistribution to ...
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### How to measure accuracy of prediction distribution?

One possibility is to use a generalized linear model for which Mathematica has the function GeneralizedLinearModelFit. For your potentially Poisson data the ...
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### Finding the covariance of two discrete random variables

This solution uses built-in functions : ...

### Selecting a random subset to match PDF of another or a given distribution

This problem is known and can even be more generalized than you have described it. Especially, when researching fields like cardiovascular diseases or aortic valve problems, it is often the case that ...

### Compiling the VoigtDistribution PDF

Here is a compiled implementation of the Voigt profile function, based on an approximation derived by Chiarella and Reichel and improved by Abrarov, Quine and Jagpal: ...
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### Adding two random variables (probability distributions)

As Eric Brown suggested you should use TransformedDistribution[]. Also I'd suggest using built in distributions if possible, here I mean DiscreteUniformDistribution[]. ...
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### Random Variate generating strange results when using ProbabilityDistribution

There seems to be a bug in version 10.1 that has been fixed in 10.3. You can always try writing your own random number generator. Here is a simple acceptance rejection method based on generalized ...
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### P-values differ in tests for normality between Mathematica and SAS

I should have looked at your code but I didn't, because I saw that the test-statistics for the tests in question were the same. What I did then is to look up how p-values are computed for Anderson-...
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### The sampling without replacement

I am a bit late but another way to use MultivariateHypergeometricDistribution: ...