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10

The executive summary You can use the built-in Ellipsoid function directly with your calculated mean and covariance. For 95% confidence, use: Ellipsoid[mean, 6 cov] That expression returns an Ellipsoid object that you can visualize as an Epilog to a ListPlot, or as an argument to Graphics (further formatting below). Ellipsoids for other common critical ...


8

The built-in function UniformSumDistribution may be useful: usd[n_] := UniformSumDistribution[n, {-.5, .5}]; Plot[Evaluate[PDF[usd@#, x] & /@ Range[20]], {x, -2, 2}, PlotStyle -> (ColorData[{"Rainbow", {1, 20}}] /@ Range[20]), Exclusions -> None, PlotRange -> All, ImageSize -> 500, PlotLegends -> ("usd (" <> ToString[#] ...


8

I will give you two similar methods. Simple Gaussian Threshold The simplest way is to remove the moving mean of the data, then compute its standard deviation ($\sigma$), then pick a level at which you want to reject the data, say at 1%, so you can remove any points that vary more than $ 3\times \sigma$ . If you know how the data is distributed about its ...


5

summing random numbers between -0.5 and 0.5. the number of numbers to be summed is very large, like a 1000000 for example. The sum of $n$ identical Uniform random variables is known as a generalised Irwin-Hall distribution, implemented in Mathematica as the UniformSumDistribution [ see kguler's answer]. The latter takes an $n$-part piecewise ...


4

The moving median is hardly affected at all by a few outliers, this can be used to identify the outliers. newData = Select[Transpose[{ data2[[10 ;;]], MovingMedian[data2, 10] }], Abs[Subtract @@ #] < 1 &] // Transpose; ListPlot[newData, PlotRange -> Full] In this piece of code 10 and 1 are arbitrarily chosen numbers that you ...


3

This is a problem known as finding moments of moments. In this case, we seek the covariance (i.e. the $\mu_{1,1}$ central moment) of various sample moments. The modus operandi for solving such problems is to work with power sum notation $s_r$, namely: $$s_r = \sum_{i=1}^n X_i^r$$ In this case, you are interested in the sample mean $ = \frac{s_1}{n}$, and ...


3

It is a bug in the caching feature. Some distributions don't have p-value corrections since those based on the empirical CDF must be derived individually. The result is correct but the p-value is inflated due to lack of correction. When the test or any underlying one is ran again it returns the cached result with no message.


2

You are attempting to model a non-linear process with a linear model. Use a non-linear model. For example: NonlinearModelFit[data, {b Log[a x] + c, c > 0}, {a, b, c}, x] That should give a more reasonable answer. However, if I understand the game correctly there are a finite number of single-use clicks available to it. It would be interesting to ...


1

Here's how to interpret statistical significance, here illustrated for a $\chi^2$ distribution: Such a distribution tells you the expected probability of finding a value of $x$ as the sum of squares of values chosen from $n$ univariate Gaussian distributions (where we call $n$ the degrees of freedom). Of course, the value of $x$ can never be negative. The ...



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