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| Another way, less general than previous ones... Notice first that Sin[2 t] // TrigExpand gives 2 Cos[t] Sin[t] Then perform a revealing change of variable: x[t_] := Sin[t]; y[t_] := 2 x[t] x'[t]; y[ArcSin[x]] ... |
| This is not exactly, the same thing, because Sign in discontinuous. So, the fist function is derivable, while the second one is not (excepted probably in the Distributions sense). D[functionWithConditional[t], t] If[t |
| You should first glance at examples from the demonstration project: http://demonstrations.wolfram.com/search.html?query=3D%20tree |
| Dear Gokul, thanks a lot for reminding me of the existence of contexts! Needs["MultivariateStatistics`"] dist = System`MultinormalDistribution[{0, 0}, {{1.7632655763946026`, -1.6637745757032427`}, \ ... |
| This is a degenerate case! A = {{1/72, 1/63, 1/56}, {1/56, 1/63, 1/72}}; MatrixForm@A A.{x, y, z} MatrixRank[A] Consider first the kernel of A: a vector V V = First@NullSpace[A] A.(k V) // Simplify Complete V by... |
| Hello! I suppose that's a correction for bias. Suppose the weight is uniform. Then Dot[weights, weights]=1/n and const=n/(n-1). But, in the general case, const = 1 / (1 + -Dot[weights, weights]) seems different from the standard... |
| Everything works very well now! Thanks a lot |
| I would like to compute the shortest distance between a number on pairs of points on a 2-dimensional Riemanniann statistical manifold (Negative Binomial distributions manifold, equipped with the Rao's metrics). This is sometimes VERY long,... |
| Hello, this is the Mean, not the total, which should convege to zero (Weyl's criterion). Claude |
| From a naive viewpoint, your can merely examine the errrors: err1 = Observeddata - Regression; err2 = Observeddata - NeuralNet; m = Map[Mean, {err1, err2}]; s = Map[StandardDeviation, {err1, err2}]; {a, b} =... |