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In this case the NaN (not a number) is returned because the calculation of the exponential overflows in double precision arithmetic. An algebraically equivalent expression, expanded in a MacLaurin se …

Usually these values are not computed alone: the entire collection of $v_i$ and $\log(1 - \exp(v_i))$ is needed. That changes the analysis of computational effort. To this end, let $$\bar x = \log\ …

Why not use a procedure that will both check the matrix for invertibility and find its inverse? A QR decomposition will do that. This is a numerically stable algorithm (employed by many least square …

This is not a bug. As we have explored (extensively) in the comments, there are two things happening. The first is that the columns of $U$ are constrained to meet the SVD requirements: each must have …

Probability calculations can produce formulas involving astronomically large or small numbers, especially when factorials are involved. Often there's extensive cancellation. The problem is that inte …

You can plot this curve accurately, on a linear scale. Let $a=1700$ and $b=300$ be the parameters. The largest value of $f(x)=x^a(1-x)^b$ for $0\lt x \lt 1$ is attained at $x_m=(a-1)/(a+b-2)$ (the mod …

Just do a little graphing and carry out the analysis suggested by the graphs. Here are plots of the reference standard Normal density and, on the right, several logistic densities superimposed on the …

It depends. But not on much, and you can predict what is likely to occur. In many situations, rounding adds $1/12$ to the variance. Consider any random variable $X$. Write $[X]$ for its rounded …

The problem is due to "leakage" from the large eigenvectors. I will present a brief analysis and then offer a solution, with code, followed by some remarks about the nature and limitations of the sol …

A solid implementation of $F$ will directly return the complementary value $1-F$ (the survival function) when requested. Exploit the symmetry of $G$ to compute $$H(x) = G^{-1}(F(x)) = -G^{-1}(1-F(x)) …