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Consultant (environmental and spatial stats a specialty), expert witness, and teacher. I can be reached through (outdated but still valid) links posted on my web site.

Twitter: @WilliamAHuber // ASA-P website: http://amstatphilly.org/


Why waste time learning, when ignorance is instantaneous?

--T(iger) Hobbes.

For any complex problem there is a simple solution. And it's always wrong.

--[Mis?]attributed to H.L. Mencken by Dava Sobel, Longitude.


34m
comment Moment Generating Function of a nonlinear transformation of an exponential random variable
+1 Very nice! You have also incidentally provided another answer to stats.stackexchange.com/questions/114481 for the case $\lambda/\log(\delta)=-2$. Note that the MGF is a confluent hypergeometric function, which makes its computation susceptible to a huge array of techniques.
38m
comment What is the name of a distribution within $[a, b]$ but with a sloped straight line density?
The power/Beta$(\alpha, 1)$ distributions can also be characterized as "log exponential" distributions: see this answer. For instance, when $X$ has an Exponential (aka Gamma$(1,1)$) distribution, then $(1/\sqrt{e})^X=\exp(-X/2)$ has a Beta$(2,1)$ distribution with linear density rising from $0$ at $x=0$ to $2$ at $x=1$. Adding a constant to $X$ rescales it and adding a constant to the entire result shifts it. Truncating that on the left gives the general form requested in the question.
48m
comment Moment Generating Function of a nonlinear transformation of an exponential random variable
(1) For the record, the correct formula for $\text{ExpIntegralE}(n,t)$ is $\int_1^\infty \exp(-t x) /x^n dx$. Differentiating it with respect to $t$ is easy, because it just produces another exponential integral. Differentiation with respect to $n$ is very messy. (2) It's not evident where the "instability issues" are: could you be more specific about that? (3) The Gamma function representation looks particularly nice and is straightforward to differentiate with respect to $t$.
1h
comment How to compare the outputs of two algorithms computing SVD?
Often it's more meaningful to compare the outputs in terms of accuracy rather than precision. To that end, have you considered providing the algorithms various inputs for which you know the answers exactly? (It's pretty easy to find such inputs for SVD: begin with the desired output $U, \Sigma, V$ and use those to calculate what the input matrix must be.) The thread at stats.stackexchange.com/questions/34396 addresses the question about the signs of the components--and shows how and why they cannot even be consistent within the same software implementation.
2h
reviewed Close How to find TP,FN,FP,TN in function ROC (Epi package)
2h
reviewed Close Can I plot three column vectors to create a three-dimensional plot?
2h
comment Algoithm to find subsets with high correlation
Because that is not in the least clear, it would be good if you would edit your question to include that criterion.
2h
revised How to combine data from different papers to test a standard scale?
edited title
3h
reviewed Leave Open Rate of change for the regression model $Y^{\frac{1}{2}}=a+b_1*log(X_1)+b_2*X_2^{\frac{1}{2}}$
3h
answered Calculate $\mathbb{E}[Z_i]$ where $Z_i = \min(X_i, Y_{i-1})$, $X \sim Beta(\alpha,1)$
5h
comment What's the Probability of having this Hypothetical Disease?
Without information about the rate at which you contact asymptomatic infected people, this question cannot be answered.
5h
comment Algoithm to find subsets with high correlation
To obtain useful results, you will need to add more constraints to this question, because any subset of $2$ elements having different values of $x_1$ and $y$ will exhibit perfect correlation ($R^2=1$) with $y$.
1d
comment Replicating stata results in R
This question appears to be about ways of encoding categorical variables for regression models and as such qualifies to stay here on CV. Without having access to the data, though, we cannot be expected to diagnose the specific problem that is described.
1d
reviewed Close How is the formula for the expected value of a function of one random variable derived?
1d
reviewed Leave Open repeating rare examples in unbalanced data classification
1d
reviewed Leave Open If I divide my data by its mean, does it still have a unit?
1d
revised How to construct a regional severity index or riskiness score?
edited tags
1d
comment Overlapping Coefficient between for two Gaussian distributions where one of them has zero variance
+1. To put this in formulas, let $y$ be the maximum of the PDF of one Gaussian and let the other have an SD of $\sigma$ which is so small that $u(\sigma)=-\log(y^2)-\log(\sigma^2)+\log(2\pi)$ is positive. By focusing on the part of the PDF of the other that rises above $y$ you can obtain an upper bound for the overlap equal to $2(1+\sigma y-\Phi(\sqrt{u(\sigma)}))$ (where $\Phi$ is the standard Normal CDF). As $\sigma\to 0$, $u(\sigma\to\infty)$, whence $\sigma y\to 0$ and $\Phi(\sqrt{u(\sigma)})\to 1$, showing that the upper bound decreases to $0$, QED.
1d
comment repeating rare examples in unbalanced data classification
Because your question does seem to be answered by the apparent duplicate, could you please edit your post to indicate how it differs from the other one and to point out which aspects of it have not been answered in the other thread?
1d
reviewed Leave Open Replicating stata results in R