counterexample   47

More Noise, Less Signal - The Big Picture
"[As] a thought experiment, I wondered what the process might look like if went another way: What would happen if you purposefully tried to assemble a “How-to” list to pursue the exact opposite goal — how to get more noise, and less signal?"

In other words, what are the exactly wrong things to do as an investor?
blog  investing  counterexample 
february 2019 by schahn
multivariate analysis - Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian? - Cross Validated
The bivariate normal distribution is the exception, not the rule!

It is important to recognize that "almost all" joint distributions with normal marginals are not the bivariate normal distribution. That is, the common viewpoint that joint distributions with normal marginals that are not the bivariate normal are somehow "pathological", is a bit misguided.

Certainly, the multivariate normal is extremely important due to its stability under linear transformations, and so receives the bulk of attention in applications.

note: there is a multivariate central limit theorem, so those such applications have no problem
nibble  q-n-a  overflow  stats  math  acm  probability  distribution  gotchas  intricacy  characterization  structure  composition-decomposition  counterexample  limits  concentration-of-measure 
october 2017 by nhaliday
measure theory - Continuous function a.e. - Mathematics Stack Exchange
- note: Riemann integrable iff continuous a.e. (see Wheeden-Zygmund 5.54)
- equal a.e. to continuous f, but not continuous a.e.: characteristic function of rationals
- continuous a.e., but not equal a.e. to continuous f: step function
- continuous a.e., w/ uncountably many discontinuities: characteristic function of Cantor set
q-n-a  overflow  math  math.CA  counterexample  list  measure  smoothness  singularity  nibble  integral 
january 2017 by nhaliday

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