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Consultant (environmental stats a specialty) and teacher.


Dec
6
comment Determine the number of revolutions the normal to a curve makes as it moves along a curve in three dimensions?
You can make this question well-defined by first restricting to curves whose normals are never zero, allowing you to define a unit normal everywhere, and assuming this unit normal is a continuous map into the unit sphere. Select two points on the unit sphere not in the image of that map. Use (say) a stereographic projection based at one of them to project the curve into the plane. Define the number of "revolutions" to be the winding number of the (projected) unit normal around the second point.
Dec
6
comment Mapping CDF's to each other
The result is false for discrete distributions. A simple example is given by two Bernoulli variables with parameters $p$ and $p'$ such that $p\ne p'$ and $p\ne 1-p'$.
Oct
25
comment How do you calculate an upper-confidence bound on a problem with 2 means?
That's right--and leave out the left endpoint of the interval altogether.
Oct
25
comment How do you calculate an upper-confidence bound on a problem with 2 means?
This is a nice exposition but it addresses a slightly different problem: the question asks for a UCL of the mean, not a symmetric CI for the mean.
Oct
24
comment Bound of Standard Normal Integral
The upper bound given by $1/\sqrt{2\pi}$ for $-1\lt z\lt 1$ and $(1/\sqrt{2\pi})|z|\exp(-z^2/2)$ otherwise is easy to integrate explicitly.
Oct
15
comment Prove that a polygon with nonnegative area is determined by at least three points.
@Sawarnik I wasn't claiming the question concerns anything other than Euclidean geometry. Pointing out that this statement is wrong in other geometries demonstrates the logical necessity of invoking some axiom that is enjoyed by Euclidean geometry.
Aug
30
comment Name for this matrix operation?
Because there are many ways to describe this operation (outer products, tensor products, etc), and it's really about a purely mathematical question, I think the math community may (a) have more interest in it and (b) be able to provide a broad and insightful collection of useful answers.
Aug
25
awarded  Yearling
Jun
19
comment Bottom to top explanation of the Mahanalobis distance?
Cross-posted at stats.stackexchange.com/questions/62092/….
May
17
awarded  Constituent
May
14
comment Prove that a polygon with nonnegative area is determined by at least three points.
But there's still something to show, because there exist two-point polygons on the sphere having nonzero area.
May
13
awarded  Caucus
May
9
comment best fraction algorithm
This sounds like a pure algorithmic/math question. Did you really intend to ask it on a Mathematica site? If so, please clarify how you expect to use Mathematica for the solution.
Apr
9
comment Probability for a regular matrix
"Isomorphism" in what category? As a linear transformation of $\mathbb{Z}^k$ or as a linear transformation of $\mathbb{C}^k$, perhaps? (The answers differ--a lot.) Or maybe as a linear transformation of $\mathbb{F}_p^k$?
Apr
3
comment Recursive/Fibonacci Induction
This is carried out at mathematica.stackexchange.com/questions/18481/… for Fibonacci numbers defined over any field (whose characteristic is not $5$ or $2$).
Apr
3
comment A question on convex/concave envelope
It is difficult to determine what is being asked here: exactly how is the input going to be specified? Do you need to determine the points where the function ceases to be differentiable or are those points given you? (If they are explicitly given, why not just compute their convex hull?)
Apr
1
comment Fejer Kernel problem
This is really a comment because it's not an answer: although it points out that the integral is invariant with respect to $f'$, it still leaves the O.P. with the problem of finding that constant ("show (1) gives you $1$").
Mar
30
comment Detect values in array that are statistically inconsistent
Option 1 is statistically terrible, for many reasons, and option 2 requires strong assumptions to be valid. Consult the stats site for better solutions and discussion.
Mar
30
comment Detect values in array that are statistically inconsistent
This is not a mathematical question nor does it have a definite answer. For instance, some processes have regular variation when the observations are expressed as logarithms (as is often the case in chemistry: pH is a log). In your first example the common logs all vary between 3.2 and 1.7, averaging around 2. However, one of them is zero: it's far below all the rest. That would make $1$ the outlier, not $1542$. A good answer to this question will therefore consider the nature of the process, its statistical characteristics, and the objectives of the algorithm.
Mar
30
comment Difficult and unusual probability problem, how to solve?
Hint: consider the case $k=1$. What's the answer? (The answer in the general case is obtained in a similar manner and relies on this one.)