whuber

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bio	website	quantdec.com
	location	Northeastern US
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Consultant (environmental and spatial stats a specialty), expert witness, and teacher.

	57,097 reputation	bio	website	quantdec.com	visits	member for	2 years, 9 months
388190 badges		location	Northeastern US		seen	4 hours ago

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May 7	comment	How should I fit a curve to my data This question is based on a misconception: consistency of an MLE does not imply this curve will even remotely approximate a power.
May 7	comment	Confusion regarding weighted average You have stated that you want to weight your data without mentioning why, so there's no basis here to formulate an objective answer to your question. (The only question in evidence is "For each name, I'm trying to find the return rate," whose answer does not involve any weighting.) Please tell us explicitly what you want to achieve.
May 7	comment	How to perform regression analysis? (Including assumptions) For more information, search our site: there are hundreds of answers addressing variations of this question.
May 7	comment	Testing hypothesis We do invite homework questions, but--as explained in our faq--we expect such questions to show partial work towards a solution and to make a focused inquiry concerning the point where you are stuck. "Have no idea" is not specific enough. If you edit this question following those guidelines we will be glad to keep it open.
May 7	comment	Hypothesis testing for normal distribution We do invite homework questions, but--as explained in our faq--we expect such questions to show partial work towards a solution and to make a focused inquiry concerning the point where you are stuck. To allow this question to remain open, please edit it accordingly.
May 7	comment	Show that $G(x)$ is a distribution function and find mean Nevertheless, assuming $F(0)=0$, $G$ is a valid CDF for all values of $x$, so I think your accusations of inconsistency are a little overblown. There's a simple typographical error in the problem statement, that's all.
May 7	comment	Comparing correlations between two groups I'm sorry, it doesn't help me: could you be more specific about what a "different" correlation would be? Let's take a very simple example of two different-sized groups: a group of three and a group of two. For the group of three there are three correlation coefficients and for the group of two there is one correlation coefficient. Suppose, hypothetically, you had perfect information about these groups so there is no uncertainty about the values of the correlations. How would one go about determining whether these two groups have "different" correlations?
May 7	comment	Random Sampling Welcome to our site, Gary! We do invite homework questions, but--as explained in our faq--we expect such questions to show partial work towards a solution and to make a focused inquiry concerning the point where you are stuck. If you edit this question following those guidelines we will be glad to reopen it.
May 7	comment	Bound on the variance for [0,1] RVs as a function of the mean There is a much, much simpler proof which is fully general: since $V[X]+E[X]^2$ = $E[X^2]$ and $\|X\|\le 1$, it is obvious that $E[X^2]\le E[1\cdot X] = E[X]$ and the result follows upon subtracting $E[X]^2$. (This is a trivial instance of Holder's Inequality, inter alia.) It can also be seen as an application of the Cauchy-Schwarz Inequality.
May 7	comment	Relationship between mutual information and change of variables It's a direct consequence of the change of variables relationship for multiple integrals.
May 7	comment	What distribution does my data follow? We are seeing Stigler's Law of Eponymy in action. :-)
May 7	comment	Normalize a periodic parameter What's the matter with just allowing $\theta$ to lie in $[0, 360]$?
May 6	comment	Comparing correlations between two groups Could you expand on what it would mean to "compare" two different correlation matrices of different sizes? What is the intended interpretation?
May 6	comment	How do I identify the “Long Tail” portion of my distribution? You might appreciate this recent answer showing ways to identify modes in a distribution. Also of interest is this thread on 1D clustering. Searching our site on "clustering" is also likely to be fruitful.
May 6	comment	Optimizing a Poisson Process BTW, if you replace `[;` and `;]` by `$` your $\TeX$ expressions will be nicely rendered.
May 6	comment	Optimizing a Poisson Process You might want to think along the following lines: define "up front" to mean that you are within the first $M$ people in line (let your partner determine $M$ before you go out). You need to attach a cost to waiting and a cost to failing to be among the first $M$. Your distributional assumptions on arrival times translate into a distribution of the sum of those costs. You might want to arrive at the gate at a time of least expected cost. This is only one of many possible formulations of this problem--you need to work out what the problem really is before you ask it!
May 6	comment	Why are $x$ and $x^2$ correlated? If you plot $x^2$ versus $x$ you obtain, of course, a portion of a parabola. When the distribution of $x$ is away from zero, the correlation is measuring the linearity of one arm of that parabola: it looks more and more linear the further from zero you get compared to the range of the values. When the distribution of $x$ is symmetric around zero, the parabola is clearly curved. That's all that's going on.
May 6	comment	Why are $x$ and $x^2$ correlated? Simulate some data with $x$ symmetrically spaced around $0$ and try again :-).
May 6	comment	Asymptotic probability concerning the largest absolute value in an iid Gaussian sample I believe that the Mills ratio for the standard Normal distribution will reveal what you want to know: look at its continued fraction.
May 6	comment	Optimizing a Poisson Process Your model is missing key information its formulation. If you show up at time $0$, you don't get to the front and so you fail to meet your objective--but there's nothing in the model that actually states, much less quantifies, your objective (of being "up front"). If you show up $1000$ hours before the concert, maybe you're at the front but you wait a long time. You need to quantify what you're trying to achieve and you need to be more explicit about the assumptions you are making.