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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 I can be reached through (outdated but still valid) links posted on my web site.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


7h
comment how we get Initial starting value in goodness of fit in R
This kind of question can be interesting, but without more information it's rather broad because the answer often depends on specifics of the probability model. Please edit it to include the details of your particular problem.
7h
comment Combination of normal and gamma distribution in R
@Glen_b Yes--the short durations lend importance to the role of the time-reversal machines! :-) Taken collectively, our comments indicate that although the thrust of this question is evident, it will be impossible to answer in detail without stipulating the meaning of the parameters in the "N" and "Gamma" distributions.
8h
comment Combination of normal and gamma distribution in R
Where are you stuck? The last sentence of the question seems clear enough: it asks you to estimate a proportion of faulty motors during two years. A careful reading of the question does raise some issues that only your teacher or textbook can address. The most salient of those is that (assuming "N(10,5)" means the distribution has a mean of $10$ and standard deviation of $5$) about one out of every 44 machines in your simulation will run for a negative amount of time!
8h
comment How to get F-test p-value
I fixed a whole lot of apparent typographical errors. Please check over the question and correct any misunderstandings I might have introduced. With the statistics you give, $H_0$ should not be rejected.
8h
revised How to get F-test p-value
added 12 characters in body; edited tags
8h
comment Course of Action for 2x2 tables with 0's in cell and low cell counts
Your terminology is likely to confuse people: ordinarily "controls" and "cases" are assigned by the experimenter. If you have no cases, you haven't done the experiment yet and there is nothing to analyze. One might guess that "controls" and "cases" just distinguish two possible outcomes that can occur, but what exactly do "A" and "B" mean? Were they determined by the experimenter or are they observations of some binary outcome, too?
8h
comment Generate two sequences that have a pre-specified rank correlation
I answered a generalization of this question at stats.stackexchange.com/questions/3961, but I suspect for your special case their might exist better solutions.
9h
comment What do the coefficients of the crossproduct of regression mean?
The SVD of $X=U\Sigma V^\prime$ gives a geometric interpretation. $X$, an $n$ by $p+1$ matrix, represents a linear transformation from $\mathbb{R}^{p+1}$ to $\mathbb{R}^n$ which is effected in three steps: a rotation $V^\prime$, independent rescalings in orthogonal directions and injection into a $p+1$-dimensional subspace of $\mathbb{R}^n$ via $\Sigma$, and a rotation $U$. The LS solution is obtained by reversing this: beginning with $y\in\mathbb{R}^n$,undo the last rotation, undo the scalings in the image of $\mathbb{R}^{p+1}$, and rotate that subspace to obtain $p+1$ coefficients.
11h
comment Compare two samples
You can regain control over your question, David, by merging your accounts: please visit stats.stackexchange.com/help/merging-accounts.
11h
revised Compare two samples
Pasted OP's response
11h
comment Remove outliers and calculate average
If you feed it a lot of values--especially with more extreme splits than 4312/4313--then statistical modeling can be used to identify the formula the program might be using. Your four cases are not enough, because (at a guess) the program is removing an unknown number of "outliers"--perhaps up to 4--with each calculation. That gives 25 possibilities, so at a minimum we would want to see 25+2 = 27 results (that show discrepancies) and preferably several times that many results.
12h
awarded  Nice Answer
12h
revised Functions of Independent Random Variables
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12h
comment Functions of Independent Random Variables
@Aksakal It depends on what school you go to or what books you read. (I have successfully taught this material at the second-year undergraduate level. There also are wonderfully accessible accounts of this theory at the undergraduate level, such as Steven Shreve's texts on stochastic calculus, which are addressed to students with just a calculus background.) But how is that relevant? Any justification--even a sophisticated one--should be preferred to an unjustified assertion.
12h
answered Functions of Independent Random Variables
12h
comment Poisson distribution with exact value of x and mean is a larger number
+1 Even Excel has a log gamma function (GAMMALN) for such purposes, suggesting how useful (and basic) taking logarithms is. I'm sure GAMMALN is implemented by means of the asymptotic expansion of $\Gamma$ (generalizing Stirling's approximation). Concerning (4), it might be a little clearer to write your approximation as $f_{X^{*}}(80) \times 1$ or even, quite suggestively, $\int_{80-1/2}^{80+1/2}\left(f_{X^{*}}(80) + O(x-80)^2\right) dx.$
13h
comment Estimating an overall summary statistic (mean) for a value reported by ten published studies
It sounds like your question might be the same as the one at stats.stackexchange.com/questions/51622, in which case you will find a simple general solution in that thread.
13h
comment Taylor approximation to penalty function
@Alecos It's no mistake: it comes from $\beta_j \approx \frac{1}{2}(\beta_j + \beta_{j0}),$ whence $\beta_{j0}(\beta_j-\beta_{j0}) \approx \frac{1}{2}(\beta_j + \beta_{j0})(\beta_j-\beta_{j0}) = \frac{1}{2}(\beta_j^2 - \beta_{j0}^2).$
13h
comment Standard deviation of a sample when you know the average
Computing the overall average of $n$ values in the database takes $O(n)$ effort. For the same $O(n)$ effort you can simultaneously collect relevant statistics about the spread of the values, such as their range and standard deviation. Why not just do that and use this information to scale the graph? In fact, for $O(1)$ effort you can get decent estimates of the spread (by randomly sampling the data), so there seems to be no practical obstacle to this approach.
13h
comment Is the F test for R² in (multiple) Regression one- or two-tailed?
@coffee F-tests are almost always one-tailed. The reason is that the null hypothesis of equal coefficients means that all variation is random, whereas under the alternate hypothesis there is an added component of variation arising from differences among the coefficients. That would cause the numerator only to increase. The other (left) tail corresponds to unusual consistency among the data. Fisher famously used it to suggest that Mendel's pea data were a little too good.