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Here is the R source code for the internal pt function: http://svn.r-project.org/R/trunk/src/nmath/pt.c The relevant code snippet is if(!R_FINITE(n)) return pnorm(x, 0.0, 1.0, lower_tail, log_p); In other words, pt automatically detects an infinite degrees of freedom parameter and calls pnorm

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If the process parameters are changing the process is out of (statistical) control, as you say. It is not necessarily producing bad product—yet. The idea is to preempt quality problems by investigating signs of process instability & fixing them as necessary, while sparing engineers' time by limiting the number of wild-goose chases they're sent on. ...

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You can proceed some distance with that assumptions, but you cannot recover a specific expression for the probability because the joint distribution can be anything. Using the restriction on the rv's we have $X_3 =1- X_2-X_1$. Using the restrictions on the constants, we have $a_3=1-a_2-a_1$. Then we search for the joint probability P( |X_1 - a_1| < ...

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The XMeans algorithm can be used to estimate the total number of clusters directly from the data, without human guidance. The Weka package has a Java implementation. An expectation maximization algorithm can also be used to automatically estimate the total number of clusters as well. There is a Weka implementation of that also. In addition, there is at ...

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The skewness and kurtosis of particular distributions are known functions of the distribution. e.g. the Normal distribution has a skewness of 0 and a kurtosis of 3 (often given as an "excess kurtosis" of 0. The formulas for skewness and kurtosis are widely available on the web, e.g. Skewness and kurtosis For any given sample, skewness and kurtosis can be ...

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I agree with what others have said -- namely that "variance" is probably the wrong word to use (seeing as the function you are considering isn't a probability distribution but a time-series). I think you may want to approach this problem from a different perspective -- just fit the two time series with LOWESS curves. You can calculate 95% confidence ...

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