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Results tagged with Search options answers only user 805
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Probability density function (PDF) of a continuous random variable gives the relative probability for each of its possible values. Use this tag for discrete probability mass functions (PMFs) too.

If you don't write down the support, you may not see what's going on -- but as soon as you do, it's a lot clearer. I am not able to understand the difference between the joint density function and …
answered Feb 14 '16 by Glen_b
give a complete definition of the pdf; it's a trivial matter to convert to my original $(0,\theta)$ case (scaling the width by $\theta$ and the height by $1/\theta$) and then to shift to your own … example. (Or you could employ the same strategy on your original example directly -- but I am very much in the vein of converting already-solved problems when I can.) More complicated pdf examples may in …
least four papers). One example is Figure 1 of Dunn & Smyth (2001) "Tweedie Family Densities: Methods of Evaluation", Proceedings of the 16th International Workshop on Statistical Modelling, Odense, Denmark, 2–6 July. (pdf preprint). It's not such a problem if everyone is clear what they're looking at] …
answered Mar 20 '18 by Glen_b
In the univariate case, one quick approximation: You could take a moderate number of bins (in the univariate case, say something on the order of a thousand, though it depends on your bandwidth - you n …
answered Nov 19 '14 by Glen_b
either the cdf or the pdf for $M$ is straightforward and can essentially be done from first principles. (See wikipedia on truncated distributions) The approach for other distributions is similar …
answered Aug 24 '16 by Glen_b
When you specify freq=FALSE area under the histogram represents proportion of the data (i.e. the histogram is a density estimate). The total area is 1. So the height is not estimating probability, th …
answered Nov 5 '16 by Glen_b
]=\int_{-\infty}^\infty (x-\mu)^k f(x) dx$See Wikipedia on Moments (mathematics). Given a pdf and the values of the parameters, can we calculate the moments of the distribution? If we can evaluate … squared. Yes, using basic properties of expectation, you can write$E[(X-\mu)^2]=E[X^2]-\mu^2$. See Wikipedia on variance. Is this an integral over all the support of the pdf? Strictly the … answered Jul 18 '16 by Glen_b As discussed in Dilip's response here, you can take the approach of doing direct integration with the bivariate density; however, I want to mention that while this is perhaps the most straightforward … answered Nov 5 '14 by Glen_b There are a number of density estimators that are piecewise constant. The scaled histogram is the most obvious: (the scaling is to make the total area 1, so that it estimates the underlying densit … answered Mar 27 '15 by Glen_b What convinces you that the Gaussian copula only applies to linear correlation? This would seem to be a counterexample: a pair of variables with a Gaussian copula, but they're not linearly related: … answered Jan 2 '14 by Glen_b better motivation. Imagine we're dealing with a sufficiently "nice" pdf, say one that's Lipschitz continuous. Then in a direct sense, as the interval in$x$gets smaller, the interval in$f$must also get … answered Jul 17 '15 by Glen_b If we have a variable$X\sim U(0,1)$and multiply it by$a$, then$aX\sim U(0,a)$. Assume that we're dealing with independent continuous uniform on$(0,a)$and$(0,b)$respectively (with$a<b\$) (Thi …
answered Aug 5 '16 by Glen_b
The mean and variance are not actually finite in either the Gaussian nor the Laplace case. You can try to use a Taylor expansion as they did in the paper you mention, but for that to actually be corr …
answered Jul 22 '16 by Glen_b
Well the pmf looks something like the second of the two plots below:
answered Oct 26 '15 by Glen_b
Indeed, even all (positive integer) moments may in some situations be insufficient to distinguish two distributions. Generally, the first few moments don't 'pin down' a distribution very well, which s …
answered Feb 26 '15 by Glen_b

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