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21 views

Summation constraint matrix

I'm trying to create an assignment script using the R package Rsymphony, but I can't seem to figure out how to convert the summations into an actual constraint matrix. I tried to figure it out based ...
22 views

Is there such thing called sum of absolute sum?

Sum of absolute difference (SAD) is common in image processing as a measure of similarity. Is there such thing called sum of absolute sum in image processing or other field? Does it have any ...
7 views

What should I expect biweight weighting values to be?

I am working on a project that involves taking the biweight sample variance of a velocity dataset. This is defined as $\sigma_{BI}^2 = N\dfrac{\sum_{|u_i|<1}(1-u_i^2)^4(v_i-\bar{v})}{D(D-1)}$ ...
21 views

What's the most accurate way to sum the standard deviation (or variance) and mean for two sets of data with different numbers of observations? [duplicate]

I was wondering what the correct way to do this is. So far I have a method of my own which I'm not sure is optimal. At the moment I am first calculating the new mean as a normalized weighted sum of ...
42 views

Proving a property of $(n-1)s^2$

I would appreciate your help as I climb the stats learning curve! I want to prove the following: "Let $x_1, x_2, ... , x_n$ be any numbers and let $\overline x = (x_1 + x_2 + ... + x_n)/n$ Then ...
27 views

What is the variance of the sum of Yi's

Seems a simple enough question, and I presume that, if Yi are normally distributed, Var(Sum(Yi)) = Sum(Var(Yi)) This feels like I'm jumping to the wrong conclusion though. Any help would be ...
45 views

Formative/composite variable as weighted additive index

I'm very new to SEM (and relatively new to stats generally). I would like to ask whether my plans generally sound reasonable before I get lost for days in the literature. The model that I try to work ...
33 views

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variance of summation/compound variable?

here is my situation. I am weighting a packet of material that has 10 individual units in it. In the end of the day I would like to know the average weight and variance of the individual units but the ...
4k views

General sum of Gamma distributions

I have read that the sum of gamma distributions with the same scale parameter is another gamma distribution. I've also seen the paper by Moschopoulos describing a method for the summation of a general ...
54 views

Random variables for which the distribution of the sum of the RV with a Gaussian RV is known

For a counter example, I am searching for random variables $Y$ such that for a independent normal random variable $X$ the distribution of $Z=Y+X$ is known parametrically. Ideally, the Shannon entropy ...
35 views

How to find the optimum ordering of a set for a nonlinear equation in decent time

Assuming I have an unordered set of tuples of the form: $(a, b)$ How can I order the set so as to optimize the following equation: $\sum_{i=1}^n\sum_{j=1}^{i-1}(a_i*b_i)(1-b_j)$ For small ...
59 views

Why is this MGF identity true?

If $X_i \overset{i.i.d.}\sim N(\mu, \sigma^2)$, we know that: $\bar{X} \sim N(\mu, \sigma^2 /n)$. But why does: \exp\left({\sigma^{2}\over 2}\sum_{i=1}^{n}(t_{i}-\bar{t})^{2}\right)= M_{X_{1}-\...
156 views

What can we conclude about the distribution of the sum of two random variables?

If we know, for independent random variables $X$ and $Y$, $P(X>x)\leq0.05$, and $P(Y>y)\leq0.05$, can we say anything about $P(X+Y>x+y)$? Can we be certain that it is less than $0.05$? Under ...
245 views

How to rewrite a sum of probabilities formula as multiplications?

I have an equation like that: $p(r|s)= \frac{p(s,r)}{p(s)}=\frac{ \sum_{w,c} p(c,s,r,w)}{\sum_{w,c,r} p(c,s,r,w)}$ I am new to probability and I want to learn that how can I write sum formula as ...
2k views