Questions tagged [sum]
The sum of two or more random variables.
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Conditional probabilities of the parameters
I have the following function
$$ x(k) = \sum_{m}^{M} e^{i(U_m k + \beta_m)} $$
Where
$$ i = \sqrt{-1} $$
The $U_m$ values come from a normal distribution and the $\beta_m$ values come from a uniform ...
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Time series benchmarking/reconciliation and revisions - are there methods that minimise revisions?
I am using the tempdisagg R package for benchmarking quarterly time series to annual time series from different (more trusted) sources (by temporally disaggragating the annual data using the quarterly ...
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Does $p=0 \implies \sum_{i=1}^{p} \phi_i L^i = 0$?
Let us take this $\operatorname{AR}(p)$ equation
$$\left(1 - \sum_{i=1}^{p} \phi_i L^i \right)X_t = \mu + \epsilon_t$$
as an example.
When $p=0$ I read this to mean
\begin{align*}
\mu + \epsilon_t &...
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Is there a clear interpretation of Corr(X, X+Y) in research?
Consider a case of $Corr(X,Z)$, often found to be high; where later, it was found that it holds exactly $Z = X + Y$. In effect, the previously found correlations were equal to $Corr(X, X+Y)$.
How can ...
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If X=Y+Z, Is it ever useful to regress X on Y?
If we have X and Y that are mathematically dependent: X = Y + Z, is it 'forbidden' to use Y as a predictor to X in linear regression? I'm trying to find a concise explanation for why it is, or isn't.
...
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Is the sum of two singular covariance matrices also singular?
I have two sample covariance matrices, computed from $n$ samples, less than $p$ variables: they are singular then.
I know that the sum of two covariance matrices is also a covariance matrix.
My ...
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Prove $P(X_1+X_2> 2C) \leq P(X_1>C)$ if $X_1,X_2$ are identical, but dependent?
If $X_1,X_2$ are dependent but identically distributed, it seems obvious that $P(X_1+X_2\geq2C) \leq P(X_1\geq C)=P(X_2\geq C)$. At least if we additionally assume that the joint distribution is ...
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Statistical Data Analysis using "Sum" Function
Most commonly when I hear descriptive data analysis using statistics these following functions are often inclded:
Mean
Standard Deviation
Variance
Range
Mode
Median etc.
Is the function "Sum&...
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Calculating the probability of the total duration of N sequential events with different cdfs describing their duration
Be patient, I am not very skilled with cdf.
I seem to have a seemingly simple problem for which I either can't seem to find material about or simply lack the vocabulary for.
Given are N sequential ...
2
votes
1
answer
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Distribution of sum of $n$ random variables with mixture of two exponential distributions
Suppose that the random variable $Y$ follows a mixture of two exponential distributions, that is
\begin{equation}
f_Y(y) = \sum_{i=1}^{2}\pi_i f(y| \lambda_i)
\end{equation}
where $\pi$ stands for ...
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votes
1
answer
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R function to compute variance of average of correlated random variables
I want to calculate the variance of the average of n correlated variables. I found a formula for that in Borenstein et al. (2009) Introduction to Meta-Analysis.
$$\operatorname{Var}\left(\frac{1}{m}\...
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Probability of a sum of random variables falling in a given range
Given a distribution $P$, two values $a$ and $b$, $x=0$, and the following process:
Draw a number $r$ from $P$ and add it to $x$, this is $x = x+r$.
Keep doing this until $x$ is higher than $a$.
...
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Sum of sample given a priori knowledge of its maximum
Given a sample of discrete random variables $X_1, X_2, \ldots, X_n \sim F$, I am looking to calculate the distribution given by the probability mass function:
$$P\left(\sum_{i=1}^n X_i = x~\middle|~\...
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1
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sumscores instead of factorscores or SEM
Suppose I would like to use sumscores after running a confirmatory factor analysis (CFA) with two latent factors. The items for each factor are then summed and in subsequent analyses these sums are ...
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Sum of Discrete Uniforms, but each value can be picked no more than N times?
Suppose there are i.i.d. variables $X_{1,..n}$ with discrete uniform distribution with the support $[1, n]$. What would be the distribution of such a sum if we introduce the condition that each value ...
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