Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [sum]

The sum of two or more random variables.

Some families of distributions are closed under sums. For instance, the sum of two independent Poisson variables is itself Poisson distributed, and the sum of two normally distributed variables is again normally distributed.

Sums of other distributions are still tractable. For instance, the sum of $r$ independent identical geometric distributions has a negative binomial distribution.

Finally, some distributions' sums can only be approximated, e.g., the sum of two lognormal distributions.

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The sum of independent lognormal random variables appears lognormal?

I'm trying to understand why the sum of two (or more) lognormal random variables approaches a lognormal distribution as you increase the number of observations. I've looked online and not found any results concerning this. Clearly if $X$ and $Y$ are…
Patty
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Central Limit Theorem for square roots of sums of i.i.d. random variables

Intrigued by a question at math.stackexchange, and investigating it empirically, I am wondering about the following statement on the square-root of sums of i.i.d. random variables. Suppose $X_1, X_2, \ldots, X_n$ are i.i.d. random variables with…
Henry
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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: $$P\left(\sum_{i=1}^n X_i = x~\middle|~\max_{i=1}^n X_i = a\right)$$ In other words, given…
StephenSwat
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If $20 $ random numbers are selected independently from the interval $(0,1) $ probability that the sum of these numbers is at least $8$?

If $20 $ random numbers are selected independently from the interval $(0,1) $ what is the probability that the sum of these numbers is at least $8$? I tried to take this question…
simran
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Finding the distribution of sum of Lognormal Random Variables

I am trying to find the distribution of sum of 2 lognormal random variables. I referred the literature available on Cross validated, Stack overflow and few papers before posting this. I used convolution to find the distribution of sum of 2…
Naive_Natural2511
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PDF of sum of truncated exponential distribution

Let $x_i$ represent samples from a Truncated Exponential distribution between $0$ and $1$, with rate parameter $\lambda$. Defining $\tilde x = \dfrac{\sum_{i=1}^{n}x_i}{n}$ What is the PDF of $\tilde x$?
Diogo Santos
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How to interpret sum of two random variables that cross domains?

suppose we have two discrete random variables: $X: \{$6 sided dice rolls$\}$ $\rightarrow \{1..6\}$ (following uniform distribution) $Y: \{$coin flips$\}$ $\rightarrow \{0,1\}$ (following uniform distribution) How can we add X+Y=Z, for Z a random…
user352102
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Generate identically distributed dependent normal random numbers with prespecified sum

How do I generate $n$ identically distributed but not independent normal random numbers such that their sum falls within a prespecified interval $[a,b]$ with probability $p$? (This question is motivated by generating a random walk that ends up at a…
Stephan Kolassa
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Finite sum of beta prime iid random variables

The beta prime distribution is infinitely divisible, as proved in Steutel and van Harn, 2003 (Appendix B). Sadly, in this book, there is no expression of the parameters of the distribution of $n$ variables iid following a beta prime distribution, as…
Bentoy13
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Sum of forecasts

I have a question regarding forecast. I'm building an inventory model around warehouses, where all warehouses have multiple customers/countries assigned. I have data on sales for all countries separately, so I can perform my forecast on this data to…
pk_22
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Probability of k zeros give the sum of n Poisson random variables is t?

Suppose that I have $X_1,X_2,X_3,...X_n$ iid random variables from a Poisson distribution of parameter $\lambda$. Given that $X_1 +X_2+X_3 +...+X_n = t$, what is the probability that exactly $k$ of $X_1,X_2,X_3,...X_n$ are zero? -- My approach: I…
The Yellow
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Square roots of sums absolute values of i.i.d. random variables with zero mean

In an earlier question, I asked about the limiting distribution of the square root of the absolute value of the sum of $n$ i.i.d. random variables each with finite non-zero mean $\mu$ and variance $\sigma^2$. The answer was (after a suitable…
Henry
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What is an intuitive explanation for Q90 (X+Y) > Q90(X) + Q90(Y) in fat-tailed variables. Non Subadditivity

In a business situation, management keeps a reserve of money for a 'rainy day' just in case costs are more than expected. The 90th percentile ($Q_{90}$ in the following) might be an indicator of how much costs might reach in adverse conditions. If…
Tim
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Expectation of sum of absolute values for correlated normal random variables

Let $x_1, x_2, \dots, x_{N}$ i.i.d. random variables $\sim \mathcal{N}\left(0,\sigma^2_x\right)$. Further, let $z\sim \mathcal{N}\left(0,\sigma^2_z\right)$, $z$ is independent from all $x_i$. We build random variables $y_i=x_i+\gamma z$. By…
Marius Andrei Zoican
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What are continuous distributions that are additive and have finite support

I'm wondering what are continuous distributions that are additive and have finite support. Joint normal distribution is continuous, and is additive in the sense that if $X,Y$ are joint normal, then $X+Y$ are still normal, but they have infinite…
T34driver
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