All Questions
Tagged with sum gamma-distribution
12
questions
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29
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Concentration inequality for sums of independent gamma random variables
I am dealing with the following problem:
Say $X_1, \ldots, X_n$ are independent Gamma random variables, each one having shape and rate parameters $\alpha_i$ and $\beta_i$, respectively. Let $S_n = \...
- 55
1
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1
answer
127
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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 ...
-1
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1
answer
200
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Consistency when we want to find the distribution of sum of random variables following each one a distribution
I want to clarify a point that disturbs me among different cases.
I am interested in formulate correctly in a general case when we know the distribution of different random variables and we want to ...
user226073
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0
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26
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How do I sample Simultaneous Sums of Gamma-Distributed Variables?
Suppose I have 7 variables $y_i$ sampled from $Gamm(a,1)$, with $a>0$. Now, I define
$$x_1 = y_1+y_2+y_3+y_4,$$
$$x_2 = y_1+y_2+y_5+y_6,$$
$$x_3 = y_1+y_3+y_5+y_7$$
What is the distribution of $x_1$...
- 416
1
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1
answer
953
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Distribution sum of correlated normal variables squared
I'm trying to deduce which distribution my data follows and how to estimate the parameters. I have four random variables $X_i \sim N(\mu_i,\sigma_i^2)$ where the means and variances are all different. ...
- 113
2
votes
1
answer
245
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Lower incomplete gamma function format in series representation and R [closed]
As known that the lower incomplete gamma function can be written as $\gamma(a,x) = x^{a}e^{-x}\sum_k^\infty{{x^{k}}\over a^{k+1}}.$ What is the format for $\sum_j^\infty{\gamma(v/p-j,rx^{p})} $ in ...
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4
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1
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130
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Question regarding the distribution of sum of random variables
Let $X_1, ... X_n$ be i.i.d random variables that have an exponential distribution with parameter $\theta$. So we know that $\sum X_n \sim \Gamma(n, \theta)$.
This makes sense by working backward. ...
- 889
1
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0
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611
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Linear combination of non central chi-squared random variables
I want to analyze the distribution of
$$X = \sum_i X_i^2$$
where independent $X_i \sim \mathcal{N}(\mu_i, \sigma_i^2)$.
If $\mu_i=0$, I can derive the distribution by passing Gamma distribution like ...
1
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1
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33
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How to explain the following discrepency when changing parameter for exponential?
Suppose $y$~ $\exp(\frac{1}{2\theta})$
then $\frac1\theta y$~$\exp(\frac12)=\frac14\chi^2_2=\frac14\gamma(1,2)$
then $\sum \frac1\theta y=\frac14\chi^2_{2n}$
then $\sum y$~$ \frac{\theta}{4} \chi^...
- 213
3
votes
1
answer
290
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Can we show this sum of Gamma CDF converges, and if so can we derive its limit?
This is a bit of a strange question, but suppose I have some random variables.
$$Y_i \sim Gamma(i,\lambda)$$
Where this comes from the fact that each $Y_i$ is defined as the sum of $i$ independent ...
- 1,779
8
votes
3
answers
4k
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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 $\...
- 787
60
votes
5
answers
36k
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Generic sum of Gamma random variables
I have read that the sum of Gamma random variables with the same scale parameter is another Gamma random variable. I've also seen the paper by Moschopoulos describing a method for the summation of a ...
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