Linked Questions
12 questions linked to/from Difference of Gamma random variables
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Difference of two Gamma random variables with the same scale parameters? [duplicate]
What is the distribution (probability density function) of the difference of two Gammas with the same scale? The parameters of each Gamma would be positive integers.
That is, I'd like to know the ...
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The sum of two independent gamma random variables
According to the Wikipedia article on the Gamma distribution:
If $X\sim\mathrm{Gamma}(a,\theta)$ and $Y\sim\mathrm{Gamma}(b,\theta)$, where $X$ and $Y$ are independent random variables, then $X+Y\sim ...
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Suppose $Y_1, \dots, Y_n \overset{\text{iid}}{\sim} \text{Exp}(1)$. Show $\sum_{i=1}^{n}(Y_i - Y_{(1)}) \sim \text{Gamma}(n-1, 1)$
What is the easiest way to see that the following statement is true?
Suppose $Y_1, \dots, Y_n \overset{\text{iid}}{\sim} \text{Exp}(1)$.
Show $\sum_{i=1}^{n}(Y_i - Y_{(1)}) \sim \text{Gamma}(n-1, ...
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probability of gamma greater than exponential
Let $X \sim Gamma(3,3)$ and $Y \sim Exp(1)$.
How do I calculate $P(X>Y)$?
I believe I rewrite it as $P(X-Y>0)$ but I am unsure how to calculate $X-Y$ for two different distributions?
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Distribution of difference of two random variables with chi-squared distribution
Supose that we have two random variables $X \sim \chi_k^2$ and $Y \sim \chi_k^2$, with the same degrees of freedom.
A chi-squared distribution cannot have zero degrees of freedom, so what would be ...
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The distribution of the linear combination of Gamma random variables [duplicate]
If $X_i\sim\Gamma(\alpha_i,\beta_i)$ for $1\leq i\leq n$, let
$Y = \sum_{i=1}^n c_iX_i$ where $c_i$ are positive real numbers.
Assume all the parameters $\alpha_i$'s and $\beta_i$'s are all known, ...
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Finding the probability X > Y
I am curious on how to find the probability a random variable X is greater than Y (given their means and variance, and also that they are independent.)
I stumbled across this post: probability of one ...
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Difference between two i.i.d Laplace distributions?
What is the PDF of the difference of two i.i.d Laplace distributed random variables?
I know that the difference of two i.i.d Normal variables is still the Normal distribution. Since the properties of ...
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Difference of two independent gamma distribution
Given two independent random variables $X\sim\Gamma(s,r)$ and $Y\sim\Gamma(t,u)$, what is the distribution of the difference, i.e. $D=X−Y$? I assume that $s$ and $t$ are integers. How can I obtain the ...
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How to test the mean difference of two Gamma distributions [duplicate]
If I don't have the data, but only have the estimates of mean and variance of two independent Gamma distributions. What type of test I can use to test the null hypothesis μ1=μ2?
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How to quantify the reliablility of an estimate
Lets say I inspect two workers.
Worker A works one hour and produces 2 goods.
Worker B works 100 hours and produces 180 goods.
So, on average, worker A produces 2 goods per hour and worker B 1.8 ...
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Distribution of $\mathbf{A}\mathbf{X}$?
Let $\mathbf{A}$ be an $m\times n$ random matrix with entries $A_{ij}$ being jointly Gaussian. Suppose all of these variables are independent of the random vector $\mathbf{X} = (X_1,\ldots,X_n)^\top$ ...
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