# Questions tagged [gamma-distribution]

A non-negative continuous probability distribution indexed by two strictly positive parameters.

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### Probability of an exponential random variable being greater than a gamma random variable?

Let V have exponential(a) density, and let W be independent of V with gamma(s,b) density. Find P(V>W). What I did for this problem is I integrated the conditional probability P(V>W|W)f(w)dw from w = ...
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### Gamma-2 Distribution in Bayesian

According to the material I have in hand for Bayesian Econometrics, we define the pdf of a Gamma-2 distributed random variable $Z$ with parameter $\mu > 0$ and degrees of freedom $\nu > 0$, ...
37 views

### shape and rate of the square of a variable having a gamma distribution

from this answer (Expectation of a squared Gamma) I would like to know the shape and rate parameters of a squared gamma. I struggle a bit here. ...
117 views

### Gamma likelihood with InverseGamma prior

I've got a gamma likelihood $\Gamma(\tau_c | \alpha_k, \frac{\alpha_k} {\tau_k})$ (parameterized with shape and rate) with an InverseGamma prior $IG(\tau_k|a_0, b_0)$. I know that the resulting ...
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### Hypothesis testing for Gamma distribution

I have a sample $X_1,...,X_n \sim \Gamma(\alpha, \beta)$, where $\alpha, \beta$ - unknown parameters of Gamma distribution. How to build a test for testing $H_0:\alpha=1$ against $H_1:\alpha>1$?
155 views

### Distribution of counts for event-sequence

I work with event sequence. Let's say I observe LED blinking. My sequence will look like black spikes on figure. Intervals between events distributed similarly (but not absolutely) to $\gamma$ with ...
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### Deriving exponential distribution from sum of two squared normal random variables

Let $X$, $Y$ be i.i.d. random variables with distribuition $\mathcal{N}(0,1/2)$ and $Z = X^2 + Y^2$. I'd like to prove based on $X$ and $Y$ pdf's that $Z$ has exponential distribuition.
This is related to my previous question: How to update Poisson conjugate prior with observations of arrival time instead of counts? Using the same notation, suppose $N \sim \operatorname{Pois}(\mu)$ ...