# Questions tagged [gamma-distribution]

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

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### How to evaluate $\int_0^\infty m^{x+1}e^{-2m}dm$ as $\Gamma(x+2)\frac{1}{2}^{x+2}$?

$\int_0^\infty \frac{m^{x+1}e^{-2m}}{\Gamma(x+1)\Gamma(2)}dm =\frac{\Gamma(x+2)\frac{1}{2}^{x+2}}{\Gamma(x+1)\Gamma(2)}$ How does the left side equal the right side? I understand that the gamma ...
114 views

### Not sure if a gamma glm or glmm is needed

I am fitting a linear model for de CO2 dataset in r, I want to predict plant uptake (always positive) using Type, conc, and treatment, a quick look at the data ...
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### What is the expected value of the logarithm of Gamma distribution?

If the expected value of $\mathsf{Gamma}(\alpha, \beta)$ is $\frac{\alpha}{\beta}$, what is the expected value of $\log(\mathsf{Gamma}(\alpha, \beta))$? Can it be calculated analytically? The ...
471 views

### Which method to use when calculating the confidence interval of GLMM Gamma Regression with the lme4 package in R

I am fitting a GLMM with family gamma using the lme4 package in R. Below is a code example to simulate the gamma GLMM fitting. ...
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### Strange behavior of Gamma prior in a setting with binomial likelihood

I am trying to use Bayes theorem to estimate the probability of a binary event. To give a (simplified) example: Let's say our a priori guess of the probability of the event per trial is 0.3 (and the ...