# Questions tagged [gamma-distribution]

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

645 questions
Filter by
Sorted by
Tagged with
74 views

### Numerical approximation to quantile function for Gamma distribution

I am building a stats/probability library in python and right now I am working on the properties of the gamma distribution. I know that its quantile function (F^-1(x)) does not have a nice closed-form ...
23 views

### What is the distribution of squared Erlang random variable?

Let $\mathbf x=[x_1, ... ,x_K]^T$, $x\sim\mathcal C\mathcal N(\mathbf 0,\sigma_x^2\mathbf I)$, I believe that the distribution of $||\mathbf x||^2=\mathbf x^{\dagger}\mathbf x$ is Erlang. Is there ...
71 views

### Generating pairs of random variables with given covariance and gamma marginals

I have shape parameters $k_X, k_Y$ and scale parameters $\theta_X, \theta_Y$, as well as a covariance $\sigma_{XY}$. How do I generate random variables $(X,Y)$ such that the marginals are gamma ...
120 views

### Prove that $U_i = \frac{1}{X_i}$ has the gamma distribution

Consider a random sample $(X_1, \ldots, X_n)$ where all $X_i$ are iid r.v. with the following density function: $$f(x, \theta) = Cx^{-(p+1)} e^{-\theta/x } 1_{[0,+\infty)}(x)$$ Find the value of $C$ ...
84 views

### Bayesian Gamma Regression Update

I'm looking for a resource that explains how to do update the coefficients for a Bayesian gamma regression using Gibbs sampling. Specifically, if $y_i \sim Gamma(\alpha,\beta_i)$ and my data ...
35 views

### Deriving Marginal Distribution of Poisson [duplicate]

How do you find the marginal distribution of a Poisson distribution given a gamma(a,b) prior?
In the textbook, there's a distribution like the following, $S=\sum_{i=}^{200}X_i\sim Gamma(\alpha = 200, \beta)$ then the textbook define a new function $P$ obtained by diving the $\beta$, so ...