Questions tagged [gamma-distribution]

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

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Posterior derivation with prior as Normal-Gamma distribution [duplicate]

I am studying Gary Koop's Bayesian Econometrics , it is bit confusing in the beginning. I will reproduce some results from the textbook here in order to smoothly move to my question. For a simple ...
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A question about parameters of Gamma distribution in Bayesian econometrics

The Wikipedia article on the Gamma distribution, lists two different parameterisation methods, one of them frequently used in Bayesian econometrics with $\alpha>0$ and $\beta>0$, $\alpha$ is ...
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Does my data come from a gamma or beta distribution? [closed]

I have data and I want to ascertain whether it is beta or gamma distribution. Once I know what the distribution is, how do I find out what the parameters are?
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Sum of exponential random variables follows Gamma, confused by the parameters

I've learned sum of exponential random variables follows Gamma distribution. But everywhere I read the parametrization is different. For instance, Wiki describes the relationship, but don't say what ...
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2answers
965 views

How to obtain the gamma distribution through convolution of two different distributions?

How can one obtain the gamma distribution through convolution of two different distributions? Could the gamma distribution be created as a non-trivial sum of $N$ random variables $X$ which have the ...
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How to calculate the boundary value for a random variable which is sum of variables with gamma and uniform distributions?

The variable is a sum of two random variable which obey gamma and uniform distributions, respectively. The parameters of the uniform distribution variable are determined, and the other's must be ...
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1answer
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How does one get the gamma distribution parameters from a word problem description?

I am specifically confused as to the meanings of the shaping and scaling parameters of the gamma distribution and how they are used in a real context. Once I find the correct parameters, I have the ...
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McKay's bivariate Gamma distribution

Given the variables $X$ and $Y$, which are correlated, $X\ge0$, $Y\ge0$ and each follow a gamma distribution with different shape parameters, i.e.,$X\sim\Gamma(a_1,\alpha)$ and $Y\sim\Gamma(a_2,\alpha)...
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1answer
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Confusion over Gamma distribution CDF

Here's a probability question (probably really simple) I'm not sure how to solve: Gamma distribution $X\sim \mathcal{G}(\alpha,\beta)$ with $\mu = 20$ and $\sigma^2 = 80$ $P(X \le 24)$ = ? The ...
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2answers
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Joint distribution of two gamma random variables

I am so puzzled by this problem. Given two variables $X_1$ and $X_2$, such that $X_i \sim \mathrm{Gam}(a_i, b)$, find the joint distribution of $X_1$ and $X_2$. I understand how to proceed if ...
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How to test whether a sample of data fits the family of Gamma distribution?

I have a sample of data which was generated from a continuous random variable X. And from the histogram I draw using R, I guess that maybe the distribution of X obeys a certain Gamma distribution. But ...
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Bivariate Gamma distribution PDF

I'm analyzing a set of data, and I like to fit a gamma distribution. I know how to do it in one dimension, but the data that I'm analyzing now are two dimensional. Is there any way that I can have a ...
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Transformation to fit gamma distribution for glm

The data simulated below has a maximum value of 4 and is interestingly skewed. The maximum of 4 is a limitation imposed by the instrument used and the data is semi-discrete, i.e., there are a ...
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Proper use and interpretation of zero-inflated gamma models

Background: I am a biostatistician presently wrestling with a dataset of cellular expression rates. The study exposed a host of cells, collected in groups from various donors, to certain peptides. ...
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1answer
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What reference can I cite for the proof that the sum of n exponential variables follows a gamma distribution?

There is a fairly common theorem, which states that: The sum of $n$ independent variables following an exponential distribution $\mathrm{Exp}(\alpha)$ follow an gamma distribution $\mathrm{Gamma} (n, ...
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A mixed model with gamma distribution: handling zeros

I have a panel cost data with some zero values (not missing values but rounded to 0). How should I handle zeros when I use SAS Proc Glimmix with Gamma distribution? Maybe change zero to very small ...
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How to sample from $c^a d^{a-1} / \Gamma(a)$?

I want to sample according to a density $$ f(a) \propto \frac{c^a d^{a-1}}{\Gamma(a)} 1_{(1,\infty)}(a) $$ where $c$ and $d$ are strictly positive. (Motivation: This could be useful for Gibbs ...
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What are the mean and variance for the Gamma distribution?

There are two forms for the Gamma distribution, each with different definitions for the shape and scale parameters. Rather than asking what the form is used for the gsl_ran_gamma implementation, it's ...
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Kullback–Leibler divergence between two gamma distributions

Choosing to parameterize the gamma distribution $\Gamma(b,c)$ by the pdf $g(x;b,c) = \frac{1}{\Gamma(c)}\frac{x^{c-1}}{b^c}e^{-x/b}$ The Kullback-Leibler divergence between $\Gamma(b_q,c_q)$ and $\...
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How to derive Poisson distribution from gamma distribution?

Let $T_1, T_2, \dots$ be iid sequence of exponential random variables with parameter $\lambda$. The sum $S_n = T_1 + T_2 + \dots + T_n$ is a Gamma distribution. Now as I understand the Poisson ...
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Conditional expection of gamma distribution on sum

I have a process which consists of a number of events and what is known is the timings between the events. What I'm trying to determine is a distribution that allows me to determine a likelyhood that ...
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How to quickly sample X if exp(X) ~ Gamma?

I have a simple sampling problem, where my inner loop looks like: v = sample_gamma(k, a) where sample_gamma samples from the ...
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1answer
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What is the expected value of modified Dirichlet distribution? (integration problem)

It is easy to produce a random variable with Dirichlet distribution using Gamma variables with the same scale parameter. If: $ X_i \sim \text{Gamma}(\alpha_i, \beta) $ Then: $ \left(\frac{X_1}{\...
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How do you calculate the expectation of $\left(\sum_{i=1}^n {X_i} \right)^2$?

If $X_i$ is exponentially distributed $(i=1,...,n)$ with parameter $\lambda$ and $X_i$'s are mutually independent, what is the expectation of $$ \left(\sum_{i=1}^n {X_i} \right)^2$$ in terms of $n$ ...