# Questions tagged [gamma-distribution]

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

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### Poisson-Gamma conjunction - calculating posterior [duplicate]

How to calculate posterior distribution step-by-step while given: some observed numbers of customers from the last days that number of clients is distributed by Poisson($\lambda$) ($\lambda$ is not ...
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### GLM Using Log-gamma Distribution

My data are skewed. Using log-normal causes a strong left-skew in the residuals. Using Gamma causes a strong right-skew in the residuals. I thought to myself, why not log transform the data and then ...
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### Fitting mixture of Gamma variate functions at once (with python)

I am trying to automate the fitting of a signal composed of several Gamma variate functions with some added noise. However, I face some troubles and I do not know how to deal with it. First I do not ...
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### Sampling from Gamma Distribution using the Rejection Method

I'm having some issues working through this practice problem. I have worked through the first portion of it, and I have the solution, but I don't understand how/why the solution does two things at the ...
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### Connecting interpretations of chi-squared distribution as both gamma distribution and normal distribution

According to this post I read http://www.clayford.net/statistics/deriving-the-gamma-distribution/ the gamma distribution $\text{Gamma}(\alpha,\lambda)$ is the theoretical distribution of wait ...
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### Can the logarithm of the sum of random variables be decomposed into the sum of independent random variables?

Suppose $X1$ and $X2$ are two independent Gamma random variables, both follow Gamma distribution but different scales (or rates), their shape can be same or different. Let $Z$ be another random ...
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### Gamma GLMM Dispersion, Random Effects, and CoV (lme4)

So I know that in glm(), with the Gamma family, one can get the dispersion parameter through the MASS package with gamma.dispersion() or can even look at the summary output as a quick estimate. How ...
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### getting negative binomial from poisson and gamma

This equation is from a statistical genetics research paper. I'm struggling to understand how they get negative binomial from the integral. x_cn is poisson and q is gamma. Is there such a rule? Or is ...
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### How to use Gamma distributions to estimate the number of failures?

I need to calculate the expected number of failures of a product within 6 years. The time until failure is said to be gamma distributed with $\alpha=2$ and $\beta=0.5$ for a mean time between ...
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### inverse Gamma Distribution and LogNormal Distribution can both discribe the data, is that a coincidence?

I am observing the fluxes of source and I am trying to learn something from it's distribution of fluxes. When I histogram my data, I can perfectly describe my data with a lognormal distribution. ...
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### Characterizing a distribution

I have a set of words which in a given year has a frequency of occurrence k. I can observe that these words follow frequencies k1, k2, k3,....kn in the following year. If I have some data in the form ...
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### What is the difference between Gamma GLM on log output and Gamma GLM with log link function?

Here are two models (with R code to provide some context): Model 1: Take the log of the output variable $y$, then apply a Gamma GLM using the default identity link function: ...
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### Relating Chi Squared and Gamma Distributions using code?

How do we relate the chi squared and gamma distributions with code? For example if we have a chi squared distribution with cdf(x, k) and we calculate ...
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### Fitting Gamma Distribution in Python with scalar factor

I have done optimization to minimize error of resulted model, however, the R-squared is still low. I try to multiply a scalar to the resulted model to obtain a better fit. The scalar will be generated ...
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### Model validation in R - Gamma GLMM

I'm trying to model a response variable y with respect to a nested variable x in R. First of all, I fitted a linear mixed model (LMM) as it follows: ...
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### Poisson and Gamma distribution for testing randomness

In genetics I want to test whether InDel (insertion and deletion in DNA) sizes occurs with the same probability. I heard that I should gamma distribution to model it. I found ...
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### Gamma Distribution CDF Intuition; Are My Parameters Correct?

I'm learning about gamma distributions and I want to make sure my reasoning is correct for an example I found here. Suppose you are fishing and you expect to get a fish once every 1/2 hour. ...
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### Optimal distribution for Acceptance Rejection Sampling

For some project I have been sampling from the Gamma distribution. I have been using the exponential distribution intensively. One method I have employed is the Acceptance rejection sampling, ...
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Please refer to the question in image I have tried to find $E(x)$ but i ended up with $\overline x$ = $\frac{\theta + 1}{\theta}$ which statisfies no option , i also tried to find $E(x-1)^2 ... 1answer 35 views ### Should I subtract lower bound from Gamma distributed data before estimating distribution parameters? I have some real world data that reflects waiting time in a system. As it's about waiting times I assume it's Gamma distributed and visual check (histogram overlaid by a fitted Gamma PDF) shows no ... 1answer 78 views ### When a probability density function is defined to be finite? In "Pattern recognition and machine learning" by Cristopher Bishop, Chapter 2.3.6 (pag. 100) says that The gamma distribution has a finite integral if$a>0$, and the distribution itself is ... 0answers 29 views ### interpreting Gamma regression coefficients - individuals not totalling sum of parts I have fit a gamma regression to a dataset, and like with traditional linear regression, I would like to calculate the contribution of each independent variable across the entire model. The problem I ... 1answer 140 views ### Gamma distribution parameters estimation [closed] I have a set of samples taken from a population distributed with a Gamma distribution, so \begin{equation} f_X(x)=\frac{\beta^\alpha}{\Gamma(\alpha)}x^{\alpha-1}e^{-\beta x} \end{equation} I should ... 0answers 292 views ### MLE for Beta distribution, with$\beta$= 3 I'm trying to calculate the Maximum-Likelihood Estimator for$\alpha$, using the beta distribution with$\beta = 3\$. I'm kind of stuck at the last bit. Perhaps I've made a mistake somewhere, or this ...
I am trying to use a Hierarchical model where there I have a normal distribution with random mean and precision: $$y \sim N(\mu, \tau)\\ \mu \sim N(M, T)\\ \tau \sim Gamma(\alpha, \beta)$$ I'm ...