# Questions tagged [gamma-distribution]

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

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### Fitting GLMMs for RT data with different condition level distributions

I have RT data that I'm looking to analyse. RT data usually follows Gamma/Inverse-Gaussian shape distributions, thus I usually fit a glmer model (in R) specifying the family as either of those ...
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### Name for a distribution between exponential and gamma?

The density $$f(s)\propto \frac{s}{s+\alpha}e^{-s},\quad s > 0$$ where $\alpha \ge 0$ is a parameter, lives between the exponential ($\alpha=0$) and $\Gamma(2,1)$ ($\alpha \to \infty$) ...
666 views

### Interpretation Beta coefficient regression gamma distribution

I am currently working on a panel data model of 30 companies over 10 years where the dependent variable is a score (decimal bounded between 0 and 1, continuous) while the independent are dummies and ...
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### Drawing from inverse gamma and inverse chi-square [closed]

I am drawing samples from $\frac{a}{\chi(b)}$. This should be the same as drawing a sample from $\frac{1}{\Gamma(\alpha, \beta)}$. I want to figure out what are $\alpha$ and $\beta$ in terms of $a$ ...
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### Application of Pareto/NBD and Pareto/GGG models for customer lifetime value estimates in high churn setting

I have been attempting to estimate customer lifetime value in the context of online classifieds (high churn context) using probabilistic models, chiefly the Pareto/NBD and Pareto/GGG techniques ...
627 views

### Showing that a Gamma distribution converges to a Normal distribution

Consider $G = \operatorname{Gamma}(p)$. As $p$ goes to $\infty$, the Gamma becomes more and more bell-shaped. How do I show that $\frac{G - p}{\sqrt{p}} \to Z \sim N(0,1)$ as $p \to \infty$? I ...
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### 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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### What can Ido if I get patterns in residuals vs predicted values using lme4::glmer() with a GAMMA distribution?

I want to model a response variable (y) as a function of two explanatory variables (x and z)....
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### Z = X1/(X1+X2) where X1 and X2 are gamma distributed [duplicate]

Suppose that $X_1 \sim \Gamma(\alpha_1,\beta)$ and $X_2 \sim \Gamma(\alpha_2,\beta)$ and let $Z = \frac{X_1}{X_1 + X_2}$ ($X_1$ and $X_2$ are assumed to be independent). I want to prove that $Z$ is ...
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### Why are Poisson distribution and Exponential distribution special case of Gamma distribution?

I am aware that Gamma distribution is used as a conjugate prior distribution for various types of rate parameters such as in Poisson distribution and Exponential distribution. People say that ...
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### Interpreting results from Generalized Linear Model, gamma family, log-link

I have a small number of observation point, and the data is continuous and very skewed. I decided to analyze the data with Generalized Linear Model, gamma family, log-link. I'm having hard time ...
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### Term for exp(beta) from a Gamma-GLM

I have read a lot about interpretation of coefficients from Gamma-GLMs (using a log-link function), e. g. from this thread How to interpret parameters in GLM with family=Gamma , and found this to be ...
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### Data transformation to fit gamma distribution in R

I'm having trouble to fit and simulate a gamma distribution using the fitdistr function from the ...
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### Gamma-Poisson conjugate prior, posterior exploding?

I've been looking for simple code that can model ad clicks per day. Notionally, gamma-poisson would be a good conjugate prior. However, I'm finding that for slightly large daily click rate values, the ...
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### Approximating the median of a $\Gamma(\alpha,1)$ distribution with $0<\alpha<1$

Is there a good approximation (or useful bounds) for the median $\nu_\alpha$ of a $\Gamma(\alpha,1)$ distribution with $0<\alpha<1$? I have only been able to find things like Berg & ...
263 views

### Loss function in for gamma objective function in regression in XGBoost?

Suppose I want to predict $y$ from a set of predictors $x$. $y$ is gamma distributed, so I want to use gamma regression with XGBoost. The help page of XGBoost specifies, for the objective parameter (...
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### How to specify Gamma parameterizations in a generalized linear model setting

I am trying to model an outcome using a generalized linear model and the Gamma distribution with a log link function using the glm() function in R. I went to ...
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### The cumulative sum of the difference between dependent Gamma variables

I want to know if it is possible to find an expression for the PDF of the storage in a linear reservoir system as described below. I am aware that there are some numerical methods that would allow me ...
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"The canonical link of Gamma GLM is $g(x)=1/x$ is often not very practical. Log-link is more appropriated in most cases." One reason I can think of is that log-link makes sure $\mu$, the ...
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### Bayesian estimation of the variance

The mean of the Gamma distribution is $\alpha/\beta$, while the mean of the Inverse Gamma is $\beta/(\alpha-1)$. Similarly, the mode of the Gamma is $(\alpha-1)/\beta$, but the mode of the Inverse ...
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### How to interpret parameters in GLM with family=Gamma

I have a question regarding parameter interpretation for a GLM with a gamma distributed dependent variable. This is what R returns for my GLM with a log-link: ...
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### Is the question requiring the use of a gamma or exponential distribution? [closed]

Incoming telephone calls to an operator are assumed to be a Poisson process with parameter $\lambda$. Find the density function of the length of time for $n$ calls to be received, and find the mean ...
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### marketing hypothesis test sample size calculation

I am trying to design a coupon promotion test to measure the increase in the volume of orders from promotion versus no promotion. To do so, I want to calculate the pre-group sample size required to ...
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### Sample Size Calculation - Two Gamma Distributed Mean

I have a similar question to Sample Size Calculation - Two Independent Means, in my case, I am measuring the number of orders our customer make which follows a gamma distribution I believe. How could ...
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### Improving a model for a positively skewed continuous data (no zeros)

I have a positively skewed continuous data (no zeros), representing transactions by amount. Variables age and income were ...
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### glmer with gamma distribution - problem fitting model

I am trying to fit the gamma distribution to my data as the residuals are not normally distributed but it has been much more difficult than I anticipated. The dependent variable is response times and ...
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### AIC doesn't agree with model checking [duplicate]

I have two glm, one with a gaussian distribution and identity link and one with gamma family and log link. The predictors are the same, the only thing that change is the response that in the gaussian ...
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### What length are some segments of a broken rod?

If a rod (of unit length) is broken into $n$ segments (assuming the $n-1$ breaks occur with uniform probability across the entire length) and $k$ of those segments are chosen at random and laid end to ...
### sampling from $\frac{1}{1+x}$ times Gamma distribution density
I am simulating a process by drawing many random variates $X$ from a Gamma distribution with parameters $\alpha$, $\beta$, f_X(x) = \frac{\beta^\alpha \, x^{\alpha-1} \, e^{-\beta x}}{\Gamma(\alpha)}...