# Questions tagged [gamma-distribution]

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

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### When to use gamma GLMs?

The gamma distribution can take on a pretty wide range of shapes, and given the link between the mean and the variance through its two parameters, it seems suited to dealing with heteroskedasticity in ...
37k views

### Choosing between LM and GLM for a log-transformed response variable

I'm trying to understand the philosophy behind using a Generalized Linear Model (GLM) vs a Linear Model (LM). I've created an example data set below where: $$\log(y) = x + \varepsilon$$ The ...
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### Which has the heavier tail, lognormal or gamma?

(This is based on a question that just came to me via email; I've added some context from a previous brief conversation with the same person.) Last year I was told that the gamma distribution is ...
30k views

### Generic sum of Gamma random variables

I have read that the sum of Gamma random variables with the same scale parameter is another Gamma random variable. I've also seen the paper by Moschopoulos describing a method for the summation of a ...
27k views

### Gamma vs. lognormal distributions

I have an experimentally observed distribution that looks very similar to a gamma or lognormal distribution. I've read that the lognormal distribution is the maximum entropy probability distribution ...
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### Good methods for density plots of non-negative variables in R?

plot(density(rexp(100)) Obviously all density to the left of zero represents bias. I'm looking to summarize some data for non-statisticians, and I want to avoid ...
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### Real-life examples of common distributions

I am a grad student developing an interest for statistics. I like the material over-all, but I sometimes have a hard time thinking about applications to real life. Specifically, my question is about ...
69k views

### The relationship between the gamma distribution and the normal distribution

I recently found it necessary to derive a pdf for the square of a normal random variable with mean 0. For whatever reason, I chose not to normalise the variance beforehand. If I did this correctly ...
165k views

### 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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### Construction of Dirichlet distribution with Gamma distribution

Let $X_1,\dots,X_{k+1}$ be mutually independent random variables, each having a gamma distribution with parameters $\alpha_i,i=1,2,\dots,k+1$ show that $Y_i=\frac{X_i}{X_1+\cdots+X_{k+1}},i=1,\dots,k$,...
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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: ... 19k views

### Weibull Distribution v/s Gamma Distribution

What is the difference between the intuition behind Gamma and Weibull distributions? Is there any relationship between the two densities ? Kindly help.
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### Is it possible to understand pareto/nbd model conceptually?

I am learning to use BTYD package that uses Pareto/NBD model to predict when will be a customer is expected to be back. However, all literature on this model is full of mathematics and there does not ...
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### Estimating gamma distribution parameters using sample mean and std

I'm trying to estimate the parameters of a gamma distribution that fits best to my data sample. I only want to use the mean, std (and hence variance) from the data sample, not the actual values - ...
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### Using R for GLM with Gamma distribution

I currently have a problem understanding the syntax for R for fitting a GLM using the Gamma distribution. I have a set of data, where each row contains 3 co-variates ($X_1, X_2, X_3$), a response ...
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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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### Which diagnostics can validate the use of a particular family of GLM?

This seems so elementary, but I always get stuck at this point… Most of the data I deal with are non-normal, and most of the analyses based on a GLM structure. For my current analysis, I have a ...
9k views

### 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 ...
25k views

From my results, it appears that GLM Gamma meets most assumptions, but is it a worthwhile improvement over the log-transformed LM? Most literature I've found deals with Poisson or Binomial GLMs. I ...
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### What kind of distribution does this have?

Currently I'm trying to figure out the distribution of the following: $X \sim \frac{\sqrt{n}}{\sqrt{Gamma(n,\beta)}}$ where the denominator follows a $Gamma(n,\beta)$ distribution. I've checked out ...
40k views

### 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 ...
27k views

### Need help calculating poisson posterior distribution given prior

I have been attempting to figure this out for hours, but gamma distribution is somehow beyond me. I have a question where we are given α=5 and ...
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### How do I identify the "Long Tail" portion of my distribution?

I have a number of series that would typically be described as normal skewed or Gamma distributed. For example, say I have a group of customers and have calculated their spend over a fixed length of ...
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### What distributions have an undefined mean but are not symmetric?

What distributions have an undefined mean but are not symmetric? I'm looking for a probability distribution function (and CDF) for which the mean is undefined, but not symmetric like Cauchy, but a ...
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### Independence of statistics from gamma distribution

Let $X_1,...,X_n$ be a random sample from the gamma distribution $\mathrm{Gamma}\left(\alpha,\beta\right)$. Let $\bar{X}$ and $S^2$ be the sample mean and sample variance, respectively. Then prove ...
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### Intuitive way to connect gamma and chi-squared distributions [duplicate]

I understand that a chi-squared distribution is a special case of the gamma distribution. However, I find claims of "the math just works out" to be an unhelpful in remembering or ...
### How to create a markov chain with gamma marginal distribution and AR(1) coefficient of $\rho$
I want to generate a synthetic time series. The time series needs to be a markov chain with a gamma marginal distribution and an AR(1) parameter of $\rho$. Can I do this by simply using a gamma ... 