# Questions tagged [gamma-distribution]

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

143 questions
Filter by
Sorted by
Tagged with
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 ...
• 1,067
8k views

### 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 $Y_i=\frac{X_i}{X_1+\cdots+X_{k+1}},i=1,\dots,k$,...
• 2,010
20k views

### 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 ...
• 262k
16k views

### 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 ...
• 12.3k
113k views

### 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 ...
• 12.3k
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 ...
• 3,592
60k views

### 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 ...
10k views

### What to do with GLM (Gamma) when residuals are not normally distributed?

Until now I have only done very basic/simple simple stats, but now I got stuck in all the literature/tips/forums ... It's about the following problem: I have the following data: ...
• 123
13k views

### Difference of Gamma random variables

Given two independent random variables $X\sim \mathrm{Gamma}(\alpha_X,\beta_X)$ and $Y\sim \mathrm{Gamma}(\alpha_Y,\beta_Y)$, what is the distribution of the difference, i.e. $D=X-Y$? If the result ...
• 307
72k views

• 1,072
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 ...
• 1,067
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 ...
• 273
6k views

### What are the assumptions of a Gamma GLM or GLMM for hypothesis testing?

What are the assumptions when doing hypothesis testing using a Gamma GLM or GLMM? Are the residuals suppose to be normally distributed and is heteroscedasticity a concern like the Gaussian (normal) ...
9k views

### Is my data gamma distributed?

I have some data which looks like this when I plot a normalized histogram. The full data set is available here and here (the second link is pastebin). It is 20,000 lines long. My guess is that it ...
• 1,889
1k views

### What is the convolution of a normal distribution with a gamma distribution?

Is there a closed form expression for the convolution of a normal distribution (ND) with a gamma distribution (GD)? There does not seem to be a direct method of solving this convolution.
• 11.9k
464 views

### What is the best point forecast for gamma distributed data?

I believe that the values I am forecasting are gamma distributed with shape $k>0$ and scale $\theta>0$. I need a point forecast (i.e., a one-number summary) that minimizes the expected error. ...
• 99.5k
22k views

### 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 ...
• 151
32k views

• 303
6k views

### Probability Interval for Gamma Distribution

There is something that I am doing wrong in the exercise below and I would appreciate some help figuring it out. Let $X_1, X_2, \ldots, X_5$ be a random sample from a $\Gamma \left(3,3 \right)$ ...
• 18.7k
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 ...
• 948
75k views

### 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 ...
• 565
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.
• 591
1k views

### 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 ...
• 828
4k views

### 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 ...
• 2,409
2k views

### Square root of an inverse gamma distributed random variable

I work on the grouped t copula and try to replicate part of the following paper: "The t copula with Multiple Parameters of Degrees of Freedom: Bivariate Characteristics and Application to Risk ...
• 53
3k views

### Analysis of variance with Weibull or Gamma distributions

I have been trying to find a method to analyse variance on Weibull and/or Gamma distributions but a Google search for anovar Weibull "gamma distribution" yields ...
• 175
2k views

### 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 ...
• 750
1k views

### What is the distribution of the ratio between independent Beta and Gamma random variables?

What would be the distribution of the following equation: $$y = \frac{a}{(a+d)^2}$$ where $a, d$ $\sim$ $\Gamma(M,c)$. Additionally, $a$ and $d$ are independent random variables.
2k views

• 2,287
1k views

• 345
2k views

### Skewness of the logarithm of a gamma random variable

Consider gamma random variable $X\sim\Gamma(\alpha, \theta)$. There are neat formulas for the mean, variance, and skewness: \begin{align} \mathbb E[X]&=\alpha\theta\\ \operatorname{Var}[X]&=\...
• 95.7k
466 views

### 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 ...
• 413
1k views

### Predicting with a GLM

I wanted to check my understanding of predicting with a GLM: A binomial/logistic regression model predicts the binomial parameter = p = P(success). To convert the probability into classes, we have to ...
• 185
Suppose $X, Y$ are iid. $\exp(2)$. Let $T$ = $X + Y$. Find $f_x (x | T = t)$. This is a problem from a practice exam. I know that $T\sim\mathrm{Gamma}(2, 2)$ since $T$ is a sum of 2 independent ...