# Tagged Questions

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

0answers
29 views

### Gamma distribution and applications

I'm looking for references to read about gamma distribution and applications in industry or in quality control. I had a look at statistical methods for reliability data (Meeker and Escobar). It has ...
1answer
35 views

### gamma and beta function relation

I am reading this, and don't understand how this is reached $$\frac{\Gamma(\alpha)}{\Gamma(\alpha+n)}=\frac{(\alpha+n)\beta(\alpha+1,n)}{\alpha\Gamma(n)}$$ The following relation mentioned on the ...
1answer
17 views

### What does it mean in real-world terms that the Chi-Squared distribution is a special case of the Gamma distribution?

Among other applications, a gamma distribution answers the question: "If the average time (or other quantity) between events is β, what is the probability that x time will elapse before α events occur?...
0answers
26 views

### Independent random variables

Let $L(\xi) = \Gamma(1,1)$. $Y_r=(n-r+1)(X_{(r)}-X_{r-1}), \ r=1,...n$ $(X_{(0)}=0)$ where $X_{(r)}$ - order statistic. Prove random variables $Y_r$ independent and have same ...
0answers
15 views

### Uninformative prior for a gamma distribution

I am seeking a vague prior for a Gamma distribution $G(\alpha, \beta)$, where both $\alpha$ and $\beta$ are unknown. My teacher suggest a prior $p(\alpha,\beta) = \exp\{-\beta\}$. However, it seems to ...
0answers
9 views

### How to find the mean and CI of a parameter knowing that its inverse follows a Gamma distribution?

I am new at MCMC and stats and I am trying to estimate several parameters using MCMC as follows: Suppose I have prior information such that I know that $(1/\delta) = 4$ on average so that I can set a ...
1answer
33 views

### Ratio of Gamma distributed variables with different parameters

I encounter a problem which I thought I can handle, however, I struggle a lot with finding a solution: The following setting applies: I want to compute the posterior probability of an event, which is ...
0answers
41 views

### Find MGF of $f(x|\theta)=\frac{\alpha x^{\alpha-1}}{3^\alpha}, 0<x<3$

Density: $f(x|\theta)=\frac{\alpha x^{\alpha-1}}{3^\alpha}, 0<x<3$ MGF: $E(e^{xt})=\int_0^3[{\frac{\alpha x^{\alpha-1}}{3^\alpha}}e^{xt}]dx$ I'd like to use a gamma distribution integral ...
0answers
29 views

### Rsquared / R2 (i.e. R²) for Gamma-GLMM?

I have successfully calculated R²c as a goodness-of-fit measure for GLMM's using the r.squaredGLMM function implemented in R's <...
0answers
22 views

### Is this uncertainty representation correct?

I have a set of execution times for some processes. But there is uncertainty in these values. I call this $$ET + \lambda ET$$, where $\lambda ET$ is the delay. I sample $\lambda$ from a gamma ...
2answers
92 views

### How to determine the distribution of dataset?

I have a dataset whose histogram showed above (the blue part), and I want to scale it for later machine learning process so I am trying to do a parameter estimation. Its histogram shows that looks ...
0answers
63 views

1answer
116 views

### Statistics guessing game

This is a game that I wanted to know the answer for. The Game There are many players in the game, who each get a guess. There is a loss distribution, $L$, where: $L$ ~ Gamma($\alpha$, $\beta$) i....
0answers
94 views

### Calculating Safety Stock with Gamma Distributed Demand

I've written some code to simulate an inventory system with gamma distributed demand to find the target stock and reorder point that will give me a 95% service level, but I think based on the ...
1answer
66 views

1answer
571 views

### How to draw fitted graph and actual graph of gamma distribution in one plot?

Load the package needed. library(ggplot2) library(MASS) Generate 10,000 numbers fitted to gamma distribution. ...