Questions tagged [gamma-distribution]

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

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12
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1answer
5k views

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 ...
7
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1answer
2k views

How is a Chi-square distribution a gamma distribution if it only has one parameter?

I know that the gamma family of distributions are a two-parameter family, but Chi-square only has one parameter. How is a Chi-square distribution a gamma distribution if it only has one parameter?
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0answers
101 views

Finding Cramer Rao Lower bound for a bivariate parameter

I am having a hard time figuring out the Cramer Rao lower bound for a random sample of size $n$ from a population with $\Gamma(p, \theta)$ with $p, \theta$ unknown. The problem doesn't say what ...
3
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1answer
309 views

Efficient estimator for the mean of a Gamma distribution

Let $X_1$,$X_2$,...,$X_n$ be i.i.d. according to Gamma($\alpha$,$\beta$). Denote the mean by $\mu := E[X_i] = \alpha/\beta$. Can you find an unbiased and efficient estimator for $\mu$? MLE gives ...
2
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1answer
66 views

Poisson distribution and minimum parameters

I am trying to work out a research problem I recently faced. I have a group of Poisson random variables and I want to find the distribution of the first sample that is equal to a specific number. In ...
3
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1answer
186 views

How to assess selected response distribution [closed]

I am trying to predict the impact of readmission events (continuous) and type of readmission (medical, surgical, other) on total hospital costs. Because costs are skewed by nature, I am using a Gamma ...
2
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1answer
353 views

mean variance relationship of the generalized Gamma

The Gamma distribution has a mean-variance power relationship of $$var(Y) = a \mu^2$$ where $a$ is a constant and $\mu$ is the mean. Is this also the case for the generalized Gamma distribution? ...
0
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1answer
3k views

Random Variate Generation for the Gamma Distribution [closed]

Why am I getting the following error when I try random generation for the gamma distribution? The code I am trying to run: rgamma <- (n = 500, shape>= 1, scale = 1) This is the error I get : ...
3
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1answer
323 views

Survivor Function vs. Hazard Function

I'm attempting to understand what the survivor and hazard functions describe under a non-traditional context. I have data comprising distances between successive points on a line ($1D$ vector): ...
1
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1answer
441 views

If I have three sets of continuous data which are not normally distributed, can I still compare them with ANOVA?

I have three sets of data from some experiments. I fitted each set to different distributions, and each one fits a different distribution. For example, Gamma, Weibull, and Lognormal. If I want to ...
0
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1answer
2k views

GLM with Gamma-Log link: How do I do Predictions?

I am rather new to regression analysis, having a completely different background. I am trying to build a model for predictions. The distribution of my dependent variable, Value (in US$), is right ...
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2answers
755 views

Limiting Distribution of Average of iid Gamma Variables

It can be shown that if $X \sim Gamma(\alpha, \theta)$, then $\overline{X_{n}} \sim Gamma(\alpha n, \theta/n)$. where $X_{1}, X_{2} \dots X_{n}$ are all iid and follow the distribution of $X$. ...
3
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2answers
4k 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 ...
2
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0answers
26 views

Motivation for Gamma, exponential, & chi-squared distributions [duplicate]

I understand the binomial, geometric, Poisson, and normal distributions. However, I don't understand the usefulness or difference between the following: Gamma, exponential, and chi-squared. So far, it ...
7
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1answer
1k views

Weibull vs. Gamma Distribution

I have data comprising distances between successive points on a line (1D vector): Traditionally in my field, such data is fitted with a gamma-distribution in an attempt to describe the distribution ...
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0answers
104 views

Transformation of two gamma variables

If you have $\frac{X}{X+Y}$ where X and Y are both independent Gamma distributions where $\alpha$ for both X and Y is different, but $\beta$ is the same for both, then how would that be different from ...
2
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1answer
682 views

Existence and uniqueness of MLE

I am aiming to show that the MLE of $(\alpha, \lambda)$ for $X_1, \dots, X_n \sim \Gamma(\alpha,\lambda)$ exists and is unique, under the assumption that the $X_i$ are all positive and unequal. I am ...
2
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0answers
306 views

Log link vs logging response variable in GAM model

hope someone might be able to help: My aim is to build a value predictor of an individual’s pension pot using customer data (based in the UK). It is to be used for reporting purposes and ...
2
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1answer
154 views

IS $\int_{-\infty}^\infty e^{-\beta\cdot g(x)}g(x)^{\alpha-1}\text{d}x={\Gamma(\alpha)\over \beta^\alpha}\ \ ?$ [closed]

Is the following statement true: Let $g(x)$ be some non negative continuous function of $x$.We know that$$\int_{0}^\infty e^{-\beta x}x^{\alpha-1}dx={\Gamma(\alpha)\over \beta^\alpha}$$ Does ...
3
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1answer
58 views

Inference using Gibbs sampling

Suppose there is a one-dimensional normal distribution $\mathcal{N}(\mu, \sigma)$ for which we want to infer the joint distribution of the parameters using Gibbs sampling. Let $D$ be the data, ...
6
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1answer
680 views

Generalized Gamma GLM

the generalized gamma distribution is a generalization of the two-parameter gamma distribution: https://en.wikipedia.org/wiki/Generalized_gamma_distribution However I cannot find an implementation in ...
2
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0answers
93 views

How to compare shape of gamma distributions to detect population change

Sorry if this question is poorly composed due to lack of stats knowledge. Any advice to point me in the right direction would be greatly appreciated: I'm hoping to detect if a dataset originated from ...
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2answers
2k views

marginal effects of a GLM

A marginal effect is the effect one independent variable on the dependent variable has when it is changed by one unit and the other independent variables constant. In the simple OLS regression ...
5
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1answer
263 views

Sum of truncated Gammas

I have a set of i.i.d. variables $X_i$ that are distributed according to a truncated $\text{Gamma}(\alpha,\beta)$ distribution, with support on $[0,w)$ where $w$ is a known constant. What's the ...
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0answers
156 views

Interpetation of estimates in Gamma-Regression with reciprocal link

I´m new to CrossValidated and this is my first question here. In the case of a generalized linear regression model where I assume that my data follow a gamma distribution, I would like to know how to ...
1
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1answer
288 views

Parameterization of Gamma Distribution

I have come upon different parameterizations of the Gamma Distribution, but not with regard to shape-scale or shape-rate. It is rather about the sign in the exponent. Wolfram lists the pdf as being ...
3
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0answers
145 views

Sum of truncated Gammas and degenerate

I have a variable $X$ which I am modelling with a mixture model: $$\begin{aligned} (X|A) &\sim \mathbb{1}_{0 \leq x < w \cdot m} \cdot \frac{\text{Gamma}(\alpha,0,\beta / m)}{k_1} \\ (X|B) &...
3
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0answers
108 views

Is the Gaussian distribution the only statistical distribution fully determined by the mean and variance?

I've read that the Gaussian marginal is fully determined by the mean and variance. What does this mean in reality? If we consider a Gaussian marginal PDF is given by $$ \pi_G(\xi|\mu,\sigma) = {1\...
2
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0answers
87 views

Generate Gamma distributed values with upper bound

I need to generate N random numbers from a Gamma distribution, but with an upper bound Pmax using Matlab. Right now, I see two ...
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0answers
61 views

RW Metropolis and ARMS fail

I've been trying to estimate a series of simulated Gamma-distributed random variables and its structural parameters with MCMC for a stochastic volatility model. However, both the random walk ...
1
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1answer
516 views

Scale and shape parameters of Gamma mixture distributions

I used the function mix (package mixdist) to fit Gamma mixture distributions. The function gives mu and sigma parameters (output ...
6
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1answer
200 views

Using empirical Bayesian estimation (Gamma-Poisson) to analyze high arrival counts (n ~= 5000)

Here's a problem I'm currently working on, as well as the empirical Bayesian approach I'm using. I'd like to make sure my approach is grounded in solid statistical theory. I have a set of entities $e=...
2
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2answers
1k views

Alternatives to fitdistr for gamma in R?

Consider the following code in R: ...
1
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1answer
4k views

sampling from a mixture of two Gamma distributions

Assuming that all the mixture parameters are known, how can one sample from a mixture of $\texttt{Gamma}(\alpha,\beta)$ distributions: $$\theta \sim \pi \texttt{Gamma}(\alpha_1,\beta_1)+(1-\pi)\texttt{...
1
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1answer
476 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 ...
2
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1answer
102 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 ...
2
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1answer
74 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?...
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0answers
33 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 ...
4
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1answer
734 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 ...
3
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0answers
416 views

Are kurtosis and skewness meaningful for comparing distributions such as gamma distributions with very pronounced shape parameters?

Are kurtosis and skewness meaningful for comparing distributions such as gamma distributions with very pronounced shape parameters? For instance, take the red distribution in the first plot here: ...
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0answers
28 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 ...
4
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2answers
2k 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 ...
3
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0answers
197 views

Distribution of the ratio of two shifted generalized gamma random variable

$X \sim \mathrm{GG}\left(p,d,\theta_{1},\mu\right)$ where $p$ is power, $d$ is shape, $\theta_1$ is scale and $\mu$ is location parameter. Also Consider $Y \sim \mathrm{GG}\left(p,d,\theta_{2},\mu\...
0
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1answer
503 views

Expectation of a hazard rate

I need to estimate the expectation of a hazard function, $E[h(x)]$. For instance, for the exponential distribution the result is equal $\lambda$ $$E[h(x)] = \int_0^\infty \! h(x)f(x)\mathrm{d}x = \...
2
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0answers
141 views

Calculating the likehood from the coeficients of logistical regression

I am doing a logistical regression and need to calculate the likehood from the null model and from each feature model and to after that get the p-value.The problem states: a) Create a model that ...
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0answers
87 views

Improve fit of a Gamma distribution

My dependent variable has a distribution as below: I fit a gamma distribution with log link using ...
9
votes
1answer
551 views

Is there another interpretation for a Gamma distribution with non-integer shape parameter?

It is well known that a random variable being Gamma distributed with integer shape parameter $k$ is equivalent to the sum of the squares of $k$ normally distributed random variables. But what can I ...
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0answers
570 views

Estimating Gamma MLE with left truncated data (using R and maxLik)

I'm trying to find the maximum likelihood estimation of the parameters of a Gamma distributed random variable using maxLik. The following code explain what I did: ...
4
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0answers
113 views

Showing independence between two functions of a set of random variables

I've been working on the following problem and I'm confused about how to get started: Let $X_1, X_2,\dots, X_n$ denote i.i.d. real valued random variables, each absolutely continuous with an ...
8
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2answers
6k views

distribution of the ratio of two gamma random variables [duplicate]

Assume that $X \sim Ga(\alpha_1, \beta_1)$ and $Y \sim Ga(\alpha_2, \beta_2)$. Define $Z= X/Y$. What 's the distribution of $Z$?