Questions tagged [gamma-distribution]

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

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Detect the correct distribution from a small sample size by using fitdistrplus in R

The simplest version of the issue that I am looking for help is: How to detect the correct distribution from a small sample size in R by using fitdistrplus A simpler version: I am generating some ...
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57 views

Expectation of ratio between product of gaussian r.v.'s and generalized gamma r.v

Given \begin{equation}\label{eq:definition_of_z} \begin{split} \textbf{Z} = \left[\begin{array}{cccc} {z}_{11} & {z}_{12} & \cdots & {z}_{1P} \\ {z}_{21} & {z}_{22} & \cdots & {...
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How to check the correctness of calculations with a gamma distribution?

I’m reading Ponomareva, Roman, and Date (2015) and trying to generate vector $P$ of the $2Ns + 3$ probability weights: $$P =\{\underbrace{p_1, p_2, \ldots, p_s, p_1, p_2, \ldots, p_s,p_1, p_2, \ldots, ...
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433 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 ...
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96 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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101 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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165 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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78 views

Transformation of sum of Gammas into Chi-squared with a Casella Bergian twist

My question is very similar to the ones asked before (I have looked at all of them on Cross-Validated) but it is more about house-keeping and making sure it matches precisely transformation theorems ...
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128 views

optim() convergence in fitting gamma distribution to separate peaks of time series data

Trying to fit gamma distribution to each separate peak of time series data (chromatography). As a peak i take local minimum-maximum-minimum part of the data each time. Since the peaks values do not ...
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1answer
249 views

Multivariate generalization of Poisson-Gamma model?

I actually assumed it would be easy to find a multivariate version of the Poisson distribution, but couldn't find any concrete solution (in terms of a well cited publication). It seems that ...
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156 views

Appropriate random effects GLMM analysis for mean count data? R

I'm trying to find the right way of using a mixed effects approach on some mean count data (animal visits per day to a feeder) in R. I have two interacting fixed effects (both factors) and 2 random ...
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143 views

Beta of transformed gamma variable

I'm trying to transform a gamma distributed variable with $\alpha=n$ and $\beta=15$ using the following formula: $$U=\frac{2S}{\beta}$$ S is actually a summation of n exponential variables ($Y_i$), ...
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558 views

Bayesian inference on gamma distribution

The likelihood of an observation $x$ under a gamma distribution is $$L(x | \alpha, \beta) \propto \beta^\alpha x^{\alpha-1} \frac {\exp(-x\beta)} {\Gamma(\alpha)}$$ Suppose I have some observations ...
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Estimating medians and modes of skewed distributions using GLMs

Edited question (less vague hopefully) I am wondering why for generalized linear models with Gamma, Poisson and Negative Binomial distributions that there appears to be no discussion about estimating ...
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1k views

Posterior predictive for Gamma distribution with unknown scale and shape

I have a question that needs clarification. The posterior predictive distribution can be described as the distribution that a new i.i.d. data point $\tilde{x}$ would have, given a set of $N$ existing ...
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889 views

Modeling discrete count data with a gamma distribution

I've encountered a statistical model in which discrete count data are modeled with a gamma distribution (supported on nonnegative reals). The model relies on the property of the gamma that a sum of ...
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224 views

Compound Poisson Distributions: When, Why, and How To Split the Problem

I've just stumbled upon the Compound Poisson Distribution (CPD) and it seems to be precisely what I need. For the purposes of this post, let's suppose I have a store that sells many items of ...
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316 views

Use of normality test to distinguish gamma from log-normal distribution

I have random population sample data that I would like to describe using a distribution. If I plot the estimated kernel density, the data appear positively skewed and using functions in R such as ...
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Standard error of mean of gamma distribution

I am trying to determine whether the means of two Gamma distributions are significantly different. To do this, I am trying to determine the Wald Statistic as ...
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1k views

Rejection sampling from a Gamma distribution using a Cauchy proposal

i'm trying to find the parameters $ \gamma,x_0$ of a standard Cauchy distribution : $$T(x)= \frac{1}{(\pi \gamma (1+(\frac{x-x_0}{\gamma})^2))} $$ To perform rejection sampling from a gamma ...
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132 views

Fitting distributions

I have some data on serving sizes of a particular food (raw oysters), and I am trying to determine what probability distribution I should select to model these data for a risk assessment (RA). The R ...
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Interpretation of gamma response distribution with inverse link function

Using glm, I have fitted a model with a gamma response distribution and tested all the model diagnostics so everything looks to be a good fit. The only problem is that the model's deviances point to ...
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Likelihood ratio test for a random variable following the Gamma Distribution

Assuming we have a random variable $X\sim \operatorname{Gamma}\left(\alpha,\beta \right )$:$\frac{1}{\Gamma (\alpha )\beta ^{\alpha}}x^{\alpha-1}e^{\frac{-x}{\beta }}$ I'd like to test the hypothesis:...
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355 views

Selecting priors for logistic functions

I have this confusion related to how to select priors for a logistic regression By Bayes theorem $P(\theta|D) = \frac{P(D|\theta)P(\theta)}{P(D)}$. Now my likelihood $P(D|\theta)$ is given by ...
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Is there a distribution appropriate for a continuous variable skewed toward zero and able to include zero?

I am interested in modelling the impact of some environmental parameters on a concentration of measured phytoplankton pigment. The concentration of pigment is skewed so that low concentrations are ...
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33 views

How to compute categorical probability given a continuous distribution?

I have a continuous target column that consists of IQ scores for kids of age 10. My main purpose is to forecast the probability that a kid is genius given 3 covariates. If a kid has IQ over 160 she/he ...
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25 views

Survivor function for generalized gamma from flexsurvreg output

I am trying to plot/generate a survival curve in Excel using the output from flexsurvreg in R. The below is a snapshot from R with the corresponding estimates (y axis values) for the time (x axis ...
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Highly fluctuating value of test statistic in Anderson Darling test

I am trying to verify whether my sampled data is from a population with a Gamma density function. My plan is to do this by means of the Anderson-Darling test. Before doing so, I thought it would be ...
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20 views

What to do if I find residuals (=deviance) patterns after aplying a GAMMA GLM in R?

I have activity data for 6 individuals (ID) obtained using two different formulas (RMS.X16 and ...
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1answer
101 views

How is the gamma distribution used in the model developed by the Imperial College COVID-19 Response Team?

The Imperial College COVID-19 Response Team report mentions, "Individual infectiousness is assumed to be variable, described by a gamma distribution with mean 1 and shape parameter 0.25." With that ...
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What is the distribution(root mean square gamma distribution)

What is the distribution when you sample from the gamma distribution and take the root mean square? Please tell me how to prove
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129 views

Bayesian Gamma Regression Update

I'm looking for a resource that explains how to do update the coefficients for a Bayesian gamma regression using Gibbs sampling. Specifically, if $y_i \sim Gamma(\alpha,\beta_i)$ and my data ...
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97 views

How do I calculate Confidence Interval for Gamma Distributed Pivotal Quantity?

I'm studying confidence intervals and then I came across the following problem: It's said that a random variable X has Skewed Exponencial Distribution with parameters $\alpha >0$ and $v \in \...
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175 views

Fitting mixture of Gamma variate functions at once (with python)

I am trying to automate the fitting of a signal composed of several Gamma variate functions with some added noise. However, I face some troubles and I do not know how to deal with it. First I do not ...
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Connecting interpretations of chi-squared distribution as both gamma distribution and normal distribution

According to this post I read http://www.clayford.net/statistics/deriving-the-gamma-distribution/ the gamma distribution $\text{Gamma}(\alpha,\lambda)$ is the theoretical distribution of wait ...
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35 views

Gamma GLMM Dispersion, Random Effects, and CoV (lme4)

So I know that in glm(), with the Gamma family, one can get the dispersion parameter through the MASS package with gamma.dispersion() or can even look at the summary output as a quick estimate. How ...
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52 views

Finding the distribution of a piecewise function of a Gamma random variable

Let random variable $X \sim \text{Gamma}(\alpha,\beta)$. I want to derive the distribution of $Y$, where: $$ Y = \left\{ \begin{array}{ll} a X - k & \quad X \geq \frac{k}{a} \...
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101 views

What is the difference between Gamma GLM on log output and Gamma GLM with log link function?

Here are two models (with R code to provide some context): Model 1: Take the log of the output variable $y$, then apply a Gamma GLM using the default identity link function: ...
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23 views

Poisson and Gamma distribution for testing randomness

In genetics I want to test whether InDel (insertion and deletion in DNA) sizes occurs with the same probability. I heard that I should gamma distribution to model it. I found ...
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69 views

interpreting Gamma regression coefficients - individuals not totalling sum of parts

I have fit a gamma regression to a dataset, and like with traditional linear regression, I would like to calculate the contribution of each independent variable across the entire model. The problem I ...
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603 views

MLE for Beta distribution, with $\beta$ = 3

I'm trying to calculate the Maximum-Likelihood Estimator for $\alpha$, using the beta distribution with $\beta = 3$. I'm kind of stuck at the last bit. Perhaps I've made a mistake somewhere, or this ...
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2k views

Gamma distribution as a member of exponential family

In my lecture notes I have that the distribution of a random variable $Y$ is said to be in the exponential family if it can be written as $f(y;\theta)=exp(a(y)b(\theta)+c(\theta)+d(y))$, where $a,b,c$ ...
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1answer
653 views

Understanding this expression of the multivariate t-distribution

I found this SO post which expresses the PDF of a multivariate t-distribution in terms of the gamma and normal distribution in python as follows $$ G = \Gamma (k = \nu /2 ; \theta = 2 / \nu)\\ Z = N (...
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Generate an autocorrelated Gamma sample of length N

How does one simulate an autocorrelated Gamma sample of length $N$? All I found online was about generation correlated variables and not an autocorrelated sample.
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134 views

In a gamma regression, how can i interpret coefficients?

My question is pretty simple, i have done a bayesian gamma regression with an inverse link, so: $\eta_i$=$\beta_0+\beta_1x_{i1}+\dots+\beta_px_{ip}$ < using an inverse link, mu is the ...
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20 views

glmer: distribution law for number of events / time

Sorry if this is a basic question but I can't find an answer that is clear enough, so I prefer to ask. I want to model a number of events (number of gaze) that depends on the behaviour that one ...
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432 views

How shape parameters are connected with mean, variance, skewness and kurtosis of generalized gamma distribution

I am writing a code in python that can generate probability distribution with given mean (m), variance (v), skewness (s) and kurtosis (k). In scipy library of python, there is a function named ...
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37 views

Variance of 1 over sum

I was given to prove that if we're given statistics of Gamma distributed random variables $X_1,X_2...X_n$ (pdf $f_{\chi}(x,\alpha,\lambda)=\frac{{\lambda}^{\alpha}x^{\alpha-1}}{\Gamma(\alpha)}e^{-{\...
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245 views

expectation of Log Noncentral Chi

Let $X$ follow non central chi distribution, the formula of $\mathbb{E}[\log(X)]$ (or equivalently $\mathbb{E}[\log(X^2)]$ where $X^2$ is Non central chi square) can be found here and here. However, ...
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47 views

Quotient of Pareto and Gamma random variables

I cannot find an explicit formula for the quotient of a Pareto random variable divided by a Gamma random variable. The only that I found is something like, for $P(X)$ pareto's like and $P(Y)$ Gamma's ...