Questions tagged [gamma-distribution]
A non-negative continuous probability distribution indexed by two strictly positive parameters.
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Modelling a skewed response variable
I have a biomarker ratio (amyloid 42/40) and I am having issues modelling it. This is the proportion of a biomarker to another biomarker and it is important in diagnosing dementia. I am using as both ...
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Distribution of $Y=-\log(X)$ when $X\sim \operatorname{Beta}(\alpha,\beta)$
I have been looking at the distribution of $Y=-\log(X)$ when $X\sim \operatorname{Beta}(\alpha,\beta)$, so $Y$ is supported on $\mathbb R_{\ge 0}$. Might this be called a negative exp-Beta ...
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Special case of parameters in the Gamma distribution function?
I am currently working with images using Voronoi tessellations and evaluating the distribution of the corresponding cell areas. These areas are said to be gamma-distributed, derived from the 1D case.
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R what is the best glmmTMB model family to fit positively skewed index data
I am attempting to create a linear mixed effects model (lmer) with an positively skewed index dataset (1-4) that results in the best fit (distribution pictured below code).
Database
...
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Problem finding a distribution for my data (glmm)
I want to do a correlation analysis of two variables ranging from zero to one (including those values), and including other possible environmental explanatory variables.
I opted for a mixed model, ...
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GLMM with log-Gaussian, log-Gamma
I need someone smarter than I am to look at this problem, and I'd appreciate it if you'd take the time. So, I am trying to predict reaction times here in a glmm using a battery of IVs. You can see the ...
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Whether and how to fit a GAM with a Gamma distribution in R
I would like to fit GAMs using elevation as a predictor and chemical concentration as a response in R via the gam() function in ...
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how to compute posterior distribution from a hurdle-gamma model?
I am modelling data from spore traps. The response is a DNA quantity, so >0. The is a lot of 0 (3/4 of data). Zero arise mainly from absence of a potential spore source while quantity depends on ...
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Gamma distribution glm standardisation
I want to model biomarkers which seem to have two distributions. I want to model the change in biomarker at two visits three years apart. However, I am trying to do this with a glm and a gamma ...
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What type of distribution is this? Log-normal, Weibull, Gamma, or something else? [closed]
I am trying to test this against various similar looking distributions to find the one which fits best or is least likely to match by random chance. These look log normal, but my attempts to convert ...
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Problem with confidence level in GLMM with zero-inflation and zigamma family
I am evaluating which treatment promotes greater root length in a root growth analysis. I have five different treatments, each with four samples, evaluated over nine days across three independent ...
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Maximum of two independent gamma variables
Let $X_1$, $X_2$ be two independent random variables with different gamma distributions, and $X = \max\{X_1, X_2\}$.
Are there known results for the distribution of $X$? Actually I only need to know $\...
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Understanding predictions from early rounds of XGboost
I have a dataset that I am modeling with gamma regression via xgboost. The target variable has a mean of around 13,000. If I run xgb.train with nrounds = 20, my fit metric improves as follows:
...
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Concentration inequality for sums of independent gamma random variables
I am dealing with the following problem:
Say $X_1, \ldots, X_n$ are independent Gamma random variables, each one having shape and rate parameters $\alpha_i$ and $\beta_i$, respectively. Let $S_n = \...
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Student T as an infinite gaussian mixture
I'm reasking this question to understand the answer. The question asks to show a gamma-weighted Gaussian distribution is equivalent to a Student t-distribution.
The accepted answer loses me when it ...
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Intuition behind relation between Gamma and Standard Normal distribution
I read if $Z$ is a random variable with a standard Normal distribution and $X=Z^2$ then $X \sim \operatorname{Gamma}(1/2, 1/2)$.
I understand the math (manipulations of formulas) behind it.
What about ...
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Maximum Likelihood of Standard Deviation
I'm trying to get a better understanding about the distribution and uncertainty of the sample standard deviation. Since I'm not a mathematician, I try to compare the math literature with some ...
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Fitting Hypergeometric distribution requires non-integer arguments?
I have a vector (length s) of observations, x are class "0" and s-x are class "1" and are drawn from a population of size N. Hence, they follow the hypergeometric distribution:
$$H(...
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Diagnostic for GLM Gamma model in R
I am applying a glm model with gamma distribution and log link function to a continuous variable defined only on R+. I have tried to fit the model but I am having some difficulty interpreting the ...
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Is there a likelihood penalization or (im)proper prior to remove estimation bias for gamma parameters?
So I am learning that maximum likelihood estimation of the parameters for a gamma distribution are biased. As far as I understand there is no guarantee in general that there exists a prior (or base ...
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Gamma regression with XGBoost
I'll try to be brief. I have two questions about what exactly happens when I train a gradient boosted ensemble of trees using, say, XGBoost in order to perform a Gamma regression. I apologize in ...
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In a GLM model with a gamma log link, how to interpret a negative coefficent of a dummy variable with a continuous response?
I am a little confused with how to interpret a negative coefficient in a GLM model using the Gamma family with a log link.
My response variable is continuous (with no zeros) and right skewed and ...
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How to choose between gamma and Gaussian given a choice of gauges?
I'm trying to make the choice between the gamma and Gaussian distributions as a prior distribution for some data. When I learned statistics a while ago, I was given the rule of thumb: if your data ...
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Why is the canonical link of a GLM with Gamma distribution the reciprocal?
I'm fitting a generalized linear model to a theoretically gamma-distributed dataset, and I'm confused about the canonical link. The gamma distribution has PDF
$$
f(y;a,\lambda) = \frac{\lambda^a e^{-\...
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What is the interleaved probability like when two Gamma distribution processes fired together?
As opposed to the similar question here:
Is there a probabilistic (not analytical) argument for why the sum of independent Poissons is Poisson?
The difference is to consider the interval between two ...
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How to find the appropriate family for a GLM
I have behavioural data on gentoo penguins from when we did research in Antarctica. I am looking at vigilance on exterior and interior nests at two different locations.
To standardise the count of ...
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Evaluating GLM with Gamma distribution vs. transformed response for predicting right-skewed price data
I am trying to predict house prices using a dataset with the following variables:
...
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Model failed to converge (gamma model, self-paced reading data)
I'm trying to run a Gamma analysis in a self-paced reading data. However, the model successively fails to converge. I've seen some answers here trying to solve this problem for other people, but none ...
Wellington Almeida
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Posterior distribution for multivariate Gamma-Normal model
Let $\theta \in \mathbb{R}_{>0}^n$ be a random variable with prior distribution $p(\theta)$:
\begin{equation}
p(\theta) = \prod_{i=1}^n \text{Ga}(\alpha_i, \beta_i)(\theta_i),
\end{equation}
where $...
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Usage of Sufficient statistic for a Gamma distribution
I need some help to understand how to utilize sufficient statistic from a data.
Suppose I observe some random process that produces $x\in X$, where all elements have a gamma distribution. As far as I ...
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Questions around modelling arrival process of randomly sized groups
I have the following situation:
I'm trying to model groups arriving to some location by some process. I assume the distribution on some interval $T$ is a Gamma-Poisson mixture where $\Lambda \sim ...
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Effect size with GLMM gamma distribution
In response to a previous question posed about effect sizes with a generalized linear mixed model with a binomial distribution, it's been clarified that estimating effect sizes is not straightforward. ...
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Interpreting R glm gamma output with interacting categorical predictors
I have a set of different gamma regressions that I ranked with AIC (with help from kind folks on CV) that show the effects of year (2019 and 2021) on "value" (an area), but I am struggling ...
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How to deal with Heteroskedasticity in a GAM model
I am running a set of GAMs (Generalized Additive Models) to model a smoothed effect. I have verified all the other necessary checks of my GAMs for the basis functions, etc. However, I find persistent ...
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Error: PIRLS loop resulted in NaN value in GLMM (glmer) model with Gamma distribution
I have a problem fitting a GLMM model with a Gamma distribution (my outcome variable is strictly positive and right-skewed) and an identity link using glmer in R. ...
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Simulate a distribution from a fitted beta-regression model for a density plot in R [duplicate]
I have produced the following figure by simulating some values from a fitted gamma regression with a low AIC value that provides the closest approximation of my raw data out of all of my models, and ...
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Equivalent to likelihood ratio test for null and fitted generalized linear model (Gamma) in R?
I have a dataset of ellipses and I am trying to perform regressions with different categorical variables to see what influences different ellipse parameters the most. As was suggested in the answer to ...
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Distribution supported on $(0,\infty)$ for which moments of its truncated distribution are elementary functions of the truncation point and power
I am looking for a distribution with a differentiable PDF $f:(0,\infty)\rightarrow (0,\infty)$ for which for any $\delta>1,z>0$, the two following integrals are finite elementary functions of $\...
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How do I use something like predict.glm (in R) with a svyglm model and why don't my predictions match my data?
I'd like to estimate "cost" using some covariates with a weighted gamma model using svyglm. The weights sum to 1, and there are about 10,000 rows in the dataframe df total, with columns ...
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What metric should I use for a Regression model with a gamma distributed target?
Background
I'm building a regression model on insurance data to predict the losses associated with a policy. I'm running an Optuna optimisation function to help me with this, but I'm struggling with ...
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Taking the limit of a Beta Distribution to yield the Gamma Distribution
The Poisson Distribution may be obtained from the Binomial Distribution by keeping $\lambda = np$ fixed and taking the limit as $n \rightarrow \infty$.
Similarly, the Gamma Distribution may be ...
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Correct setup for a Bayesian gamma model
I am interested in understanding how center volume affects a quality metric in a healthcare application. Each program's performance is reported as an observed/expected (O/E) ratio where the expected ...
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Reference for Moments of Gamma Distribution random variable [duplicate]
I want a reference that explain the $n^{th}$ moment of the gamma random variable having shape and scale parameters for the gamma distribution, specifically the following moment equation
\begin{...
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How to calculate quantiles for a gamma distribution?
I would like to compute quantiles for a gamma distribution. I found a purported example here given as
$$\text{quantile}(a, b, p) = \frac{\gamma^{-1}(a, \Gamma(a) p )}{b}$$
where $\gamma^{-1}$ is the ...
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Relationship Between Chi-Square/Gamma & t/lst distributions?
I'm trying to understand $\chi^2_n$ & $\Gamma(\theta, k)$ distributions. Currently I believe they're comparable to t (aka $t_v$) & location-scale-t (aka $lst(\mu, \sigma^2, v)$) distributions ...
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Which distribution is this? [closed]
Context
I'm working on a project where I need to understand the impact of some variables on satisfaction (y). My y variable is an NPS measure, ranging from 0 to 10 and does not have float values, only ...
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In a GLM, how do the dimensions of the linear predictor and the range of the link function always align?
Let $\mathbf{\vec y}$ be the response vector.
Then, we can write the exponential family as :
$$
\large p(y;\boldsymbol{\eta})=h(y) \exp \left(\boldsymbol{\eta} \cdot \mathbf{T}(y)-A(\boldsymbol{\eta})\...
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Why is this derivation of the mean of the gamma distribution using the log-partition function incorrect?
I am using this formulation of the exponential family :
$$
\large f_{X}(x;\boldsymbol{\eta})=h(x) \exp \left(\boldsymbol{\eta} \cdot \mathbf{T}(x)-A(\boldsymbol{\eta})\right)
$$
The gamma distribution ...
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Resolving heteroscedasticity in Gamma GLMM glmmTMB
I am investigating the effect of predictor variables population.size (continuous), farm.type (categorical) and control measure y.n (binary) on my response variable outbreak duration (continuous). I ...
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What Glmm method is best to analize Mortality Rate as a response variable
I am investigating the effect of two explanatory variables (one continuous and one binary) on my continuous response variable (Mortality rate). This variable is a proportion and resembles a gamma ...