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Questions tagged [gamma-distribution]

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

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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 ...
Gabriele Bettineschi's user avatar
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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 ...
GiulioSurya's user avatar
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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 ...
Corbin's user avatar
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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 ...
wanyancan's user avatar
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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 ...
Alice's user avatar
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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 ...
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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. ...
Maeldun's user avatar
2 votes
1 answer
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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 $\...
cfp's user avatar
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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 ...
Mark's user avatar
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3 votes
1 answer
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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 ...
Connor's user avatar
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4 votes
2 answers
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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{...
learning statistics 's user avatar
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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 ...
Galen's user avatar
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1 vote
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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 ...
profPlum's user avatar
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3 votes
2 answers
104 views

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 ...
João Bugelli's user avatar
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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})\...
Sagnik Taraphdar's user avatar
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1 answer
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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 ...
Sagnik Taraphdar's user avatar
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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 ...
Tamsin Harper's user avatar
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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 ...
Tamsin Harper's user avatar
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Fisher information for gamma-Poisson distribution

I have $Y$ that is a gamma-Poisson distribution with mean $\mu$ and $\kappa$ is the overdispersion. I'm trying to obtain fisher information but i don't know how to solve expected value of trigamma ...
ali's user avatar
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Difference in Gamma Distributions have Poisson? [duplicate]

Today I learned about a Double Stochastic Process for the first time. Apparently a Cox Process is a Double Stochastic Process. Here is my attempt to summarise this: Cox Process: A point process (I ...
Uk rain troll's user avatar
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How to account for spatial autocorrelation when the outcome (distance cycled) is continuous?

I aim to predict distance cycled based on population density, recreational area density, infrastructure density, road intersection density, and average gradient (hilliness). The response variable, ...
Eugeni's user avatar
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1 vote
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Given conjugate prior and posterior distributions, what is the PRIOR predictive distribution? [closed]

I am doing an assignment on my statistics class. We had 1 lecture about bayesian parameter estimation, where we were taught about the following formula (and it's discrete form, if $h(\theta)$ was ...
ampersander's user avatar
2 votes
1 answer
134 views

Completeness of Gamma family

Let $X_1,...,X_n$ has a Gamma$(\alpha,\alpha)$ distribution. Find the minimal sufficient statistics. Is this a complete family? My attempt: I found the Minimal sufficient statistics is $T(x)=(\...
Cyno Benette's user avatar
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Understanding of Gamma distribution as precision prior in Bayesian inference for Gaussian

Christopher M. Bishop in his book "Pattern Recognition and Machine Learning" nicely explains where does Student t-distribution $St(x|\mu,\lambda,\upsilon)$ originate into. In Chapter 2, it ...
baronett's user avatar
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Maximum Entropy distribution of a ticking clock

Say I have a clock that emits "ticks". An ideal clock looks like a dirac comb. It has: perfect periodicity of ticks (there is a precise fixed time interval between any two consecutive ticks)...
kram1032's user avatar
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Interpreting and transforming GLM output parameters with a Gamma log link

I built a GLM model in R with a Gamma log link and where my response variable is "1 - effectiveness". I would like to report the results of my model directly in terms of "effectiveness&...
Javier Fajardo's user avatar
4 votes
1 answer
492 views

How to interpret the coefficients of Tweedie GLM with log link?

I'm trying to model cost data which have 0s. It seems that gamma is not an appropriate distribution and zero inflated gamma seems to be a bit of an overkill, but Tweedie seems to be appropriate with ...
user395714's user avatar
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103 views

posterior predictive of a normal distribution with normal prior over mean and Gamma prior over precision

What is the posterior predictive of a normal distribution with normal prior over mean and Gamma prior over precision. Thus, what is the distribution of x given: \begin{equation} x \sim \mathcal{N}(x; \...
Snowy Baboon's user avatar
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Finding an accurate distribution to my data of large sample of the sum of daily rainfall at a specific location

I have a rather large sample of the sum of daily rainfall at a specific location in mm. I am currently attempting to find the best fitting distribution using the ...
Sargnagel's user avatar
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Map from Normally distributed Variable to Gamma distributed Varaible [duplicate]

I need to find some function $f:\mathbb{R} \rightarrow \mathbb{R}^+$ such that If $\; \; x \sim \mathcal{N}(x; \mu, \sigma^2) \; \;$ then $\; \; f(x) \sim \mathcal{G}(y; \alpha, rate=\beta)$ Where $\...
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Expected Value / Variance of Gamma to the Negative Integer

For random variable $Z$ from a $Gamma(p), p > 0$ distribution we know that the expected value of $E[Z^s]$ is simply the gamma function at $p+s$ divided by the gamma function at $p$, for $p+s$ > ...
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