# Questions tagged [gamma-distribution]

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

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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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### 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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### 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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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 $T(x)=(\... 0 votes 0 answers 105 views ### Understanding of Gamma distribution as precision prior in Bayesian inference for Gaussian Christopher M. Bishop in his book "Pattern Recognition and Machine Learning" nicely explains where does Student t-distribution$St(x|\mu,\lambda,\upsilon)$originate into. In Chapter 2, it ... • 11 0 votes 0 answers 27 views ### Maximum Entropy distribution of a ticking clock Say I have a clock that emits "ticks". An ideal clock looks like a dirac comb. It has: perfect periodicity of ticks (there is a precise fixed time interval between any two consecutive ticks)... • 255 0 votes 0 answers 59 views ### Interpreting and transforming GLM output parameters with a Gamma log link I built a GLM model in R with a Gamma log link and where my response variable is "1 - effectiveness". I would like to report the results of my model directly in terms of "effectiveness&... 4 votes 1 answer 492 views ### How to interpret the coefficients of Tweedie GLM with log link? I'm trying to model cost data which have 0s. It seems that gamma is not an appropriate distribution and zero inflated gamma seems to be a bit of an overkill, but Tweedie seems to be appropriate with ... 0 votes 0 answers 103 views ### posterior predictive of a normal distribution with normal prior over mean and Gamma prior over precision What is the posterior predictive of a normal distribution with normal prior over mean and Gamma prior over precision. Thus, what is the distribution of x given: x \sim \mathcal{N}(x; \... • 331 0 votes 0 answers 53 views ### Finding an accurate distribution to my data of large sample of the sum of daily rainfall at a specific location I have a rather large sample of the sum of daily rainfall at a specific location in mm. I am currently attempting to find the best fitting distribution using the ... 0 votes 0 answers 41 views ### Map from Normally distributed Variable to Gamma distributed Varaible [duplicate] I need to find some function$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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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 $p+s$ > ...