Questions tagged [gamma-distribution]
A non-negative continuous probability distribution indexed by two strictly positive parameters.
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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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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)=(\...
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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 ...
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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)...
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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&...
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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 ...
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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; \...
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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 ...
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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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How borked is my attempted notation for a multilevel gamma regression with AR(1) autocorrelated residuals?
I have no math background and am in way over my head trying to figure out the correct notation for my model: a multilevel random-slopes gamma regression with log link and AR(1) autocorrelated ...
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For Gamma distribution, use MLE or MoM?
For Gamma distribution, is it better to use MLE(maximum likelihood estimation) than MoM(method of moments) to estimate the shape and scale parameters?
Also, in python SciPy, does gamma.fit use MLE? I'...
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Interpreting results of GLM with gamma regression in R
I am fairly new to R and multiple regression analyses so I could use some help interpreting my results. For my research I am trying to find predictors for the amount of blood loss during surgery. For ...
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What is the derivative of gamma variates with respect to the shape parameter?
Given a gamma distribution with unit scale and shape $\theta$, and given an arbitrary variate $x$, what is the derivative of the variate $x$ with respect to $\theta$?
In other words, I would like to ...
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Use a GLM/GAM model with Gamma family & identity link despite warning?
What I have tried and done so far:
I am running GLMs and GAMs on my positive, continuous response variable.
I have determined that the Gamma distribution would fit my data best by plotting various QQ ...
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Tweedie distribution with zeros being the second most common value
I want to perform a multilevel glm model. I have a continuous non-negative outcome variable (not count data), with many 1 values, second most common value at zero, and then a right tail of positive ...
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How to simulate data for a Gamma glm?
I am wondering about whether there might actually be different ways to simulate data for say a Gamma GLM, which in turn relates to what might be the parametrization that the ...
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Calculating Parameters for extrapolation curve using Gompertz and Gamma using Flexsurv
I'm computing some extrapolation curves for a pharmacoeconomic analysis and I'm struggling to get the parameters of the curve for Gompertz and Gamma.
I'm using flexsurv
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Mixed-effects model when the response has two distinct distributions for two levels of an explanatory factor
I have a continuous response variable called "distance," which was measured in two different years (2019, 2020), and each year exhibited a significantly different distribution. In 2019, the ...
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Feature extraction methods for a distribution as exogenous variable in regression models
I have age distributions for more than $m>100$ different populations, each of varying sizes $(n_1, n_2, \dots, n_m)$. I'd like to create a regression model where these age distributions are used as ...
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Sampling from a gamma distribution and computing its likelihood
I would like to conduct a model comparison analysis of a process that is modelled with a gamma distribution. To illustrate, let's consider the example of sampling the time of incidents in a factory. ...
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Kolmognorov Smirnov test p values is 0
I am trying to use Kolmogorov-Smirnov test to check the goodness of fit of the distributions for the dataset. I have dataset consisting of 100,000 samples and I apply expectation-maximization ...
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How to fix this plot of histogram and pdf in R?
I am studying statistics and am working with R for the first time. I have some data that I am trying to represent it graphically. I have plotted a histogram and am trying to model it with gamma ...
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Understanding gamma mixture model
I am trying to understand the gamma mixture models, especially the significance of the 'loc' parameter in scipy.stats. In the code below, I generate a mixture ...
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Interprete Multinomial Naive Bayes when working with real non-negative values
I am currently working on an algorithm that aims to reduce dimensions and map data within the non-negative orthant. Subsequently, the mapped data is utilized as input for a classifier. The classifiers ...
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Understanding LOO / WAIC for Bayesian models selection
I'm trying to select between two models. 1. has a Truncated Normal likelihood and 2. has a Gamma likelihood. 1. has a much higher WAIC/LOO score but the posterior predictive in 2. (specifically the ...
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How to interpret coefficients of a GLM (Gamma family with identity link)
I'm trying to interpret a coefficient of a glm model with the gamma family and the identity link function. The outcome is continuous, positive and right-skewed. Transformation did not yield a normal ...
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Probability distribution of actual time spent if randomly sampled at a known mean rate
I was experimenting with tagtime, which randomly asks the user what they're doing at a known mean rate $\lambda$. Let's say that every time I am sampled, I give a yes/no answer. If I answer yes $k$ ...
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GAM plots: partial effects, shifted y-axis, or predictions - which representations/interpretations are correct/accurate?
I have two GAMs fitted with a Gamma distribution, with the same model structure with a continuous response variable and one continuous covariate, two categorical covariates, and one random effect:
<...
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Distribution of the exponential of a Gamma distributed random variable
I have a random variable $X$ that follows a Gamma distribution.
$$ X \sim \text{Gamma}[\alpha, \beta] $$
I want to know the distribution of $Y$, i.e.,
$$ Y = a - \exp\left(-b X\right) $$
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Distribution of Weighted Sample Variance
Say we have $N$ independent Gaussian variables $X_i$, each drawn from a mean-zero Gaussian with variance $\sigma_i^2$, where in this case I assume I know the $\sigma_i^2$. Define the weighted average ...
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Transforming grouped income data into continuous distribution
I have data with income information provided in grouped, income ranges.
However, for my research purpose, I want to estimate a continuous distribution, in other words from the shares of each income-...
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Finding appropriate parameters for Gamma when bootstrapping a GLM
I'll illustrate what I want to do with a Poisson GLM first. I have a GLM with only factor co-variates, thus, to bootstrap this GLM what I can do is e.g. take a single random observation without the ...
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Is there an implementation of xgboost for a single target variable but using multiple regression parameters
Is it possible, using custom cost functions or otherwise, to run xgboost regression for a single target variable, but rather than outputting just the conditional mean (conditioned on the feature ...
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How can I fit a distribution to a dataset while forcing it through an exact point in r?
This code was kindly recommended to me in my original question. It returned the same parameter estimates as the software called CRAFT by Aon Benfield. I have also managed to replicate it for the ...
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Fitting a set of points to a distribution by adding up to three degrees of freedom with Python [closed]
I have a set of points whose shape is as below:
Its set of x and y points is as follows: x=[0.14741,0.180288,0.195,0.245342,0.25614,0.289377,0.315789,0.357143,0.431034,1.785714,2,2.323529,2.586207,3,...
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Modeling continuous positive data with variance structure similar to Tweedie with 1.2 variance power, but without excess zeros
I'm working on a project where I need to model continuous positive data. I found that a Tweedie distribution with a variance power around 1.2 and a dispersion parameter just above 1 fits my data quite ...
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Statistics Interview Question
Imagine you are solving difficult Math problems and you expect to solve one every 1/2 hour. Compute the probability that you will have to wait between 2 to 4 hours before you solve four of them.
I ...
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GLM: Differing results for Interaction Effects depending on the link-function
I want to test whether whether a dispositional risk factors moderates the relation between a situational risk factor and a negative outcome in a regression model (including several control variables).
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Fisher information and Expected Information for Gamma Distribution
I would like some help with calculating the Fisher Information $I_o(\beta)$ and the expected information for a gamma distribution defined by
\begin{align*}
f_X(x) = \frac{\beta^\alpha x^{\alpha - ...
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Appropriateness of Tweedie GLM for modeling average daily driving distance with unknown numerator and denominator
I have a dataset of cars and want to model a variable called average daily driving distance. The variable was calculated before I received the dataset as:
average daily driving distance = total ...
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Help fitting glmm with positive, right skewed, continuous data
I am trying to fit a glmm in R, with a right-skewed response variable that is theoretically continuous, but in my case ranging between 0.4 and 1.8 with more lower values (it's a biological ...
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Is unit deviance (statistics) equivalent to the loss function (machine learning)
In this page from scikit learn, about GLM, the notion of unit deviance is introduced as loss function (from the machine learning perspective).
I want to know if there is equivalence between these two ...
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Gamma Distribution MLE After New Condition
I found the MLE of $\theta$ where $(x_1,...,x_n)$ is a sample from a $Gamma(\alpha, \theta)$ distribution where $\alpha>0$ is known to be $\frac{\alpha}{\bar{x}}$. However, suppose it is now known ...
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Why the means fluctuate so wildly when using models with gamma inverse and identity? It's like taking a trippy journey
My dependent variable is reading time. My two predictors are categorical.
I conducted a lmer model with the default family and the performance package indicated that the response distribution fits ...
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Why do we want to constrain E[ln(x)] in some maximum entropy models?
If we look at the table of distributions in the exponential family, we will see some sufficient statistics have $\log(x)$, which means we have put constraints on $\mathbb{E}[\log(X)]$ when formulating ...
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bayesian problem using inverse gamma: negative initial values
My study involves a dependent variable measuring reading times (minimum value = 0.3) and two categorical variables (y = "quick" or "slow"; t = "cute" or "ugly") ...
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GLM Power Calculation
I need to do a power calculation for a cost analysis. I believe my model will be a GLM with a gamma distribution and a log link. I would prefer not to use simulations to do the calculation, but I can'...
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Standardizing coefficients in gamma distributed model - piecewiseSEM
I am running a sem using piecewiseSEM package. One of my three models is gamma distributed. I wanted to calculate scale standardized coefficients as it would be ...
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Distribution of the ratio of Dirichlet/Gamma variates
It can be seen that the following random variates have the same distribution:
$\frac{X_1 + X_3}{X_2 + X_3}$, where $(X_1, X_2, X_3) \sim \text{Dirichlet} (\alpha_1, \alpha_2, \alpha_3)$
$\frac{Y_1 + ...
