# Questions tagged [gamma-distribution]

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

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### Can a mixed model random slope include a between-subjects factor in a repeated measures design?

I'm after some statistics help with generalised linear mixed models. I have built a model using glmer from the lmerTest package in R to fit my data with a gamma distribution. The formula is as follows:...
1 vote
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### confidence interval formula of gamma distribution? [closed]

i want a help can someone tell me the formula for confidence interval of gamma distribution? for alpha and beta Parameters i couldent find them? and there also this problem i dont know which pdf of ...
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### Investigating the existence of plasticity (random intercept model vs. random slope model) in a response variable that is not normally distributed

I wanted to explore if the change in speed between day and night is similar among a set of individuals. To me, the logic way of testing this hypothesis is running a random intercept model and a random ...
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### Distribution for Fraction of Success in a Binomial Setting

So the actual original question I am trying to solve is a little bit different than the title: In a binomial setting with probability of success $p$, I keep examining observations until a fraction of ...
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1 vote
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### Finding p-value given observation [closed]

Test the following hypothesis $$H_0: \lambda=\lambda_0$$ $$H_1: \lambda \neq \lambda_0$$ null distribution to be ~$gamma(20,20\lambda_0)$ given $\lambda_0=1$ and an observed sample =0.8, find the p-...
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### Calculating the probability of the total duration of N sequential events with different cdfs describing their duration

Be patient, I am not very skilled with cdf. I seem to have a seemingly simple problem for which I either can't seem to find material about or simply lack the vocabulary for. Given are N sequential ...
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### PDF of the exp-gamma distribution

exp-gamma distribution is defined as the density of the random variable log(X) when X is a gamma random variable. I am trying to obtain its PDF. Unfortunaltely, the only formula I have found is from a ...
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### How to specify a parameters for Gamma distribution?

I have a task: A frequency claim distribution, $K$ is a compound Poisson-Gamma distribution. The mean of the Poisson distribution is gamma distributed with mean equal to 1 and variation equal 2. Find ...
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### Generating function for Gamma distribution expectation

I encountered this formula in my assignment: $$X\sim \Gamma(\alpha, \beta), 1\le k < \alpha$$ $$E(X^{-k})=\frac{\beta^k}{\prod^k_{i=1}(\alpha-i)}$$ And I wonder what would happen if $k$ is ...
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### Choosing priors for the parameters of Gamma distribution

Suppose that $X_1, X_2, \cdots, X_n$ is a sample drawn from a Gamma distribution with parameter $\alpha$ and $\beta$. Then, the likelihood function can be written as follows: L(\...
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### Random numbers with exponentiated gamma distribution? [closed]

How to get random numbers following "exponentiated gamma distribution"? I tried to search some functions in R and this is what i got: https://rdrr.io/cran/Newdistns/man/expg.html I want to ...
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### Intersection of multiple gamma distributions

Let's say I own a few hundred McDonalds locations. In a subset of those (say 100) I observe vegans eating there and I estimate the arrival time of vegans at these 100 restaurants using a Poisson ...
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### Law of Total Variance

I trying to experiment with law of total variance in order to empirically recreate theoretical results. In particular I am interested in verifying that: $$Var(Y) = E[Var(Y|X)] + Var(E[Y|X])$$ Let's ...
1 vote
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### Help with interpretation of a zero-inflated gamma model

Background: I'm in fairly over my head here, working on a project for class where we had to choose our own publicly available dataset to analyse and I chose one with a zero-inflated continuous ...
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### Can beta regression be used with continuous numerical data?

I am trying to fit a generalized linear model with Gamma distribution in R, but when I examine the residuals they are not normally distributed. I have a continuous numerical response variable, ...
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### Help understanding gamma posterior of exponential likelihood

The posterior of $\text{Exp}(x;\lambda)$ with prior $\text{Gamma}(\lambda;\alpha, \beta)$ is $\text{Gamma}(\lambda|\alpha+n, \beta + n\bar x)$ where $n$ is the number of observations and $\bar x$ is ...
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### Using GLM: Gaussian, Poisson vs Gamma

I am trying to perform a GLM analaysis using R for an outcome that is: Bounded by 0 - 10 In steps of 1 (Numerical Rating Scale for Pain: 0 - 10) I have a set of demographic factors, age, sex etc, ...
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### Properties of $\chi^2(1)$ multiplied by a real value "$a$"

Is it true that the $\chi^2$ distribution with $k=1$ (noted $\chi^2(1)$) multiplied by a real value $a$ is equal to $\chi^2(a)$ ? If not, is there a particular distribution for $a\cdot\chi^2(1)$? If ...
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### Overdispersion strategies for exponential curve fitting GLM?

I have price-volume (demand curve) data that follows the exponential function. I used a Bayesian model via PyMC3 to visualize the posterior distribution. This model is simply linear regression in log ...
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