Questions tagged [gamma-distribution]

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

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Poisson-Gamma conjunction - calculating posterior [duplicate]

How to calculate posterior distribution step-by-step while given: some observed numbers of customers from the last days that number of clients is distributed by Poisson($\lambda$) ($\lambda$ is not ...
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GLM Using Log-gamma Distribution

My data are skewed. Using log-normal causes a strong left-skew in the residuals. Using Gamma causes a strong right-skew in the residuals. I thought to myself, why not log transform the data and then ...
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Fitting mixture of Gamma variate functions at once (with python)

I am trying to automate the fitting of a signal composed of several Gamma variate functions with some added noise. However, I face some troubles and I do not know how to deal with it. First I do not ...
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63 views

Sampling from Gamma Distribution using the Rejection Method

I'm having some issues working through this practice problem. I have worked through the first portion of it, and I have the solution, but I don't understand how/why the solution does two things at the ...
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Connecting interpretations of chi-squared distribution as both gamma distribution and normal distribution

According to this post I read http://www.clayford.net/statistics/deriving-the-gamma-distribution/ the gamma distribution $\text{Gamma}(\alpha,\lambda)$ is the theoretical distribution of wait ...
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Can the logarithm of the sum of random variables be decomposed into the sum of independent random variables?

Suppose $X1$ and $X2$ are two independent Gamma random variables, both follow Gamma distribution but different scales (or rates), their shape can be same or different. Let $Z$ be another random ...
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Gamma GLMM Dispersion, Random Effects, and CoV (lme4)

So I know that in glm(), with the Gamma family, one can get the dispersion parameter through the MASS package with gamma.dispersion() or can even look at the summary output as a quick estimate. How ...
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29 views

getting negative binomial from poisson and gamma

This equation is from a statistical genetics research paper. I'm struggling to understand how they get negative binomial from the integral. x_cn is poisson and q is gamma. Is there such a rule? Or is ...
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Fisher Information for Gamma

Question: Find the fisher's information for $\mathcal{G}(\alpha, \beta)$ ,$\beta$ known. Attempt: Since $\mathcal{G}(\alpha, \beta)$ ,$\beta$ known. $$f(x|\alpha) =\dfrac{x^{\alpha-1}e^{x/\beta}}...
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How do I show that $Y=2\sqrt{X_1X_2}\sim$Gamma$(2p,1)$?

Suppose that $X_1\sim $Gamma$(p,1)$ and independently, $X_2\sim $Gamma$(p+1/2,1)$. Show that $Y=2\sqrt{X_1X_2}\sim$Gamma$(2p,1)$. This problem followed a section on bivariate transformations, so I ...
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MLE of shifted Gamma

Let $X = (X_1,\dots, X_n)$ and $X_1,\dots, X_n$ be i.i.d Gamma($p,a,A$) random variables where $p$ and $a$ are known. Find the MLE of $\theta =A$. We have \begin{align*} f_{\theta}(x) &=\...
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How to interpret parameters of GLM output with Gamma log link

I am having tough time interpreting the output of my GLM model with Gamma family and log link function. My dependent variable if "Total Out-of-pocket cost" and my independent variables are "Private ...
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Compounding a gamma distribution with another distribution to yield a gamma

I have a gamma distributed random variable $X$, with its mean $\mu$ distributed as some other function $$ X \sim \text{Gamma}(\mu,k)\\ \mu \sim P(\theta) $$ What is the distribution $P(\theta)$ such ...
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Why Are they doing exponential distributions?

With many thanks for help in why my exercise is using a Gamma distribution, I am still confused by another part. The plot: The commentary: We may suspect from the above that there is some sort of ...
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Why would they pick a gamma distribution here?

In one of the exercises for my course, we're using a Kaggle medical dataset. The exercise says: we want to model the distribution of individual charges and we also really want to be able to ...
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1answer
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Variance for events occurring with gamma and geometric distribution

I am presented with a problem as follows: A listener is receiving messages with a wait time in between two consecutive messages that is exponentially distributed with a mean of 1 time unit. After any ...
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20 views

Distribution transformation when having same mean and variance

Is it possible to transform the distribution to Gaussian, with same mean and variance? For example, The Gamma RV. X with K=7.5 and theta=1.0. --> The Gaussian RV. X' with not changing mean and ...
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Pareto/NBD with time-varying covariates

I am trying to incorporate time-varying covariates into the Pareto/NBD model (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.597.3165&rep=rep1&type=pdf) Model assumptions start at ...
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Concave downward link function for a glm?

I seem to occasionally find datasets where the relationship between X and Y is concave downward. It seems like it should be trivial to find a link function that fits a concave downward curve, but they ...
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Distribution of the sample variance $S^2$ from a normal population [closed]

Let $X_1, X_2, X_3, ….., X_n$ be $N(\mu, \sigma^2)$ distributed. Then what is the distribution of $S^2$ I have already proven that if $X_i$ are $N(\mu, \sigma^2)$, then $\frac{(n-1)S^2}{\sigma^2}$ ...
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Posterior (conjugate) prior of two parameter Gamma likelihood

This question is related to a previous question on this site. Assume some data is generated from Gamma distribution $p(x\mid\alpha,\beta) \sim \operatorname{Gamma} (\alpha,\beta)$, and both parameters ...
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1answer
115 views

Gamma GLM - Derive prediction intervals for new x_i

In a Gamma GLM, the statistical model for each observation 𝑖 is assumed to be $Y_i \sim Gamma(shape, scale)$, where $E(Y_i) = \mu_i = f(X_i\beta)$, and $f$ is the link function. I've used MLE to ...
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1answer
163 views

Gamma Distribution for generating random numbers

I defined a gamma distribution with following parameters: shape,scale = 4.2503, 7037. This dribuation is used to generate random numbers. The random numbers will be recalculated to the x-asix value. ...
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Distribution of X/(X+Y)of gamma variables [duplicate]

Does anyone know how to calculate the distribution of $$X/(X+Y)$$ X ~ G(p,a) Y~G(p,b) G is gamma distribution
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How Gamma generalized linear model with zero dependent variable value is derived?

I understand that Gamma distribution generates only positive values. And this is reflected in R gamma family glm function which ...
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Name for a distribution between exponential and gamma?

The density $$f(s)\propto \frac{s}{s+\alpha}e^{-s},\quad s > 0$$ where $\alpha \ge 0$ is a parameter, lives between the exponential ($\alpha=0$) and $\Gamma(2,1)$ ($\alpha \to \infty$) ...
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Is it possible to calculate the scale param θ for the Gamma distribution, given shape param K and a quantile value Q?

Stats-ophils, I am running into a problem, in which I'd like to generate a Gamma distribution (in Julia) and I know the value of the quantile Q(0.9) = 130 as well as the shape parameter k=2. Is it ...
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1answer
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How do I get the CDF of a gamma distribution with mean and sd?

I have the mean and standard deviation of my data, which I determined follows a gamma distribution. I don't understand the function I found online for the CDF of a gamma distribution because of the ...
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Failed to get Uniform distribution from Gamma distribution

I read in Chapter 6 in this book that $p(K)\propto 1$ is equivalent to $e^{-K}\sim Gamma(0,0)I(0,1)$ where $K$>0 and is uniform distribution, e.g., $K \sim Uniform(0,100)$; $I(a,b)$ is the ...
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What kind of regression to use with heavily skewed data?

I have data with an explanatory variable $X$ (I think I can treat this as continuous, as scores 1-100 on a certain test) and a response variable $Y$ (continuous variable, never lower than 0). Both ...
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What’s the difference between k-theta and alpha-beta parameterization for gamma distribution?

In my book “Mathematical statistics with Applications”, written by Wackerly, it’s stated that there are two methods for parameterization of gamma distribution. The first one is k-theta and the second :...
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Finding the distribution of a piecewise function of a Gamma random variable

Let random variable $X \sim \text{Gamma}(\alpha,\beta)$. I want to derive the distribution of $Y$, where: $$ Y = \left\{ \begin{array}{ll} a X - k & \quad X \geq \frac{k}{a} \...
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How to use Gamma distributions to estimate the number of failures?

I need to calculate the expected number of failures of a product within 6 years. The time until failure is said to be gamma distributed with $\alpha=2$ and $\beta=0.5$ for a mean time between ...
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inverse Gamma Distribution and LogNormal Distribution can both discribe the data, is that a coincidence?

I am observing the fluxes of source and I am trying to learn something from it's distribution of fluxes. When I histogram my data, I can perfectly describe my data with a lognormal distribution. ...
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Characterizing a distribution

I have a set of words which in a given year has a frequency of occurrence k. I can observe that these words follow frequencies k1, k2, k3,....kn in the following year. If I have some data in the form ...
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What is the difference between Gamma GLM on log output and Gamma GLM with log link function?

Here are two models (with R code to provide some context): Model 1: Take the log of the output variable $y$, then apply a Gamma GLM using the default identity link function: ...
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1answer
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Relating Chi Squared and Gamma Distributions using code?

How do we relate the chi squared and gamma distributions with code? For example if we have a chi squared distribution with cdf(x, k) and we calculate ...
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Fitting Gamma Distribution in Python with scalar factor

I have done optimization to minimize error of resulted model, however, the R-squared is still low. I try to multiply a scalar to the resulted model to obtain a better fit. The scalar will be generated ...
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1answer
63 views

Model validation in R - Gamma GLMM

I'm trying to model a response variable y with respect to a nested variable x in R. First of all, I fitted a linear mixed model (LMM) as it follows: ...
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Poisson and Gamma distribution for testing randomness

In genetics I want to test whether InDel (insertion and deletion in DNA) sizes occurs with the same probability. I heard that I should gamma distribution to model it. I found ...
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Gamma Distribution CDF Intuition; Are My Parameters Correct?

I'm learning about gamma distributions and I want to make sure my reasoning is correct for an example I found here. Suppose you are fishing and you expect to get a fish once every 1/2 hour. ...
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Optimal distribution for Acceptance Rejection Sampling

For some project I have been sampling from the Gamma distribution. I have been using the exponential distribution intensively. One method I have employed is the Acceptance rejection sampling, ...
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Finding method of moments estimator of $\theta$ in $\Gamma(\theta,\theta)$ distribution

Please refer to the question in image I have tried to find $ E(x) $ but i ended up with $\overline x $ = $\frac{\theta + 1}{\theta} $ which statisfies no option , i also tried to find $ E(x-1)^2 ...
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Should I subtract lower bound from Gamma distributed data before estimating distribution parameters?

I have some real world data that reflects waiting time in a system. As it's about waiting times I assume it's Gamma distributed and visual check (histogram overlaid by a fitted Gamma PDF) shows no ...
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When a probability density function is defined to be finite?

In "Pattern recognition and machine learning" by Cristopher Bishop, Chapter 2.3.6 (pag. 100) says that The gamma distribution has a finite integral if $a>0$, and the distribution itself is ...
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interpreting Gamma regression coefficients - individuals not totalling sum of parts

I have fit a gamma regression to a dataset, and like with traditional linear regression, I would like to calculate the contribution of each independent variable across the entire model. The problem I ...
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Gamma distribution parameters estimation [closed]

I have a set of samples taken from a population distributed with a Gamma distribution, so \begin{equation} f_X(x)=\frac{\beta^\alpha}{\Gamma(\alpha)}x^{\alpha-1}e^{-\beta x} \end{equation} I should ...
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MLE for Beta distribution, with $\beta$ = 3

I'm trying to calculate the Maximum-Likelihood Estimator for $\alpha$, using the beta distribution with $\beta = 3$. I'm kind of stuck at the last bit. Perhaps I've made a mistake somewhere, or this ...
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How to measure trends in the frequency of events

for my master thesis i want to figure out which website visitors increased / decreased the intervals between their visits during 3 months. Eventually, I want to segment them into increased and ...
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Marginal Distribution of Hierarchal Model Normal distribution with unknown mean and precision

I am trying to use a Hierarchical model where there I have a normal distribution with random mean and precision: $$ y \sim N(\mu, \tau)\\ \mu \sim N(M, T)\\ \tau \sim Gamma(\alpha, \beta) $$ I'm ...