Questions tagged [gamma-distribution]

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

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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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Statistical significance testing of an observation derived from Gamma distributed population [on hold]

I have genetic mutation data for whole genome collected in bins of 3000bp. When I plot this data the distribution looks like a gamma distribution. I estimated the parameter for the above ...
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Distribution of the sample variance $S^2$ from a normal population

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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77 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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56 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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58 views

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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186 views

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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65 views

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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22 views

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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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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100 views

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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163 views

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 ...
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How was the pdf of the generalized gamma distribution in GAMLSS reparametrized?

I am trying to bring together the definition of the Generalized Gamma distribution in R-package GAMLSS by Rigby and Stasinopoulos and the general definition of the Generalized Gamma distribution, ...
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Probability question in Mat

My teacher give me this question: Using MATLAB, generate 10000 Random Vectors of size 500 with the PDF of Gamma distribution. Find the PDF of maximum and minimum of the generated Random vectors. (Use ...
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PDF of human population weight distribution

I have a lot of data on human weight coupled with information about gender, age, country and platform (desktop or mobile user). Looking something like this: ...
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Hypothesis testing for the Gamma distribution - Rejection region

Suppose under $H_0$, a test statistic $T$ has a gamma distribution with paramaters $\theta$ and $k$. Suppose also that the distribution of $T$ under $H_1$ is unknown. What is the appropriate rejection ...
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Proving $\Gamma\left(\frac{1}{2}\right)=\sqrt\pi$ using the expected value of standard normal variable

I'm looking to prove that $\Gamma\left(\frac{1}{2}\right)=\sqrt\pi$ using the fact that $E(Z^2)=\int_{-\infty}^{\infty} \frac{1}{\sqrt{2\pi}}e^{\frac{-z^2}{2}} z^2\, dz$ (where $Z$ is a standard ...
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Which gamma regression model to use for extrapolation?

I'm looking for a regression model which would satify these requirements: My target variable follows the exponential distribution, so to my understanding I should use gamma loss function. I have ...
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147 views

Truncated Gamma Distribution

The Gamma distribution is the conjugate prior of Poisson distribution. What about the Truncated Gamma distribution? Is it still the conjugate prior of Poisson distribution?
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Numerically/approximately integrating over independent gamma variables

Problem Statement For a problem in biology, I am testing out a joint distribution of the form: $$ X \sim Multinomial(\frac{\theta_1}{\sum \theta_i}, ...,\frac{\theta_n}{\sum{\theta_i}}) \\ \theta_i \...
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In an MCMC model, what happens if the observed data contains negative and positive observations, but a strictly positive model (Gamma) is used?

Suppose that we observe data that range from negative to positive support. Now, suppose we use a likelihood specification that is a Gamma, or some other distribution with strict positive support. I ...
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MLE For Gamma Distribution [duplicate]

The $(\alpha, \lambda)$ Gamma distribution has density function $f(x| \alpha, \lambda) = \frac{\lambda^\alpha x^{\alpha-1} e^{-\lambda x}}{\Gamma(\alpha)}$ for $x>0$ How can we obtain an MLE ...
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FITDIST: Why am I getting this shape for the gamma distribution?

I am using fitdist to fit a gamma distribution based on this link: How to draw fitted graph and actual graph of gamma distribution in one plot? My code is as follows: ...
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Poisson Gamma Distribution in R - Creating Enrollment Modeling Curve

I'm trying to create an enrollment curve for a clinical trial based on the following variables: Country start up timelines (staggered), Number of sites, Number of total subjects needed, Number of ...
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Do mismatches in areas of peak density affect the KS-test more than mismatches in low-density areas?

In the following plot you see my empirical data (black) plotted against a hypothesised distribution (blue). However, a KS-test shows that there is no indication that my sample follows this ...
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627 views

Gamma glm log link - what does predicted values mean

Does the predict function in R for gamma glm with log link predict the actual values or the mean value? There is a gamma glm model in R with log link. Using predict(model,data,type = 'response') to ...
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180 views

Shift data to use Gamma glm with “identity” link?

I am trying to fit a glm using the Gamma family and the "identity" link. As I am analyzing nutrient concentrations in coastal waters (that can not be negative and are unlikely to be zero) I assume the ...
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160 views

Gamma Distribution Sufficient Statistics

I've been asked to show the gamma distribution can be written in the form $p(x|\alpha, \beta) = f(x) g(\alpha, \beta) e^{h(\alpha,\beta)^T T(x)}$ where $T(x)$ is a sufficient statistic. .... I have ...
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103 views

Inverse of Gamma Distribution [closed]

I am using python to calculate Inverse of a CDF of gamma distribution (using scipy. stat.gamma.fit). But for probability value 1, it is coming infinite. If it is replaced from 1 to 0.99 it works but ...