Questions tagged [gamma-distribution]
A non-negative continuous probability distribution indexed by two strictly positive parameters.
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Finding a confidence interval for shifted exponential distribution
Let $X_1,\ldots, X_n$ are i.i.d. random variables such that: $$f(x;\sigma ,\theta)=\frac{1}{\sigma}e^{\frac{-(x-\theta)}{\sigma}}, x\gt \theta$$ where $\sigma \gt 0 $ and $\theta \in R$ .
a) if ...
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1answer
31 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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16 views
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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0answers
59 views
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. ...
2
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1answer
22 views
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, ...
2
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1answer
47 views
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 ...
3
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1answer
33 views
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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1answer
49 views
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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14 views
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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1answer
79 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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0answers
47 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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20 views
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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16 views
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 ...
2
votes
1answer
53 views
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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1answer
21 views
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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42 views
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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0answers
44 views
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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2answers
148 views
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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2answers
196 views
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 ...
5
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1answer
133 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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2answers
167 views
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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0answers
25 views
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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18 views
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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19 views
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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39 views
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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0answers
34 views
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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1answer
334 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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0answers
93 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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1answer
126 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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1answer
65 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 ...
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0answers
42 views
two independent Poisson Arrivals
I have two types of customers (type 1 and type 2) enter a shop. Their arrival processes are independent and follow Poisson process with the arrival rates of $\lambda_1$ and $\lambda_2.$
Consider two ...
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12 views
How much data is considered “sparse” for fitting a mixed (Beta Geometric) distribution with 4 shape parameters?
I'm using CamDavidsonPhillips Customer Lifetime Value library to calculate CLV, and it uses a distribution based on Peter Fader's work on the subject that fits a Gamma distribution to model customer ...
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1answer
27 views
Point mass at zero and a chi square distribution with one degree of freedom
I am unclear about the critical value of a point mass at zero and a chi square distribution with one degree of freedom. How to find this?
2
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1answer
34 views
Apply 3 sigma formula in gamma distribution?
Let say i have some data that follows gamma distribution, and i calculated the Mean and Standard deviation of the gamma distribution.
I also know that there are some outliers(Noise) in the data i ...
2
votes
2answers
135 views
What are the assumptions of a Gamma GLM or GLMM for hypothesis testing?
What are the assumptions when doing hypothesis testing using a Gamma GLM or GLMM? Are the residuals suppose to be normally distributed and is heteroscedasticity a concern like the Gaussian (normal) ...
5
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1answer
130 views
Expected value of last Gamma RV in a sum
I've got a sum of $X_i \sim \text{Gamma}(k, \theta)$ i.i.d. random variables. I'm trying to find the expected value of the final $X_i$ that takes the sum above a certain value, i.e., to find the value ...
4
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1answer
61 views
What is the best point forecast for gamma distributed data?
I believe that the values I am forecasting are gamma distributed with shape $k>0$ and scale $\theta>0$. I need a point forecast (i.e., a one-number summary) that minimizes the expected error. ...
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78 views
What is the problem in my CDF derivation?
Let $Z = \frac{XY}{aX+bY+c}$ where the random variable $X$ and $Y$ follows gamma distribution such that
$X\sim G(\lambda_x,\theta_x)$ and $Y\sim G(\lambda_y,\theta_y)$
The CDF of $Z$ can be ...
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0answers
29 views
Gamma family GLM fails after removal of highly influential point
I have some data where distribution seems light a rough Gamma distribution. I am therefore investigating the relationship in r using a Gamma family Generalized Linear Model. When I investigate the ...
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1answer
84 views
glmer model convergence question
We are working with a longitudinal dataset, with three variables: WAIP, BPSRRI and group. WAIP and BPSRRI are measured repeatedly for 10 times and group refers to the group assignment of our subjects ...
5
votes
2answers
116 views
Independence of ratios of independent variates
If $X= x_1/(x_1+x_2)$ and $Y= (x_1+x_2)/(x_1+x_2+x_3)$ where
$x_1,x_2,x_3$ independent chi-square variates with d.f $n_1,n_2,n_3$
respectively, are $X$ & $Y$ independent?
I know the condition ...
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0answers
24 views
Is my data suited for an ANOVA?
I have two types of "media" (surface and sediment). I have six toxin variants "variant". All the toxins originate in the surface water, but I want to know if certain toxins are more likely to ...
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0answers
480 views
Gamma distribution as a member of exponential family
In my lecture notes I have that the distribution of a random variable $Y$ is said to be in the exponential family if it can be written as
$f(y;\theta)=exp(a(y)b(\theta)+c(\theta)+d(y))$, where $a,b,c$ ...
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50 views
Gamma distribution
We consider the gamma pdf of a random variable $Y$ that is given by:
$$f(y) = (s^a \Gamma (a))^{-1} y^{a-1}e^{-\frac{y}{s}},$$
where $y \geq 0$, $s$ is the scale parameter and $a$ the shape ...
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1answer
48 views
Is the convolution of independent normal and gamma also a Pearson distribution?
The answer here What is the convolution of a normal distribution with a gamma distribution? gives the pdf of convolution of normal and gamma random variables. Is there a known random variable to which ...
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1answer
239 views
Canonical link of Gamma Distribution [duplicate]
I wonder why my professor said that Gamma's canonical link is $\frac{1}{\mu}$. My thoughts are:
EDIT: $\theta$ is the canonical parameter.
Since
$$\mathbb{E}_\theta(Y)=b^{'}(\theta)=-\frac{1}{\theta}...
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1answer
165 views
Understanding this expression of the multivariate t-distribution
I found this SO post which expresses the PDF of a multivariate t-distribution in terms of the gamma and normal distribution in python as follows
$$
G = \Gamma (k = \nu /2 ; \theta = 2 / \nu)\\
Z = N (...
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0answers
30 views
Generate an autocorrelated Gamma sample of length N
How does one simulate an autocorrelated Gamma sample of length $N$? All I found online was about generation correlated variables and not an autocorrelated sample.
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0answers
53 views
In a gamma regression, how can i interpret coefficients?
My question is pretty simple, i have done a bayesian gamma regression with an inverse link, so:
$\eta_i$=$\beta_0+\beta_1x_{i1}+\dots+\beta_px_{ip}$ <
using an inverse link, mu is the ...
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0answers
136 views
hypothesis testing - gamma distribution
Let W = Y/B0 be a Random variable that has a gamma(2n,1) distribution. [Y has a gamma(2n,B) distribution and W = Y/B].
i) Suppose you want to test H0 : B ≤ B0 against H1 : B > B0 for some B0 > 0. How
...
