Questions tagged [gamma-distribution]
A non-negative continuous probability distribution indexed by two strictly positive parameters.
563
questions
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1answer
15 views
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 ...
2
votes
1answer
62 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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0answers
28 views
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 ...
0
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0answers
43 views
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 ...
0
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1answer
20 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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0answers
42 views
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} \...
2
votes
1answer
64 views
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 ...
0
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0answers
23 views
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. ...
2
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0answers
38 views
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 ...
1
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0answers
61 views
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:
...
1
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1answer
20 views
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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0answers
22 views
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 ...
0
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1answer
40 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:
...
1
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0answers
18 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
71 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
25 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, ...
3
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1answer
54 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
votes
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 ...
0
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1answer
56 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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0answers
20 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 ...
1
vote
1answer
85 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 ...
1
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0answers
97 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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21 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 ...
0
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0answers
17 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
63 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, ...
0
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1answer
22 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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0answers
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:
...
0
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0answers
60 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 ...
4
votes
2answers
151 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 ...
5
votes
2answers
289 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
votes
1answer
143 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
182 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 \...
0
votes
0answers
26 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 ...
0
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0answers
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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25 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:
...
0
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0answers
52 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 ...
2
votes
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 ...
1
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1answer
518 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
155 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 ...
1
vote
1answer
143 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 ...
0
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1answer
87 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 ...
3
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0answers
46 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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0answers
16 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 ...
0
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1answer
42 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
votes
1answer
37 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
204 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
votes
1answer
134 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
votes
1answer
75 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. ...
2
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0answers
82 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 ...
0
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0answers
33 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 ...
