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

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Calculating the likehood from the coeficients of logistical regression

I am doing a logistical regression and need to calculate the likehood from the null model and from each feature model and to after that get the p-value.The problem states: a) Create a model that ...
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40 views

Improve fit of a Gamma distribution

My dependent variable has a distribution as below: I fit a gamma distribution with log link using ...
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24 views

Is there another interpretation for a Gamma distribution with non-integer shape parameter?

It is well known that a random variable being Gamma distributed with integer shape parameter k is equivalent to the sum of the squares of ...
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33 views

Estimating Gamma MLE with left truncated data (using R and maxLik)

I'm trying to find the maximum likelihood estimation of the parameters of a Gamma distributed random variable using maxLik. The following code explain what I did: ...
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12 views

How to find gamma coefficients?

I am trying to replicate this paper "Gleditsch, Kristian Skrede and Michael D. Ward. 2006. "Diffusion and the International Context of Democratization", International Organization 50: 911-933" and I ...
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20 views

Showing independence between two functions of a set of random variables

I've been working on the following problem and I'm confused about how to get started: Let $X_1, X_2,..., X_n$ denote $i$.i.d. real valued random variables, each absolutely continuous with an ...
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10 views

The probability distribution of rth order statistic after transformation

If I have a sample from a Rayleigh distribution, then I transform this sample to a sample from Gamma distribution by using the fact that the summation of the square of a Rayleigh variable is a Gamma ...
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25 views

Calculate log-odds posterior distribution

Given a gamma-posterior distribution $p(\theta|y)$ I want to compute the posterior distribution for the log-odds: $log\frac{\theta}{1-\theta}$ I tried to solve it with the change of variables ...
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2answers
38 views

Calculate posterior distribution (gamma-prior, poisson-likelihood)

I want to calculate the posterior distribution given a gamma-prior and a poisson likelihood. The task is from a textbook and I just have the solutions (without a walkthrough). Please find all given ...
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1answer
77 views

Gamma distribution with shape and scale parameter related to its skewness [closed]

I have two set of gamma distribution . standard deviation is related to its population mean Given unequal standard deviation, how do I make sure the population mean is equal (null hypothesis is ...
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1answer
29 views

P.d.f for Gamma posterior with Exponential data

I am trying to perform a simple exercise: Sample $N$ points from $\text{Exponential}(\lambda=0.1)$ Assume a $\text{Gamma}(\alpha,\beta)$ prior for the parameter $\lambda$ above Build a p.d.f for the ...
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43 views

Distribution for Sum of Square Normal Variables with Arbitrary Variance

Let $X_1\sim N(0,\sigma_1^2), X_2\sim N(0,\sigma_2^2),\dots,X_n\sim N(0,\sigma_n^2)$ where generally $\sigma_1\neq\sigma_2\neq\sigma_3\dots\neq\sigma_n$. What is the distribution of the statistic $$Y ...
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19 views

Transformation of sum of Gammas into Chi-squared with a Casella Bergian twist

My question is very similar to the ones asked before (I have looked at all of them on Cross-Validated) but it is more about house-keeping and making sure it matches precisely transformation theorems ...
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23 views

optim() convergence in fitting gamma distribution to separate peaks of time series data

Trying to fit gamma distribution to each separate peak of time series data (chromatography). As a peak i take local minimum-maximum-minimum part of the data each time. Since the peaks values do not ...
3
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1answer
43 views

Link function in a Gamma-distribution GLM

In a GLM, if the response variable has a Gamma distribution, why is the inverse used as the link function, i.e.: $\mu = -(X\beta)^{-1}$? In particular, why is the inverse the canonical link? Does it ...
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1answer
20 views

Generate Example data for which it is difficult to distinguish between Gamma, Weibull and log-normal fit using R?

I'm trying to generate a data set, as a demonstration case, to show a case in which it is difficult to distinguish between Gamma, Weibull and log-normal distribution. To do this I generate some data: ...
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1answer
118 views

Multiple peak fit - decomposing a graph into visible and hidden peaks of the same probability distribution

I have a graph as a set of coordinates (x, y), where x is a progressing time and y is proportional to an amount of molecules (chromatography results). Visible peaks on the graph look like of gamma ...
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1answer
35 views

How to sample from a truncated CDF that is a tranformation of a gamma distribution?

I would like to sample from a cumulative distribution function $G$, which is a transformation of a 2-parameter Gamma : $G = q * F_{\gamma} + (1-q)$ where $F_{\gamma}$ is the Gamma CDF. In my case, it ...
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1answer
93 views

GLM - which probability distribution to use for abundance data?

I'm fitting a generalized linear model to try to understand how the abundance of a species of freshwater fish varies in response to some environmental variables. I'm using the AIC to choose between ...
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8 views

Appropriate probabilistic distribution for data consumption by ISP customers

I'm trying to work out which probabilistic distribution I should use for describing a population of objects where the measured variable is bound between 0 and infinity. Specifically, which would be ...
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36 views

Non-Gaussian state-space models

I am curious why most literature mentions that only gaussian state-space models (such as kalman) are analytically tractable. I was curious about posterior inference on a Gamma chain, why would it be ...
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1answer
33 views

Bayesian estimate of a Gamma distribution scale parameter

I saw a material showing Bayesian estimation on a Gamma distribution scale parameter. As shown below. I think in the 2nd formula, the denominator should be integrated by theta, which is the formal ...
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1answer
47 views

Posterior distribution for Gamma scale parameter under the Jeffreys prior

What is the posterior distribution for parameter $b$ with $X \sim Gamma(a,b)$, under the Jeffreys prior? We can assume that $a$ is known. The Jeffreys prior is the square of the Fisher information ...
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22 views

Conjugate prior for three-parameter gamma distribution with unknown threshold

What is the conjugate prior for a three-parameter Gamma distribution with shape $\alpha$, rate $\beta$, and threshold $\mu$ when $\alpha$ and $\beta$ are known and $\mu$ is unknown? That is, my ...
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2answers
53 views

Inverse gamma convergence in probability

I am trying to prove the consistency of MLE for a beta distribution. The problem now reduces to the following: Assume $Y=\frac n X$ and $X$ ~ Gamma(n,$\frac 1 \theta$), prove that $Y$ converges to ...
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1answer
112 views

Statistics guessing game

This is a game that I wanted to know the answer for. The Game There are many players in the game, who each get a guess. There is a loss distribution, $L$, where: $L$ ~ Gamma($\alpha$, $\beta$) ...
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66 views

Calculating Safety Stock with Gamma Distributed Demand

I've written some code to simulate an inventory system with gamma distributed demand to find the target stock and reorder point that will give me a 95% service level, but I think based on the ...
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1answer
65 views

Limiting distribution of $\frac{\sqrt{n}\left(\bar{X_n}-\mu\right)}{\sqrt{\bar{X_n}}}$ from mean of Gamma$\left(\mu,1\right)$?

Given $\bar{X_n}$ is mean of random sample with size $n$ from Gamma distribution with parameter $\alpha=\mu$ and $\beta=1$. I wanna find the limiting distribution of ...
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13 views

Calculate the non centrality parameter (ncp) for non central gamma distribution

How can I calculate the non centrality parameter (ncp) for non central gamma distribution, if I know the α and β parameter, and also the 0.975 quantile value ? How to do it in R ?
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1answer
151 views

How can I determine Gamma distribution parameters from data

I have a time series of weekly retail sales data that I would like to model for an inventory control simulation I am working on. From my research it looks like weekly retail sales like this are best ...
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2answers
86 views

How to test H0: “this sample is drawn from a gamma distribution” against HA: “this sample is drawn from two different gamma distributions”

This is a targeted follow-up to " all of these data points come from the same distribution." How to test? I have a sample of strictly positive data. I fit a gamma distribution to it and ...
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1answer
40 views

Is Gamma distribution appropriate for sales transaction data?

I have a sales data for a certain type of grocery products at stores' transaction-level (sales data gathered through cashiers' scanners). As you can imagine, for the most part, the number of units ...
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2answers
140 views

Interpretation of a negative price coefficient in a log model with gamma distribution

Usually demand models have negative price coefficients, which means that the higher the price, the lower the demand. Many researchers in business look at price coefficients for a "sanity check", i.e. ...
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28 views

substituting zeros in a Gamma regression

I modeled some right skewed data with a Gamma GLM (log link). This is common practice in my field. However, some observations have a value of zero and the Gamma distribution is only defined on the ...
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1answer
88 views

PDF and CDF of sum of two independent $\Gamma$-distributed random variables [duplicate]

Let $X \sim \Gamma(m, p)$ with a shape parameter $m$ and a scale parameter $p$ and $Y \sim \Gamma(m, q)$ with a shape parameter $m$ and a scale parameter $q$, and let $X$ and $Y$ be independent. ...
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1answer
344 views

How to draw fitted graph and actual graph of gamma distribution in one plot?

Load the package needed. library(ggplot2) library(MASS) Generate 10,000 numbers fitted to gamma distribution. ...
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1answer
212 views

What distributions are possible for an arrival rate?

I'm really struggling to find a good statistical distribution. I've tried Poisson and Gamma so far, but without success (best I've got was a p-value of 0,00005 with a Pearson Chi-Square test). So I ...
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41 views

Fitting a non-linear model where observations at each time are random variables drawn from a different (non-Gaussian) distribution

I have a non-linear (and not clearly linearizable) function of a few parameters that models a response over an independent variable (time): $$ f(t;\lambda_1,\lambda_2,\lambda_3). $$ The function $f$ ...
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11 views

Sample size gamma regression

I would be very grateful if you could please advise on sample size.... I have estimated a sample size using R - library(pwr) using command "pwr.f2.test(u = 6, v = NULL, f2 =0.02 , sig.level =0.05 , ...
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1answer
29 views

Inverse gamma distribution definition

Wikipedia says the pdf for the gamma function is: \[ X \sim \operatorname{Gamma}(\alpha,\beta) \implies \Pr(X=x) \propto x^{\alpha-1}e^{-\beta x} \] If $Y = 1/X$, then \[ \Pr(Y=y) = \Pr(X=1/y) ...
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48 views

Problem with Newton--Raphson Implementation of Inverse-Linked Gamma GLM in R

Recently, I've been trying to implement functions in R that use Newton--Raphson to find the MLE of parameters for various GLMs. My focus has (thus far) been on data with responses $y$ that are ...
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1answer
33 views

Relationship between Gamma and chi squared distributions [duplicate]

What is the relationship between the Gamma distribution and the chi-squared distribution?
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3answers
174 views

Which parameter should be considered as “scale” parameter for Gamma distribution?

From Wikipedia and probably all statistics textbooks, we know that in the density of a Gamma random variable $$f(x; k, \theta) = \frac{1}{\Gamma(k)\theta^k}x^{k - 1}e^{-\frac{x}{\theta}}, \quad x > ...
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13 views

normality tests of residuals in repeated measures design

I have a repeated measures design where I have plotted the residuals and the majority of my data are not normally distributed. As I understand it, repeated measures designs are quite robust when using ...
4
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1answer
45 views

Ancillary statistics:Beta distribution is free of $\beta$?

I am reading Robert V. Hogg Introduction to Mathematical Statistics 6th Version page 409, second paragraph. $X_1, X_2$ is a random sample from a Gamma $\text{G}(\alpha,\beta)$ distribution with ...
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19 views

Help with transformations

I am working with these transformations and I'm not sure why I can't solve this problem. It's pretty easy but my math isn't working out...I may fundamentally misunderstand something. $X1, X2, X3$ are ...
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1answer
68 views

Diagnostics for quasipoisson glm for continuous data

I'm a little confused about how to use the quasipoisson family in the glm function. It was recommended by someone that I use it for my analysis, even though the data are continuous - and as such, I ...
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32 views

Proper approach to Gamma-distributed data prediction with measurement errors in outliers

My task is to predict Gamma-distributed data with a large number of extreme-valued outliers caused by measurement error (i.e. the machine that records the values intermittently malfunctions). My ...
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18 views

What is the distribution of a parameter which is expressed as a difference between constant and a Gamma distribution?

I have a variable $x_0$ which is an initial value of a process, it is a constant. The change in the process $\Delta x_t$ follows a Gamma distribution with parameter $(\alpha_t, \beta)$. What will be ...
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62 views

Conjugate Gamma Prior

If I have a normal distributed variable $N(\mu,\sigma^2)$ so with fixed $\mu$ the conjugate prior for $\lambda:=\frac{1}{\sigma^2}$ is given by the gamma distribution $\propto ...