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

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19 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
39 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
41 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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10 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
54 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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10 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
72 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
68 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
20 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 ...
3
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2answers
105 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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26 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
45 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
91 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
193 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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0answers
35 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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10 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
21 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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35 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
22 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
155 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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9 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 ...
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1answer
34 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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18 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
39 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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24 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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17 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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40 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 ...
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33 views

What is the intuition behind the expected transaction value for a customer in the gamma-gamma model?

I was reading the paper RFM and CLV: Using Iso-Value Curves for Customer Base Analysis by Peter S. Fader, Bruce G. S. Hardie and Ka Lok Lee, in an attempt to gain some intuition behind the methods ...
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19 views

How to find the UMPT for Gamma distribution

I have the gamma distribution given by; $$f_{\theta} (x) = \frac{1}{\Gamma(\theta)} x^{\theta -1} e^{-x}; x > 0 , \theta > 0$$ How can I obtain a UMPT for this function? I have tried using the ...
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1answer
37 views

How to find full gamma function from the result?

I have a data set and fitted this data as a gamma distribution in R. Below is me code and result: ...
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20 views

Multivariate generalization of Poisson-Gamma model?

I actually assumed it would be easy to find a multivariate version of the Poisson distribution, but couldn't find any concrete solution (in terms of a well cited publication). It seems that ...
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37 views

conjugate prior for my model parameter

This question is related to the another thread that I posted: Help with Variational Bayes on a weighted linear regression model To reiterate, I have the model as follows: $$ y_i \sim ...
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2answers
39 views

what problems can occur when substituting zeros for gamma regression

It is common practice to substitute the zeros of an outcome variable for a gamma GLM with a very small number like 1 or 0.1 if the number of these zero observations does not exceed say 10% of all ...
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1answer
94 views

Help with Variational Bayes on a weighted linear regression model

I am trying to setup VB to do a weighted linear regression for vector observations. My setup is that I have $N$ numbers of $d$-dimensional vector observations. I would like to model the noise as being ...
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31 views

Appropriate random effects GLMM analysis for mean count data? R

I'm trying to find the right way of using a mixed effects approach on some mean count data (animal visits per day to a feeder) in R. I have two interacting fixed effects (both factors) and 2 random ...
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41 views

Beta of transformed gamma variable

I'm trying to transform a gamma distributed variable with $\alpha=n$ and $\beta=15$ using the following formula: $$U=\frac{2S}{\beta}$$ S is actually a summation of n exponential variables ($Y_i$), ...
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21 views

How to obtain corresponding p-values for count data assuming a negative binomial distribution?

Unfortunately I have basic knowledge of statistics. I have an issue with the analysis of my data. Briefly, I have a vector of counts (values from 0 to n, they can be also non-integers). I would need ...
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310 views

Farlie-Gumbel-Morgenstern copula

I have the Farlie-Gumbel-Morgenstern copula and I want to generate two gamma marginals and find an expression for the linear correlation. I understand that to get the random variates $(u,v)$ I need to ...
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1answer
43 views

GLM vs least squares with Gamma errors

To illustrate the usefulness of GLMs in comparison to the least square method I did a simple program in which I add random noise to a straight line (Y=m*x + b; red line in the attached plot). The ...
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1answer
60 views

Max n for which sum of exponential distribution is bigger then gamma variable

I am currently preparing to the actuarial exam and it is one of the exercises from previous years I encountered and have no idea how to deal with: Let us assume that $X_1, X_2, ..., X_n$ are ...
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1answer
39 views

What distribution has this non-central Chi-Squared -like moment generating function?

I'm new here so please criticize errors! My moment generating function looks like this (after some tidying): $E[e^{wY(t)}] = \frac{1}{\left(1-2\theta(t) w\right)^{k/2}} ...
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1answer
31 views

MLE of Gamma when only given observations [closed]

i've been given 10 observations of X, where X is a random variable. the observations are 141 16 46 40 351 259 317 1511 107 567 and now given they are gamma distributed, how do you find the MLE using ...
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62 views

R - fitting a gamma distribution given the CDF?

I'm trying to develop a prediction model of the success or failure of a test run based on its current running time (in my data, from observation, the longer a test runs the more likely it is to fail). ...
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54 views

Estimating medians and modes of skewed distributions using GLMs

Edited question (less vague hopefully) I am wondering why for generalized linear models with Gamma, Poisson and Negative Binomial distributions that there appears to be no discussion about estimating ...
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1answer
79 views

Gamma parameterization and how to randomly generate $\sigma$'s for use in `rnorm(n, $\mu$, $\sigma$)`

Say I have a normal distribution parameterized with a mean ($\mu$) and precision ($\tau = 1/\sigma^2)$. In JAGS, I would specify a prior for $\tau$ as ...
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36 views

Weibull vs Gamma Distribution

I have a set of experimental data which comprises distances between successive points: Under most contexts, our data fits well with a γ-distribution. However, in a few distinct cases, the γ is no ...
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29 views

Prediction Error for a Poisson Process

So I have a fleet of cars. I've sampled their breakdown rates (per hour driven) for the last 10 years. Their breakdown rate follows the gamma distribution. I am trying to do two things. Predict ...
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1answer
62 views

Testing a vector for gamma distribution

I asked this question on stackoverflow before but I was told that I better ask this question here! So... I have a problem with a certain vector. I'm tying to find out IF it's gamma-distributed and (if ...
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44 views

derive loss function for gamma regression

In the R package mboost there is a family called "GammaReg" which implementes "negative Gamma log-likelihood with logarithmic link function". Still, I don't really ...
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1answer
60 views

Name of rv that results from integrating over gamma in gamma product prior on poisson

If $d$ is an arbitrary random variable with parameter(s) $\Psi$ and positive support, $g \sim \mathrm{Gamma}(\alpha, \beta)$, $x \sim \mathrm{Poisson}(gd)$, and $g$ and $d$ are independent, then ...