# Tagged Questions

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

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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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 ...