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

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2
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1answer
82 views

Is a gamma distribution bounded between 0 and 1 the same as a beta distribution? [on hold]

After making the assumption that monetary losses could be well represented by a gamma distribution (Boland, 2007), mostly negatively skewed, and being interested in loss ratios (ie. lost value / total ...
0
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1answer
10 views

Estimate parameters of three parameters gamma distribution

I need to estimate parameters of three parameters gamma distribution. Can anybody please give me a clue in which software and by which commands I can do it? Thank you
1
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0answers
26 views

Help me out with real-life Gamma distributions

I'm working with some data relating to maintenance and parts failures. I've got a pure math background with only a little bit of probability, and I'm currently learning by doing. I've got a list of ...
1
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1answer
32 views

KL divergence between a gamma distribution and a lognormal distribution?

Is there a closed-form formula for the KL divergence $D_{KL}(X,Y)$ where $X \sim \mathrm{Gamma}(k,\theta)$ and $Y \sim \mathrm{LogNormal}(\mu,\sigma^2)$ ? Many thanks.
3
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1answer
65 views

If $X$ takes on a Gamma Distribution, how can I find $X^2$, $X^3$, etc?

I am trying to take consecutive powers of a Gamma Distribution. For example, if $X \sim \textrm{Gamma}(k, \theta)$, I would like to find $X^2$, $X^3$, and in general $X^m$ for $m>0$. The pdf ...
1
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0answers
23 views

How do you approach transformations when modeling?

I'm working with a simple univariate dataset and I've built several models for it. Some I think are fairly decent given that datas structure. In order to get a decent model I had to do some ...
3
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2answers
33 views

Hierarchical Gamma-Poisson CDF?

What is the most computationally efficient way to evaluate the CDF $$P(X \leq x | r,v)$$ where $$ X \sim Poisson(\lambda)$$ and $$ \lambda \sim Gamma(r,v)$$ I can't see the next obvious step after ...
4
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3answers
84 views

Hypothesis test for correlation between Gamma random variables

I have two Gamma random variables. I need a hypothesis test to detect a possible correlation between them.
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0answers
42 views

How to sample the degrees of freedom of a Wishart distribution?

SHORT VERSION: Given K precission matrices drawn from a single Wishart distribution, I try to infer the degrees of freedom of this Wishart. How can I do it? Is there some place where this derivation ...
3
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1answer
101 views

Convergence from Gamma to Normal Distribution

I came across this problem: Problem If I have $X_1, X_2, ..., X_n$ $n$ iid random variables which pdf is $$ f_X(x) = \begin{cases} \dfrac{x^{\mu-1} e^{-x}}{\Gamma{(\mu)}} &0<x<\infty, ...
2
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1answer
34 views

Gamma GLM predicting the second parameter of the Gamma

The gamma distribution has two parameters, I understand that the linear predictor predicts $\mu = g^{-1}(X\beta)$ where $g$ is the link function but how does the linear predictor specify the second ...
1
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0answers
13 views

Question on Inverse-Wishart Distribution when reading Peter Hoff's book

I have a couple of questions when reading the chapter 7 The Multivariate Normal Model of Peter Hoff's "A First Course in Bayesian Statistical Methods". First, could anyone give me any resource about ...
2
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1answer
73 views

Maximize the profit of a product given a Gamma distribution

I'm having trouble translating this problem into a workable form: A bakery sells rolls in units of a dozen. The demand X (in 1000 units) for rolls has a gamma distribution with parameters ...
1
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0answers
24 views

How to prove NegativeBinomial(r,p) converges to Gamma(r,1) as p->0

Let $X\sim NegBin(r,p)$ and $Y\sim Gamma(r,1)$. How can I prove that $pX \overset{dist}\to Y$ as $p\to 0$. Is this statement the same as $X\overset{dist}\to Gamma(r,1/p)$. Thanks.
0
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0answers
27 views

How to estimate Extreme value distribution parameter

Assume that I have non-negative Gamma random variables $\{X_i,i=1\dots n\}$ and I want to find $M_n=\max\{ X_i\}$. I want to apply generalized extreme value distribution (GEV), but how to find $\mu$, ...
0
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1answer
58 views

goodness of fit gamma distribution matlab

I have a set of observations obs. If I plot the histogram of the observation I see that they could come from a gamma distribution ...
1
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0answers
31 views

Gamma vs tweedie distribution for large productivity dataset

I'm running some GAMs using the mgcv R package on a dataset with ~8.5k observations, where productivity is the response and environmental conditions are the covariates. However I am unsure of which ...
0
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1answer
80 views

Need help calculating poisson posterior distribution given prior

I have been attempting to figure this out for hours, but gamma distribution is somehow beyond me. I have a question where we are given α=5 and ...
0
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0answers
9 views

Performing OLS with gamma transformation

In some specific areas it is common to perform OLS regresion with beta distribution transformation. The α and b parameters are calculated by the sample's μ and σ^2. While the transformed dependent ...
2
votes
1answer
96 views

When is distribution of $|X+Y|^2 $ equivalent to $|X|^2+|Y|^2$?

I am trying to compute the distribution of the following $$Z=\bigl(X+Y\bigl)^2$$ BUT I have that both $X$ and $Y$ are Nakagami with parameter $m$. (A Nakagami random variable is the square root of a ...
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0answers
38 views

What is the distribution of these functions of Nakagami random variables?

I am new to this forum and hope I can get help. A Nakagami random variable $X$ with parameter $m$ has the following pdf $$X\sim \frac{2m^m}{\Gamma(m)\Omega^m} x^{2m-1}e^{-\frac{m}{\Omega}x^2}$$ ...
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0answers
47 views

Use of normality test to distinguish gamma from log-normal distribution

I have random population sample data that I would like to describe using a distribution. If I plot the estimated kernel density, the data appear positively skewed and using functions in R such as ...
0
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0answers
26 views

Inequality of gamma distribution

Let $X_{\alpha} \sim \text{Gammma}(\alpha,1),\alpha >0$ with distribution function $G_{\alpha}$ and $X_{\beta} <_{(c)} X_{\alpha}\,\forall ~0<\alpha<\beta<\infty$. Then show ...
0
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0answers
70 views

Interpretation of priors in example

Suppose you have 3 variances $W_{1},W_{2},W_{3}$ that can be expressed as $W_{j}=q_{j}V$ with $j = 1,2,3$. According to one model, $W_{3}$ should be pronounced and $W_{1}$, $W_{2}$ should be small to ...
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0answers
25 views

Understanding the variance to mean power function in Poisson gamma models

I have a biology background and try to understand what it means that the distribution of snps over the genome follows a Poisson gamma (PG) model. It is accepted that each chromosome contains Poisson ...
0
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1answer
31 views

Binsize for Compound Poisson Gamma Distribution

Having data of a (putative) Poisson-Gamma process I am looking for a method to define the correct binsize for analysing my data. I need a certain range (!) of binsizes (for instance starting with ...
0
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0answers
37 views

appropriate sample size to fit non-normal distribution parameters

I have a population that, in theory, I could determine exactly. I am not doing so, however, because on my poor home computer, it would be too computationally intensive. Each calculation takes 45-90 ...
0
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0answers
31 views

Logistic Regression - Non normal distribution

I have a computer science background & I am trying to teach myself stats by solving some regression problems I have some sales data which is gamma distributed(I guess) I can send this to a ...
2
votes
1answer
50 views

Help understanding the results of the Lilliefors test

I have a set of annual rainfall data for Thailand which is gridded, so I have approximately 30x18 grid squares. I am trying to test whether the gamma distribution is suitable for my data, so I am ...
0
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0answers
15 views

Generalized minimum chi-square estimators?

I need to implement the generalized minimum chi-square estimators (alternative to L-moments method and maximum likelihood estimate (MLE)) for estimate the parameters of the gamma distribution. My ...
1
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1answer
54 views

Adding a variance structure when fitting a gamm with Gamma distribution

I am using the code below to fit a gamma GAMM introducing a variance structure that informs the model that variance of the response variable is much larger in one of the levels of the factor coast ...
-2
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1answer
31 views

How to simulate a prior for a Poisson distribution? [closed]

I would like to simulate random variates from a Poisson distribution to act as prior for a predictive model, but I fail to do it correctly. Here is my attempt: ...
3
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2answers
140 views

Goodness of fit (cdf: empirical vs theoretical)?

I have a data-set with n = 90, probably follows the gamma distribution (and others). I used the maximum-likelihood estimation (MLE) to estimated the alpha and beta parameters of the gamma distribution ...
2
votes
2answers
98 views

Jointly sufficient statistic?

A random sample $X_{1},...,X_{n}$ is pulled from a gamma distribution. Are there jointly sufficient statistics based on these observations for the two unknown parameters? The definition of a gamma ...
0
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1answer
38 views

to find the values of gamma distribution knowing the parameter value of a poisson

I have a variable X, and information available to me is that the parameter $\theta$ is around 2.2 $X\sim \mathbf{Poisson}(\theta)$ How can I determinate the value of the parameters $\alpha$ and ...
3
votes
1answer
49 views

Distribution of Trace of non-centered Wishart matrix

I am looking for the distribution of trace of the non-central Wishart matrix with different variations along different axes. Is there a general formula for such distribution? If not, is there a ...
0
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0answers
34 views

Is there a Poisson-Gamma-Gamma model?

An example to elucidate my problem: The total claim amount can be modelled by a Poisson-Gamma model as it is assumed that the events (e.g. accidents) are Poisson distributed and the claims are Gamma ...
2
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0answers
30 views

Gamma distribution different derivations

According to this link - http://cnx.org/contents/2d28fe6a-5000-454e-a2b9-6fbca9e9b56c@3/THE_GAMMA_AND_CHI-SQUARE_DISTR the waiting time of the kth event in a poisson process is gamma distributed. ...
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0answers
23 views

Values for the parameters of a Gamma in a Gamma-Poisson distribution

I need values for the parameters $ \alpha,\beta$ of a Gamma distribution that represent the parameter $\theta$ in a Poisson distribution,so its expected value. I'm using these distribution to ...
1
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0answers
15 views

Error type I for $X_i \sim Exp(\theta)$

Let $ X_i$ be i.i.d $Exp(\theta)$ for i=1,...,4.We want to test $H_0: \theta =6$ versus $ H_1: \theta = 2$. Consider the following test: $$\text{Test: Rejects H_o} \iff \frac{X_1 + X_2}{2}>4.5$$ ...
0
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1answer
55 views

R- Is there a package for modeling Evolving Behavior of eCommerce vistors from click-stream data?

I am referring to the model outlined in an oft-cited paper by Fader and Moe : (https://marketing.wharton.upenn.edu/files/?whdmsaction=public:main.file&fileID=3817) I am trying to predict whether ...
0
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0answers
73 views

Generate mixture model from data with features

I want to build a mixture model from my data, but using features of my data to calculate each component in the model. The data: For each point I have 34 associated features. Each feature is a boolean ...
0
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0answers
37 views

Confusion about nonlinear transformation of gamma and inverse-gamma distributions

I have a question about the variance of a transformed random variable, illustrated by a particular example. Let $X_1, ..., X_n$ and $Y_1, ..., Y_n$ be independent random variables drawn from an ...
1
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1answer
147 views

Specifying a Laplace prior using a Gaussian random variable with Gamma variance

I need to place a Laplace prior on a random variable, however, I want to use a Gaussian distribution whose variance is Gamma(1,1) distributed, i.e., \begin{align} x &\sim N(\mu,\sigma^2)\\ ...
1
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1answer
197 views

Multiplicative error and additive error for generalized linear model

If the following generalized linear model was used, how should I interpret the error term? link function: natural log distribution: Gamma distribution i.e., $\ln E(Y)=X\beta$ and $E(Y)=\exp(X\beta)$ ...
3
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1answer
76 views

How to verify if values are from Gamma distribution?

I have a set of numbers generated from Gamma distribution. How can I verify that these values were all randomly generated from Gamma or satisfy Gamma distribution?
5
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1answer
156 views

How to choose between exponential and gamma distributions

I have same data and I would like to choose a model for it. To start with I fit an exponential distribution and a gamma distribution. Now I wanted to do a simple likelihood ratio test . However, I ...
1
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1answer
109 views

why simulated gamma distributed data have negative kernel values?

I know that Gamma distribution does not allow 0 or negative values. I was doing some simulation and when I write this code in R ...
3
votes
1answer
85 views

Numerical stability of IWLS for Gamma models with log-link

The combination of a $\Gamma$-distribution with the log-link function in a generalized linear model can be a useful model. However, in my experience the iterative weighted least squares (IWLS) ...
1
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1answer
107 views

Why is Gamma(0,0) equivalent to the Jeffreys prior

I'm trying to use some code that includes Gamma priors for Poisson (rate) and Exponential (rate) distributions. I want to make the priors noninformative. I read that using a Gamma(0,0) is equivalent ...