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

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7 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 ...
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1answer
16 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 ...
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0answers
18 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 ...
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0answers
23 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
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1answer
32 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 ...
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0answers
9 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 ...
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0answers
13 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 ...
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1answer
28 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
72 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
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2answers
61 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 ...
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1answer
30 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 ...
2
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0answers
10 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 ...
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0answers
27 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
28 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
12 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
13 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: $$\text{Test: Rejects H_o} \iff \frac{X_1 + X_2}{2}>4.5$$ ...
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1answer
18 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 ...
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0answers
33 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 ...
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0answers
29 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 ...
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1answer
71 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
57 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
69 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?
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1answer
61 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
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1answer
59 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) ...
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1answer
55 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 ...
4
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2answers
166 views

Expectation of a squared Gamma

If a Gamma distribution is parameterized with $\alpha$ and $\beta$, then: $$ E(\Gamma(\alpha, \beta)) = \frac{\alpha}{\beta} $$ I would like to calculate the expectation of a squared Gamma, that is: ...
2
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0answers
60 views

Basic idea of zero inflated two part models(hurdel) and application to big data (machine learning)

I'm currently working on the data which has 90% 0s in response variable. Based on my research, it seems zero inflated models could be a solution to this. However, while I was reading related ...
2
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1answer
29 views

Dirichlet sample by normalising Gamma RVs

I know that if you sample $K$ random variables $(X_1, X_2, \dots, X_K)$ from Gamma distributions using shape parameters $(\alpha_1, \alpha_2, \dots \alpha_K)$ and a scale parameter $\theta = 1$ such ...
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0answers
11 views

Accounting for minimum dependent measure in data when fitting a distribution

I have what is possible a naive question. I am current comparing various models (i.e. distributions). And the comparisons do not involve different distributions but rather how the model is fed the ...
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0answers
20 views

Gamma linear regression, errors with two factor interaction. None with three factor

First off, I am aware I have not enough data to be performing a regression with this number of parameters, lets overlook that for now - I'm interested only in why I get an error with one model, and ...
2
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1answer
91 views

Generalized linear model: link function Power(-1)

During study our of statistics in my psychology coursework, we had to teach ourselves how to use generalized linear models in SPSS (only basic knowledge). For an exam we may also use generalized ...
3
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1answer
65 views

Ratio of correlated sample variances (gamma distributed)

for $N$ samples of two correlated random variables $X \sim N\left(0,\sigma_X^2\right)$ and $Y \sim N\left(0, \sigma_Y^2\right)$ with correlation $\rho$, I am analyzing the ratio of the sample ...
5
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1answer
103 views

Product of Gamma by Beta rv

If $X$ has a beta distribution $ \beta(\alpha,b)$, $Y$ has a gamma distribution $\Gamma (K,\theta)$ and $X$ is independent of $Y$. What is the distribution of the product $P=XY$ . Thanks!
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112 views

Generalized linear model with lasso regularization for continuous non-negative response

I have a big data problem with a large number of predictors and a non-negative response (time until inspection). For a full model I would use a glm with Gamma distributed response (link="log"). ...
1
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1answer
75 views

Issues with regression and prediction

I am having a lot of fun with regression analysis at the moment, and by fun I mean bashing myself repeatedly over the head. I have a set of 200 data points, by filtering on a property of interest, I ...
2
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1answer
104 views

How to fit a mixture of Gamma distributions to the PMF of a discrete distribution?

I have a PMF of some discrete distribution that has been numerically computed. Note that I do not have any samples to work with here, so techniques like Maximum-Likelihood and Expectation-Maximization ...
6
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1answer
93 views

In a Poisson process measured with some efficiency, is the measured count still Poisson?

Situation: Say I have a Poisson process, like radioactive decay, producing R particles per second. I measure with a detector. There is a probability P that a particle will be detected by the ...
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1answer
45 views

Generating gamma random field with given covariance matrix

I have to generate multivariate gamma distributions with given positive-definite covariance matrix. Anyone can suggest me a method? Thanks,
4
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2answers
197 views

Distribution for percentage data

I have a question about the correct distribution to use for creating a model with my data. I conducted a forest inventory with 50 plots, each plot measures 20m × 50m. For each plot, I estimated ...
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47 views

R: Which distribution to use with gbm for gamma distributed data?

When I use GLMs I can use the option family="Gamma" for analysing data consisting of positive real numbers. Also package gbm ...
3
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0answers
241 views

Neyman-Pearson lemma: critical region and hypothesis testing

Let $X_1,X_2,...,X_n$ be i.i.d r.v's with common p.d.f. $$ \mbox f(x)=\frac{x^5e^{-x/\theta}}{5!\theta^6} $$ where $\theta$ > 0. Show that the Neyman-Pearson lemma produces a test of ...
2
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1answer
57 views

Difference of two independent gamma distribution

Given two independent random variables $X\sim\Gamma(s,r)$ and $Y\sim\Gamma(t,u)$, what is the distribution of the difference, i.e. $D=X−Y$? I assume that $s$ and $t$ are integers. How can I obtain the ...
1
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1answer
37 views

How should I construct a prior distribution with a particular kind of count data

For context I will first explain the overall problem that I am working on. I am given a catalog of product names and I am also given a large text dataset that may contain mentions of these catalog ...
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1answer
39 views

Statistical Practices Using Sparse Data: Methods for Approximating Standard Deviation

Suppose I know that for a discrete, non-negative r.v. $X$ that $X | X \geq 1$ has $\mu = 3.3$ while when $X \geq 0$ has $\mu = 2.1$. That is, the subset of the population that already has a value ...
0
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0answers
27 views

Combination of normal and gamma distribution in R [closed]

I have to solve this problem: A machine comes with a 2 year warranty. As a statistician you are told that (i) The total number of hours for which a machine is used over the course of 2 years follows ...
2
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2answers
99 views

Identifying distribution of a variable

Consider a variable that can take both negative and positive values, and that has the following density plot: I am trying to identify the distribution of this variable. The density plot resembles ...
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0answers
49 views

How do I partition variance among nested random effects for non-normal data and an unbalanced design?

I have a dataset of plant drought tolerance values (called TLP_DRY) that I would like to partition variance for among the nested levels Biome/Study site/Species to figure out whether most variation in ...
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1answer
257 views

Why does fitdistr does not work with gamma?

I am tring to find a probability density for some waiting time, but I am having a hard time. Fitdistr does not work with Gamma. Am I missing something? Is there ...
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1answer
95 views

Parametrization of Gamma and Negative Binomial in R

I have some Poisson data {${y_1,...,y_n}$} and a Gamma prior, and I wish to construct a predictive posterior distribution. As I understand, if my Gamma hyperparameters are $\alpha$ (the prior number ...
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0answers
111 views

Standard error of mean of gamma distribution

I am trying to determine whether the means of two Gamma distributions are significantly different. To do this, I am trying to determine the Wald Statistic as ...