# Tagged Questions

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

29 views

### False rejection rate of simulated values in R [on hold]

I need to create a table of Estimated Rate of False Rejection of Null Hypothesis in testing at the Nominal $0.05$ level for selected $n$ and $k$ in simulating values from the Gamma Distribution with ...
14 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 $\mu$, ...
9 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 ...
13 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 ...
45 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 ...
7 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 ...
92 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 ...
27 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 $$X\sim \frac{2m^m}{\Gamma(m)\Omega^m} x^{2m-1}e^{-\frac{m}{\Omega}x^2}$$ ...
24 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 ...
24 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 ...
67 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 ...
19 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 ...
25 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 ...
22 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 ...
27 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 ...
34 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 ...
10 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 ...
24 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 ...
30 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: ...
85 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 ...
75 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 ...
35 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 ...
22 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 ...
31 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 ...
29 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. ...
19 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 ...
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: $$\text{Test: Rejects H_o} \iff \frac{X_1 + X_2}{2}>4.5$$ ...
28 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 ...
47 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 ...
30 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 ...
89 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)\\ ...
100 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 $E(Y)=\exp(X\beta)$ ...
72 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?
79 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 ...
67 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) ...
71 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 ...
170 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: ...
62 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 ...
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 ...
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 ...
23 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 ...
106 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 ...
70 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 ...
109 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!
118 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"). ...
81 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 ...
112 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 ...
97 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 ...
47 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,
255 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 ...