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

learn more… | top users | synonyms

2
votes
1answer
51 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?
1
vote
1answer
39 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
42 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
vote
1answer
39 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
votes
2answers
163 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
votes
0answers
46 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 ...
1
vote
1answer
25 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 ...
0
votes
0answers
9 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 ...
0
votes
0answers
11 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
votes
1answer
75 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
votes
1answer
51 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
votes
1answer
94 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!
3
votes
0answers
79 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
vote
1answer
71 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
votes
1answer
77 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
votes
1answer
87 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 ...
0
votes
1answer
33 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
votes
2answers
121 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 ...
1
vote
0answers
29 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
votes
0answers
203 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
votes
1answer
51 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
vote
1answer
35 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 ...
1
vote
1answer
38 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
votes
0answers
23 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
votes
2answers
94 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 ...
0
votes
0answers
38 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 ...
1
vote
1answer
126 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 ...
1
vote
1answer
78 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 ...
1
vote
0answers
85 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 ...
2
votes
1answer
129 views

Analysis of variance with Weibull or Gamma distributions

I have been trying to find a method to analyse variance on Weibull and/or Gamma distributions but a Google search for anovar Weibull "gamma distribution" yields ...
4
votes
0answers
80 views

Can likelihood be changed when the prior changes?

I have a data which follows gamma distribution and want to know the uncertainty of the parameters of this data. $\text{Data} \sim \text{Gamma} (\alpha, \beta)$ Parameters $\alpha \sim \text{Gamma} ...
1
vote
0answers
62 views

Asymptotic Distribution of beta distribution parameter

I am trying to create a t-interval for the first shape parameter of a Beta distributed variable based on a random sample. $ f(x;\theta,\beta) = ...
2
votes
1answer
86 views

estimate a distribution parameters only by data mean and std. dev

I need to estimate a truncated gamma distribution parameters (shape , scale). But, I only know the data mean and std. dev. I do not know the data set. Given the mean and std. dev. of a data set from ...
1
vote
0answers
43 views

Error of data fitting by gamma.fit() in Python

I need to find gamma fit for data in Python 3.2. param = gamma.fit(samp) // samp is a list of floating point numbers I got error: ...
2
votes
1answer
118 views

How to find the distribution of data with data fitting

I need to do data fitting to find the distribution of given data. I need to find the PDF function of the distribution. I can use data fitting functions in MATLAB and Python. It looks like a ...
2
votes
0answers
103 views

Rejection sampling from a Gamma distribution using a Cauchy proposal

i'm trying to find the parameters $ \gamma,x_0$ of a standard Cauchy distribution : $$T(x)= \frac{1}{(\pi \gamma (1+(\frac{x-x_0}{\gamma})^2))} $$ To perform rejection sampling from a gamma ...
0
votes
2answers
61 views

performing parameter updates on Gamma distribution

I have the following form for a joint distribution $$ P(w, \lambda, \phi \vert y) = P(\phi) \times P(w \vert \lambda) \times P(\lambda) \times \prod_{i=1}^{N}P(y_i \vert w_i, \phi, \lambda) $$ I ...
2
votes
2answers
100 views

Prior Gamma distribution: Select appropriate alpha given beta and median

I am trying to programatically select a prior distribution from the Gamma family of distributions. The primary criteria that I need to satisfy is that the median of the distribution should be a given ...
0
votes
1answer
28 views

updating posterior parameters when involving conditioning

I have a setup where the joint posterior is written as: $$ P(w, \lambda, \phi \vert y) = P(\phi) \times P(w \vert \lambda) \times P(\lambda) \times \prod_{i=1}^{N}P(y_i \vert w_i, \phi, \lambda) $$ ...
1
vote
1answer
43 views

Updating the hyper parameters for conjugate distributions

I have a joint distribution which can be written down as follows: $$ p(\Theta | D) \propto p(D|\Theta) \; p(w|\lambda) \; p(\lambda) \; p(\phi) $$ where $\Theta = \{w, \lambda, \phi\}$. The prior ...
4
votes
0answers
87 views

Gamma regression with weights using glm

Is there anyway to give weights to a gamma regression so that the variance is allowed to be different, dependent on a particular parameter(in this case sampling event)? When I try to run my code : ...
2
votes
1answer
61 views

Calculating a marginal distribution for the joint density distribution of an exponential distribution with a rate given by a Gamma distribution

This is a follow-up question from one I asked over at MathOverflow: http://mathoverflow.net/questions/158806/is-there-a-simple-closed-form-solution-for-the-joint-density-distribution-of-an The ...
0
votes
1answer
56 views

Interpreting estimates of a Gamma distribution

I have 399 claim amount of data, i want to fit them using a Gamma distribution. I have done so in Matlab software However i am getting this as my result: [phat,pci] = gamfit(data) phat = ...
2
votes
2answers
493 views

Manually fitting a mixture distribution in matlab

I am trying to fit a mixture model containing a gamma and an exponential distribution: The general form, using the pdfs, is: p * gammapdf + (1-p) * exponentialpdf. The pdfs for the Gamma and ...
2
votes
0answers
130 views

R codes for Tweedie compound Poisson gamma [closed]

I have modeled claim frequency data using Poisson regression and claim amount using gamma. I have seen the Tweedie compound Poisson gamma distribution used to model aggregate claim data. I am quite ...
2
votes
1answer
27 views

SUM of AICc vs SUM of LL and then AICc

I have a technical question concerning calculating AICc for two possible models. For the data set I am working with there are 12 subjects and 10 phases of the experiment. Two different models, a ...
13
votes
2answers
585 views

Which has the heavier tail, lognormal or gamma?

(This is based on a question that just came to me via email; I've added some context from a previous brief conversation.) Last year I was told that the gamma distribution is heavier tailed than the ...
0
votes
0answers
72 views

Model selection in Gamma GLM with identity link

I have used Gamma distribution in my GLM with identity link. I want to do backward model selection with drop1 command in R as described in Zuur, 2009. But I get this warning message: ...
0
votes
1answer
61 views

Parameters with categorical and gamma distributions in posterior distribution

I'm following a very good IPython notebook (the whole list can be found here) in which some sampling techniques are explained. However, I don't understand the use of a categorical variable in a change ...
3
votes
1answer
161 views

How do you estimate the predicted probability of an integer value from a negative binomial regression equation?

I'm trying to estimate the predicted probabilities of an observation being a particular integer, $y$, after a negative binomial regression model. Long's Regression models for categorical and limited ...