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

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24 views

How to test whether two gamma distributions have the same mean [duplicate]

What is the appropriate test of whether two gamma distributions have the same mean? I've tried t.test, but my sample size is small. ...
1
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1answer
26 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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14 views

Combination of normal and gamma distribution in R

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
73 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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9 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 ...
0
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1answer
53 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
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1answer
40 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
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0answers
61 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
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1answer
73 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
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0answers
59 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
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0answers
38 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
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1answer
69 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
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0answers
29 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
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1answer
77 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
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0answers
56 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
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2answers
40 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
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2answers
73 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
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1answer
20 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
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1answer
33 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 ...
2
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0answers
35 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
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1answer
37 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
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1answer
37 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
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2answers
113 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
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0answers
69 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
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1answer
24 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 ...
12
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2answers
333 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
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34 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: ...
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1answer
50 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
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1answer
83 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 ...
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25 views

Distribution. How to work out what distribution data fits from visual analogue scales

I am having some problems figuring out what distribution my data best fits into. My data is from a 100 mm visual analogue scale, so data points range from 0 to 100. Participants were asked to score ...
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1answer
65 views

Proof that Pareto is a Mixture of Exponential and Gamma

I need to proof that the Pareto random variable is a mixture of the Gamma and Exponential distribution but need help with one part of the proof. Consider $X$ being Exponential with parameter ...
0
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0answers
33 views

Is it possible to fit a multilevel Weibull/generalised gamma survival model?

I am imagining a situation in which I have individual patient survival data from a number of clinical trials of a particular drug. The drug can be used for a wide variety of cancers which have ...
3
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1answer
82 views

Help with proof of the value of skewness of a Gamma distribution

I am kind of at my wits end for this proof. Given $Y$ is Gamma with parameters $\alpha$ and $\beta$, the MGF is given by $(1-\beta t)^{-\alpha}$. I need to find mean, variance and skewness. So I ...
3
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1answer
68 views

Mean service time of a $M/E_2/1$ queueing system?

Consider a $M/E_2/1$ queueing system, where the customer arrival rate is $\lambda$ and the service time distribution has a gamma distribution with parameters $2$ and $\mu$, i.e. with p.d.f. ...
2
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0answers
35 views

AIC doesn't agree with model checking [duplicate]

I have two glm, one with a gaussian distribution and identity link and one with gamma family and log link. The predictors are the same, the only thing that change is the response that in the gaussian ...
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2answers
71 views

Ordered gamma variables led to an ugly integral

Suppose $X_1,X_2,...X_n$ are i. i. d. random variables with p. d. f. $$f(x)=xe^{-x}I_{(0,\infty)}\!(x)$$ and let $Y_1,...,Y_n$ be the order statistics for these variables. a) Find the conditional p. ...
2
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92 views

How to compare models with different distributional assumptions for response variable in GLM?

Let's say I have measurements $Y$ which are all positive, and the distribution seems to be somewhat skewed. I'm modelling $Y$ in GLM framework. Now I could set my GLM using different distributional ...
4
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1answer
94 views

Probability Interval for Gamma Distribution

There is something that I am doing wrong in the exercise below and I would appreciate some help figuring it out. Let $X_1, X_2, \ldots, X_5$ be a random sample from a $\Gamma \left(3,3 \right)$ ...
2
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1answer
58 views

Conditional distribution of a discrete random variable given a continuous one

I can´t solve a conditional distribution problem using the simple Bayes´ Theorem for PDFs. The thing is, I know that X|Y ~ Poisson(Y) and that ...
0
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83 views

Modeling conditional variance (heteroskedasticity) using the gamma distribution

The application is that I want to know how $X$ maps not only to $y$, but to the variance of $y$. I think I've worked out a reasonable solution for doing so using the gamma distribution and the ...
0
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0answers
44 views

How to justify using a gamma distribution for biological image analysis

I am trying to characterize objects within the nucleus of a cell. These objects are brighter than the background, and when I remove the background and map the frequency distribution of the objects I ...
5
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1answer
102 views

Independent gamma and normal distribution

Let $Z = X + Y$ where $X \sim N\left(\mu, \sigma^2 \right)$ and $Y \sim \Gamma\left(k, \theta \right)$ using this parametrization of the Gamma distribution. Also assume $X$ and $Y$ are independent. ...
0
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1answer
165 views

Estimation of the shape parameter of gamma distribution in Winbugs

I want to estimate the shape parameter of gamma distribution in Winbugs. I select gamma distribution as prior for shape parameter. Data set is generated using MATLAB as: ...
2
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1answer
232 views

Weibull Distribution v/s Gamma Distribution

What is the difference between the intuition behind Gamma and Weibull distributions? Is there any relationship between the two densities ? Kindly help.
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44 views

Fitting distributions

I have some data on serving sizes of a particular food (raw oysters), and I am trying to determine what probability distribution I should select to model these data for a risk assessment (RA). The R ...
2
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1answer
48 views

Posterior distribution of the parameter knowing the prior

I have exponentially distributed probability of event $E$ $$P(E|a) = a \exp(-aE),$$ where $a$ is the rate parameter of the exponential distribution. Now the probability distribution for $a$ is a ...
2
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1answer
118 views

Sufficient statistic for function of parameter

Suppose we are estimating $\tau(\theta)=\theta e^{-\theta}$ from $X_1,...,X_n \sim \mathrm{G}(\theta,r)$ (G is the gamma distribution) then it is easily shown that $T=\sum_{i=1}^n \ln(X_i)$ is ...
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109 views

Interpretation of gamma response distribution with inverse link function

Using glm, I have fitted a model with a gamma response distribution and tested all the model diagnostics so everything looks to be a good fit. The only problem is that the model's deviances point to ...
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1answer
103 views

Intuition for Gamma-Poisson / Negative Binomial

I have a data set which intuitively seems Poisson-like, but it's overdispered. So I'm investigating negative binomial. From this question and this page I understand one way of viewing this is to ...
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29 views

The mode of multivariate Gamma distribution

Let X, Y, Z be i.i.d. distributed Gamma random variables. What could the mode of the vector $(X, X+Y, X+Y+Z)$ be? Does the mode of a random vector equal the combination of the marginal modes?