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

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30 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 ...
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1answer
23 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
8 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
7 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
65 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
43 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
93 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
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69 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"). ...
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1answer
66 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
57 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
79 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
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1answer
29 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
98 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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16 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
188 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
48 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 ...
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1answer
33 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
35 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 ...
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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
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2answers
90 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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34 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
117 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
73 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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81 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
123 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 ...
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74 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} ...
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58 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
81 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 ...
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41 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
112 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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98 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
59 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
97 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 ...
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1answer
26 views

updating posterior parameters when involving conditioning

I have a setup where the joint posterior is written as: $$ P(w, \lambda, \phi \vert y) = P(\phi) \times P(w \vert \lambda) \times P(\lambda) \times \prod_{i=1}^{N}P(y_i \vert w_i, \phi, \lambda) $$ ...
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1answer
39 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
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74 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
52 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
55 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
427 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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112 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
26 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
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2answers
529 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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0answers
64 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
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1answer
57 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
142 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 ...
0
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0answers
30 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
106 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
45 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
129 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
88 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. ...