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

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31 views

What distribution has this non-central Chi-Squared -like moment generating function?

I'm new here so please criticize errors! My moment generating function looks like this (after some tidying): $E[e^{wY(t)}] = \frac{1}{\left(1-2\theta(t) w\right)^{k/2}} ...
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1answer
22 views

MLE of Gamma when only given observations [closed]

i've been given 10 observations of X, where X is a random variable. the observations are 141 16 46 40 351 259 317 1511 107 567 and now given they are gamma distributed, how do you find the MLE using ...
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22 views

R - fitting a gamma distribution given the CDF?

I'm trying to develop a prediction model of the success or failure of a test run based on its current running time (in my data, from observation, the longer a test runs the more likely it is to fail). ...
2
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0answers
42 views

Estimating medians and modes of skewed distributions using GLMs

Edited question (less vague hopefully) I am wondering why for generalized linear models with Gamma, Poisson and Negative Binomial distributions that there appears to be no discussion about estimating ...
0
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1answer
38 views

Gamma parameterization and how to randomly generate $\sigma$'s for use in `rnorm(n, $\mu$, $\sigma$)`

Say I have a normal distribution parameterized with a mean ($\mu$) and precision ($\tau = 1/\sigma^2)$. In JAGS, I would specify a prior for $\tau$ as ...
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0answers
18 views

Weibull vs Gamma Distribution

I have a set of experimental data which comprises distances between successive points: Under most contexts, our data fits well with a γ-distribution. However, in a few distinct cases, the γ is no ...
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0answers
23 views

Prediction Error for a Poisson Process

So I have a fleet of cars. I've sampled their breakdown rates (per hour driven) for the last 10 years. Their breakdown rate follows the gamma distribution. I am trying to do two things. Predict ...
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1answer
43 views

Testing a vector for gamma distribution

I asked this question on stackoverflow before but I was told that I better ask this question here! So... I have a problem with a certain vector. I'm tying to find out IF it's gamma-distributed and (if ...
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15 views

derive loss function for gamma regression

In the R package mboost there is a family called "GammaReg" which implementes "negative Gamma log-likelihood with logarithmic link function". Still, I don't really ...
4
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1answer
56 views

Name of rv that results from integrating over gamma in gamma product prior on poisson

If $d$ is an arbitrary random variable with parameter(s) $\Psi$ and positive support, $g \sim \mathrm{Gamma}(\alpha, \beta)$, $x \sim \mathrm{Poisson}(gd)$, and $g$ and $d$ are independent, then ...
0
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1answer
43 views

GLMM with Gamma distribution vs. Gaussian distribution with log transformation

Is there really a difference in result if I use a GLMM with Gamma distribution vs. a model with a Gaussian distribution with log transformation? If so, how do I choose between the two methods? See ...
2
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1answer
27 views

Backtransform coefficients of a Gamma-log GLMM

I am analysing data from an exclosure experiment, this means for several years, goats were kept outside a fence and inside the fence, plants could grow without being grazed. Outside the fence, grazing ...
0
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1answer
56 views

Fit gamma distribution to dataset with R [closed]

I have this dataframe below: ...
2
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1answer
37 views

Assessing deviation from the mean without Chebyshev's inequality

I have a set of experimental data which comprises distances between successive points: And a simulation which attempts to recapture the experimental data by choosing points at random and ...
0
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0answers
29 views

Help with highly skewed data

I have a response variable which is highly skewed and has a high percentage of zeros. I am looking for some guidance around what modeling technique to use and the process to follow. As an ...
1
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1answer
22 views

Using sample standard deviation as the dependent variable in a Gamma regression

I need to do a regression with sample standard deviation of a distribution as the dependent variable. The approximation the number of trials is the independent variable. My question is: what should ...
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0answers
47 views

Relationship between the Gamma and Beta distributions

I was looking at a proof of the following fact Let $X \sim \mbox{Gamma}(\alpha, 1)$ and $Y \sim \mbox{Gamma}(\beta, 1)$ where the paramaterization is such that $\alpha$ is the shape parameter. Then ...
5
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1answer
278 views

How can you convert a gamma distribution into normal distribution? [closed]

A region has 200 stores served by a single distribution center. Demand of X during lead time (the time interval between order placement of X and arrival of X) at each store is forecasted to be gamma ...
0
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0answers
42 views

Fitting Data with Ties Using unique() Walk-Around and ks.test

I'm looking for a distribution that best fits my data. Looking at the frequency plot, seems like the distribution could follow a Gamma or Weibull distribution. With that in mind, I use the ...
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1answer
70 views

Hazard function of a gamma distribution

The system we are working on is biological, more specifically the distribution of specific events across a chromosome. This can be thought of as 1D array (the chromosome) across which points can be ...
1
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1answer
68 views

Intuitive meaning of the limit of the hazard rate of a gamma distribution

For a Gamma distribution with shape parameter $\alpha >1$ and scale parameter $\beta > 1$, one can show that its hazard rate function $h$ is increasing and satisfies \begin{equation} ...
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2answers
51 views

Square of gamma random variable [duplicate]

If i have a random variable with distribution $X \sim \Gamma(\alpha,\beta)$ then what would be the distribution of $Y = \lambda X^2$ (with $\lambda$ a scaling factor)? Can I say that $Y$ will follow a ...
3
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1answer
31 views

Must the response variable be gamma distributed to appropriately use a gamma-log model?

I'm responsible for challenging a gamma model with log link. The developer claims that an assumption of the gamma-log generalized linear model is that the response variable, in this case average ...
4
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1answer
56 views

Attainable bounds for correlations for Gamma random variables?

I'd need to know if it's possible to reach [-1,1] bounds with Pearson's correlation with a generic pair of Gamma random variables. The problem as you may imagine is there's no known closed form for ...
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0answers
55 views

Transform sum of gamma distribution to chi square distribution

Let's say that I have a random sample $Y_1, Y_2, \dots, Y_n \sim\Gamma(\alpha, \theta)$. I can work out using the moment generating function that the distribution of $\sum Y_i$ is $\Gamma(n\alpha, ...
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12 views

Distribution of dispersion submodel

In double generalized linear models where we assume $y$ follows an exponential dispersion model, where the mean can be modelled as $$g(\mu_i)=x_i^T\beta,$$ and the dispersion $(\phi)$ can be modelled ...
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0answers
29 views

bayes estimate possion distribution function

Let {X\, ...,Xn) be random sample from random variable which has Poisson distribution with parameter A. Assume that the prior distribution A for is Gamma(1, 1) and that you have observed sample of ...
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0answers
18 views

Distribution of the duration of a markov-process in a specified state during a specified time

I have a continuous time markov chain with two states $A$ and $B$. The transition rate $A\rightarrow B$ is $\lambda$ and $B\rightarrow A$ is $\mu$. Imagine that $P(X{t_0}=A)=1$ (the process starts in ...
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63 views

Posterior predictive for Gamma distribution with unknown scale and shape

I have a question that needs clarification. The posterior predictive distribution can be described as the distribution that a new i.i.d. data point $\tilde{x}$ would have, given a set of $N$ existing ...
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45 views

Poisson/Negative Binomial/Gamma log-link for continuous dependent variable (scale DV)

In my research about sport injuries in football, I am trying to obtain Incidence Rate Ratios (IRR) comparing my categories with the reference category. I have number of days a player was absent due to ...
2
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1answer
75 views

Gamma Distribution and Life of Component?

I came across an old exam question as follows: If the life of one computer component (in years) has Gamma distribution with mean $6$ and variance $18$, how can we find the probability that this ...
1
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1answer
50 views

Independence-Metropolis-Hastings Algorithm

IMHA is an importance-sampling version of MCMC, where the proposal is drawn from a fixed distribution g. Usually, g is chosen to be an approximation to f. The acceptance probability becomes ...
3
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1answer
126 views

Zero-inflated Poisson and Gibbs sampling, proofs and sampling

I am trying to figure out zip-inflated Poisson (ZIP) model. In this model, random data $X_1, .., X_n$ are of the form $X_i=R_iY_i$, where the $Y_i$'s have Poisson distribution ($\lambda$) and the ...
5
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1answer
316 views

Distribution of the quotient of two gamma random variables with different rate parameters?

I have a question about how to derive the distribution of the quotient of two random gamma variables drawn from two different Gamma distributions with the same shape, but different rates. For example, ...
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119 views

Most Powerful Test and Rejection Region of Gamma Distribution

Let $X_1,\ldots,X_n$ be a random sample from a Gamma $(\alpha,\beta)$ population, where $\beta>0$ is a known constant. The rejection region of the most powerful test for $H_0:\alpha=1$ against ...
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1answer
119 views

Test if two gamma distributed populations are different

I have data from two populations of different sizes. Both have Gamma distributions with different shapes and scales (as estimated in r): fitdistr(x/10000, "gamma") #186 members shape 0.586219900 ...
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50 views

combining samples from different gamma distributions normalized by means

I'm trying to figure out what to do with some experimental data from a psychoacoustic experiment. The data come from multiple subjects and are approximately gamma distributed; I am treating them as ...
2
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1answer
84 views

Construct the likelihood if measurement uncertainties have a Gamma distribution

I want to construct my likelihood. General case: If my data do come from a line of the form $y = mx + b$ and the uncertainties are normally distributed with mean zero and known variance ...
2
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0answers
128 views

Modeling discrete count data with a gamma distribution

I've encountered a statistical model in which discrete count data are modeled with a gamma distribution (supported on nonnegative reals). The model relies on the property of the gamma that a sum of ...
2
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0answers
47 views

Compound Poisson Distributions: When, Why, and How To Split the Problem

I've just stumbled upon the Compound Poisson Distribution (CPD) and it seems to be precisely what I need. For the purposes of this post, let's suppose I have a store that sells many items of ...
0
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0answers
59 views

Fitting gamma distribution to data set with one zero observation

I am using maximum likelihood estimation to fit a gamma distribution to shelf life data. Specifically, the data I have is the time (in days) between the day a product was sold and the day the first ...
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13 views

likelihood and gibbs for univariate UE model

This is the first time when i post something here. I would like to ask how can i compute the likelihood of the following model? i put only the product of the densities and that is it? I think the ...
2
votes
1answer
92 views

GLM with Gamma distribution of errors: negative residuals?

I'm trying to understand how the Gamma distribution, which is always positive, is used to describe errors when using a GLM. In practice, errors can be negative, as I get negative residuals when ...
0
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0answers
44 views

When to pick Scale or Rate for Gamma/ Inverse Gamma parameters? Picking up the correct conjugate prior

I am very confused about the following problem. I think my question is both theoretical and applied. When I model a Gamma distribution, when do I use this model, so I guess Inverse Gamma: ...
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1answer
40 views

Gamma Distribution with Percentages

I am dealing with a set of data that appears to follow a gamma distribution or a lognormal distribution but the only issue is that the data set is in percentages and both of these distributions don't ...
0
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0answers
30 views

Bivariate gamma distribution with one parameter marginal

Suppose two random variables X,Y>0, have a joint gamma distribution. Its marginal for X is G(a,b) and that for Y is G(a,c). For identification purposes, normalization is needed.does anyone know if ...
2
votes
1answer
122 views

Expected value of Y = (1/X) where $X \sim Gamma$

I'm having some confusion over this statement here. Let $T_i \sim Exp(\lambda + \theta)$ and if they are all iid then $\sum_n T_i \sim Gamma(\alpha = n, \beta = 1/(\lambda + \theta))$ I want to find ...
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1answer
227 views

Sufficient statistic for a Gamma distribution

I am confused about the steps I need in order to solve the equation below. I must use conditional distribution (and NOT the factorization theorem). Q: $X_1, . . . , X_n$ is a random sample from a ...
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99 views

How to find the appropriate family for glm models?

As suggested over at stackoverflow I poste the question here instead: I have a data frame with three variables, where "Resp" is my response variable (count data), F1 is a categorical predictor (4 ...
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0answers
28 views

To obtain Pearson type III parameters and shift value

How to obtain Pearson type III parameters and shift value? I am using R and if you can give me an instruction, it would be helpful. I have used pearsonFitML function from PearsonDS package, but I can ...