Questions tagged [inverse-gamma]

The inverse gamma distribution is a right-skew, continuous distribution for a random variables taking positive values.

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Closed form posterior for product of inverse Gamma and Normal distribution

I am currently reading a book about mixture analysis, and in the textbook a posterior for the parameters $\mu1,\mu2,\sigma_1^2,\sigma_2^2$ of a two-component gaussian mixture is derived as follows (S ...
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Why does the inverse gamma distribution look essentially the same when increasing the variance?

I have a function in R which for a given mean $\mu$ and variance $\sigma^2$, spits out the parameters for the shape, $\alpha$, and rate, $\beta$ of the inverse gamma distribution with that mean and ...
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Interpretation of the rate parameter of a Gamma distribution

I am toying with mixture models, especially in a bayesian context and the Gamma (or the inverse Gamma) distribution appears quite often. For example, inverse Gamma is used as a conjugate prior for the ...
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hypothesis testing - gamma distribution

Let W = Y/B0 be a Random variable that has a gamma(2n,1) distribution. [Y has a gamma(2n,B) distribution and W = Y/B]. i) Suppose you want to test H0 : B ≤ B0 against H1 : B > B0 for some B0 > 0. How ...
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Hierarchical Bayesian Regression, Can an Inverse-Gamma distributed Variance look Normal or t?

Using Peter Hoff's book, A First Course in Bayesian Statistical Methods, I used some of my own data to fit a Hierarchical Bayesian Regression following his example. In his book, he utilized a Gibbs ...
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Is there an analytic distribution for the sum of random variables distributed IID inverse gamma?

How about their ratio? I have looked at the related distributions section on Wikipedia and tried playing with the pdf's by hand. I could have been a little more specific about the case that is ...
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Bayesian Linear Model Posterior as Sum of Squares?

As part of a homework, I am asked to do the math from the Normal-Inverse Gamma linear regression model. Starting from priors $N(\beta_0, \sigma^2 A)$ and $IG(\alpha_0, \delta_0)$ and with the help ...
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Excel: Still have to use the normal approximation with GAMMA.INV for high values of alpha?

The GAMMAINV function from Excel 2003 had a propensity for generating NA error messages for high alpha values as the iterative process failed to reach convergence. It was therefore common to use a ...
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Pearson 5/Inverse Gamma/ Double Pareto

My current research deals with landslide size frequency distribution which has been fit to a three-parameter inverse gamma function and a double Pareto function by previous researchers. I am trained ...
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Confidence Interval for Inverse Gamma Distribution

I would like to understand if there exists any method to find confidence interval for the parameters of inverse gamma distribution.
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How to generate random variables from a defined density via R?

Given probability distribution: $f_x(x)=(x+1.5)^{-1.75}e^{-x/400}$, Let $t=x-1.5$. (I want to generate a random set $x$ from this distribution) Generate ...
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Conjugate inverseGamma prior and Multivariate normal?

I do know that inverse gamma is a conjugate prior for univariate normal distribution. I guess it's also a conjugate prior for multivariate normal distribution. I'm trying to get the closed-form ...
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Relationship between inverse gamma and gamma distribution

I have the following posterior distribution for $v$ $$f(v)\propto v^{-p/2}\exp\left(-\frac{1}{v}\frac{s}{2}\right)$$ and so clearly $$v\sim\text{Inverse-Gamma}\left(\frac{p}{2}-1,\frac{s}{2}\right)$$ ...
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Jeffreys prior for inverse gamma distribution

Does anybody have the experience of dealing with Jeffreys prior? I am working with hierarchical model at the moment where the parameter σ^2 from normal distribution is said to be chosen according to ...
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Is a power of an inverse gamma random variable itself inverse gamma?

If $X$ is an inverse gamma distributed random variable, then would $X^p$ also be distributed as inverse gamma? I found someone asked about the square root of inverse gamma, but I didn't find a direct ...
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Thompson sampling with multivariate posterior distribution

I'm implementing Thompson sampling for a multi armed bandit problem (see http://en.wikipedia.org/wiki/Thompson_sampling). The underlying Bayesian model is a Bayesian Linear Regression, which has a ...
I'm trying to calculate the variance of the inverse gamma distribution using the method of movements. According to wikipedia the variance should be: \sigma^2 =\frac{\beta^2}{(\alpha-1)^2(\alpha-2)}\$...