# 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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### How to write a gamma equation from these coefficients R?

A similar question is out there enter link description here, but I find that the answer was not comprehensive enough to cover other scenarios. ...
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### Derive cauchy distribution as a scale mixture of normal distributions

I doing Bayesian modelling these days. I found that cauchy distribution can be written as a scale mixture of normal based on following source. Link So I started to derive this. Somehow, I am not ...
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### Bayesian estimation of the variance

The mean of the Gamma distribution is $\alpha/\beta$, while the mean of the Inverse Gamma is $\beta/(\alpha-1)$. Similarly, the mode of the Gamma is $(\alpha-1)/\beta$, but the mode of the Inverse ...
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### Merits of reparameterizing the Gamma and inverse Gamma

Wikipedia states that the PDFs for the Gamma distribution is: $$f(x|\alpha,\beta) = \frac{\beta^\alpha}{\Gamma(\alpha)}x^{\alpha-1}\exp(-\beta x)$$ However, in Rasmussen 2000, the pdf for the ...
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### Effect of sample reduction in normal-inverse gamma

I am trying to interpret/explain a result that I obtained while generating a posterior distribution, and maybe add some informations to what I had so far. The environment that I am using is the ...
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### Variation on inverse gamma: 1/X^r ~ inv_Gamma(?, ?)

(it's the first time that I write here, sorry if miss some convention) If X ~ Gamma(a, b) then 1/X ~ inv_Gamma(a, b) therefore if If X ~ Gamma(a, b) then 1/X^r ~ inv_Gamma(?, ?) My brain is ...
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### Gamma likelihood with InverseGamma prior

I've got a gamma likelihood $\Gamma(\tau_c | \alpha_k, \frac{\alpha_k} {\tau_k})$ (parameterized with shape and rate) with an InverseGamma prior $IG(\tau_k|a_0, b_0)$. I know that the resulting ...
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### inv-gamma distribution as prior for multivariate normal distribution

it's known the conjugate priors for multivariate normal distribution are the normal & inverse-whishart distributions. but i'm interest in very specific case where the correlation matrix is $R$ ...
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### What is the correct to model inverse gamma distribution [closed]

I tried to use below R code to model inverse gamma distribution (alpha=1,beta=1). However, the resulting histogram is not alike the one plotted in the wiki. Could anyone provide any hint about this? ...
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### Calculating the parameters of a Normal distribution using alpha and beta from Inverse-gamma (conjugate prior)

How is it possible to calculate the variance $\sigma^2$ for the Normal distribution if only $\alpha$ and $\beta$ (based on data) from the Inverse-gamma distribution are available? I followed the ...
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### Why is Inverted Gamma (3,0.0005) a diffuse prior when variance of this random variable is small?

A few times I came across the statement that an Inverted Gamma (3, 0.0005) prior for the variance is quite diffuse but proper. Hence, my understanding is that the prior variance of this random ...
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### Sampling from an Inverse Gamma distribution

I am using Gibbs sampling in the MCMC estimation of a stochastic volatility model. One of the posterior distributions is an Inverse Gamma distribution.I was struggling with the sampling procedure or ...
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### Python Bayesian invgamma.rvs - joint posterior of normal distribution sampling

(My question is inspired by this blog post: The Bayesian analysis of normal distributions with Python. If you read it, you will get a good background on what I am asking.) I am trying to model the ...
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### Show that $\frac{X}{X+Y}\sim Beta(\alpha,\beta)$ [duplicate]

Let IG denote Inverse-Gamma distribution Inverse-Gamma. If $X\sim IG(\alpha,1)$ and $Y\sim IG(\beta,1)$. Show that $\frac{X}{X+Y}\sim Beta(\alpha,\beta)$ I tried with jacobian transformation ...
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### Inverse gamma distribution definition

Wikipedia says the pdf for the gamma function is: $X \sim \operatorname{Gamma}(\alpha,\beta) \implies \Pr(X=x) \propto x^{\alpha-1}e^{-\beta x}$ If $Y = 1/X$, then \[ \Pr(Y=y) = \Pr(X=1/y) \...
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### Posterior distribution of linear regression with normal and inverse gamma prior

If I have the following model: $$y\sim N_n(X\beta, \sigma^2 I_n)$$ with prior distributions: $$\beta\sim N_n(\beta_0, B_0)$$ and $$\sigma^2 \sim IG(\alpha_0/ 2, \delta_0/2)$$ What would be the ...
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### Is this an Inverse Gamma? [duplicate]

My professor wrote in an assignment that a random variable with an Inverse-Gamma 1 distribution has density function f_{ig}(\sigma|d,s) = C_g^{-1}(d,s)\cdot \sigma^{-(d+1)}\cdot \exp\left(-\frac{1}{...
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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 ...
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 ...