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Tagged with sufficient-statistics gamma-distribution
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Usage of Sufficient statistic for a Gamma distribution
I need some help to understand how to utilize sufficient statistic from a data.
Suppose I observe some random process that produces $x\in X$, where all elements have a gamma distribution. As far as I ...
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Completeness of Gamma family
Let $X_1,...,X_n$ has a Gamma$(\alpha,\alpha)$ distribution. Find the minimal sufficient statistics. Is this a complete family?
My attempt: I found the Minimal sufficient statistics is $T(x)=(\...
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minimal sufficient statistics of 1-parameter Gamma distribution
If $x_i \sim Gamma(\alpha, \alpha)$, are the minimal sufficient statistics still $\Pi_i x_i$ and $\sum_i x_i$ (same as when $x_i \sim Gamma(\alpha, \theta)$ where $\alpha \neq \theta$)? My reasoning ...
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Conditional distribution of complete sufficient statistics being ancillary of $\alpha$
Regarding the distribution and statistics as described here, I need to show that the conditional distribution of $\overline{X}$ given $X^*=x^*$ does not depend on $\alpha$. I remember my professor ...
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Gamma distribution: ratio of 2 CSS not containing $\beta$
Let $X_1,...,X_n$ be iid and follow $Gamma(\alpha, \beta)$, where $$f(x,\alpha, \beta)=\frac{x^{\alpha-1}e^{-x/\beta}}{\Gamma(\alpha)\beta^\alpha}$$ I already showed that $\overline{X}$ and $X^*=\...
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Gamma Distribution Sufficient Statistics
I've been asked to show the gamma distribution can be written in the form $p(x|\alpha, \beta) = f(x) g(\alpha, \beta) e^{h(\alpha,\beta)^T T(x)}$ where $T(x)$ is a sufficient statistic.
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I have ...
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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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Jointly sufficient statistic?
A random sample $X_{1},...,X_{n}$ is pulled from a gamma distribution. Are there jointly sufficient statistics based on these observations for the two unknown parameters?
The definition of a gamma ...
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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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