All Questions
Tagged with sufficient-statistics poisson-distribution
12
questions
1
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2
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56
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How does the result $\dfrac{1}{n^T} \dfrac{T!}{\prod_{i = 1}^n Y_i!}$ tell us what distribution $T(\mathbf{Y})$ is?
This follows on from my question here.
I have the following problem:
Let $Y_1, \dots, Y_n$ be a random sample from a Poisson distribution $\text{Pois}(\lambda)$. Recall, the $\text{Pois}(\lambda)$ ...
- 2,096
3
votes
1
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241
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Why is $T(X) = X_{1} + ... + X_{n}$ a sufficient statistics for Poisson $\lambda$ instead of $\frac{1}{n}\sum{X_{i}}$
From Wikipedia:
If $X_{1},\dots, X_{n}$ are independent and have a Poisson distribution with parameter $\lambda$, then the sum $T(X) = X_{1} + ... + X_{n}$ is a sufficient statistic for $\lambda$.
...
- 4,754
1
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1
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969
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Sufficient statistic for the distribution of a random sample of Poisson distribution
Let $X_1,...,X_n$ be a random sample from a Poisson distribution with mean $\lambda$ and $T = \sum_{i=1}^n X_i $ . Show that the distribution of $X_1,...,X_n$ given T is independant of $\lambda$ so ...
- 430
2
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1
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283
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Reparametrization and its effect on sufficient/complete/minimal statistics
Suppose $X_1 \sim Pois(\lambda_1), X_2 \sim Pois(\lambda_2), X_3 \sim Pois(\lambda_1+\lambda_2)$. Separately I can find a sufficient, complete and minimal statistic for each of them. But considering ...
- 3,520
3
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1
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1k
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Sufficient statistic for poisson
Possion have mean and variance of the same value, and obviously the mean of samples is a sufficient statistic
Is the variance of the sample a sufficient statistic as well?
1) If not, how do I prove ...
- 53
1
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1
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1k
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Poisson sufficient statistics problem
I have the following problem:
Let $Y_1, \dots, Y_n$ be a random sample from a Poisson distribution $\text{Pois}(\lambda)$. Recall, the $\text{Pois}(\lambda)$ distribution has the probability function ...
- 2,096
1
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2
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199
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Finding the form $g(T(\mathbf{y}), \lambda) \times h(\mathbf{y})$ for sufficiency statistic examples
I'm studying some notes that present examples of sufficiency:
Let $Y_1, \dots, Y_n$ be i.i.d. $N(\mu, \sigma^2)$. Note that $\sum_{i = 1}^n (y_i - \mu)^2 = \sum_{i = 1}^n (y_i - \bar{y})^2 + n(\bar{y}...
- 2,096
1
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2
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8k
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Sufficient statistic for Poisson in wiki?
In Wikipedia:
https://en.wikipedia.org/wiki/Sufficient_statistic#Poisson_distribution
it says that $X_1+\cdots+X_n$ is a sufficient statistic for the parameter of the Poisson distribution and its ...
- 19
0
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0
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2k
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Explain sufficient statistic for Poisson distribution [duplicate]
The Wikipedia entry on this topic is, to me, very confusing. It states that:
If X1, ...., Xn are independent and have a Poisson distribution with parameter λ, then the sum T(X) = X1 + ... + Xn is a ...
- 4,352
1
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1
answer
85
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Sufficient statistic vector of single parameter?
Can the sufficient statistic for a single parameter be a vector?
In my case, I am finding the sufficient statistics for the Poisson parameter in a HMM mixture. The parameter enters my log likelihood ...
- 163
1
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2
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2k
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Sufficiency of two Poisson disributions
If $X_1,X_2$ constitute a random sample of size n=2 from a Poisson Population show that the mean of the sample is a sufficient estimator of the parameter $\lambda$ .
Since the sum of Poissons is ...
- 1,253
4
votes
0
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166
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Sufficient statistics of posterior (with Poisson data)
Suppose that, for year $t$, the data $y$ is Poisson with mean $a + bt$. Assume also a uniform prior on $(a,b)$. If we have $n$ years of data then I think the posterior for $(a,b)$ will be
\begin{...
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