Consistent estimator for parameter from Rayleigh distribution.

Thread starter pirce
Start date Aug 30, 2011
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Distribution Parameter Rayleigh

In summary, a consistent estimator is a statistical method used to estimate a population parameter that becomes more accurate as the sample size increases. For the Rayleigh distribution, this can be calculated using the maximum likelihood estimation method. It is significant because it allows us to estimate unknown parameters with confidence even with limited data. However, there are assumptions that need to be met, such as independent and identically distributed data. Consistent estimators can also be used for other distributions, but the calculation method may vary. It is important to choose the appropriate estimator for each situation.

Aug 30, 2011

pirce

Welcome

Using MLE I found that estimator [tex]\alpha[/tex] parametr from Rayleigh distribution is described by formula
[tex]\hat{\alpha}=\sqrt{\frac{\sum_{n}^{i=1}x_i^2}{2n}}[/tex]
but I can't proof that this estimator is consistent estimator.

Would you be mind and help me with my problem.

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Aug 31, 2011

bpet

Wouldn't you just need to show that E[X^2] = 2a^2 ?

Related to Consistent estimator for parameter from Rayleigh distribution.

1. What is a consistent estimator?

A consistent estimator is a statistical method used to estimate a population parameter that provides increasingly accurate estimates as the sample size increases. In other words, as more data is collected, the estimator will approach the true value of the parameter.

2. How is a consistent estimator calculated for a parameter from the Rayleigh distribution?

A consistent estimator for the parameter from the Rayleigh distribution can be calculated using the maximum likelihood estimation method. This involves finding the value of the parameter that maximizes the likelihood of the observed data being generated from a Rayleigh distribution with that parameter.

3. What is the significance of a consistent estimator for the Rayleigh distribution?

A consistent estimator for the Rayleigh distribution is important because it allows us to estimate the unknown parameter with a certain level of confidence, even if we only have a limited amount of data. This is especially useful in situations where collecting a large amount of data is not feasible.

4. Are there any assumptions that need to be met when using a consistent estimator for the Rayleigh distribution?

Yes, there are a few assumptions that need to be met when using a consistent estimator for the Rayleigh distribution. These include the data being independent and identically distributed, and the data being generated from a Rayleigh distribution in the first place.

5. Can a consistent estimator be used for any other distributions?

Yes, consistent estimators can be used for other distributions as well. However, the method for calculating the estimator may differ depending on the distribution and the specific parameter being estimated. It is important to select the appropriate estimator for each specific situation.