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Statistics beginner here.

I have a sample data set which is Rice distributed, $R \sim R(\nu,\sigma)$. However, I'm interested in fitting $R^2$. According to Wikipedia,

  • If $R ∼ Rice ⁡ ( ν , 1 )$ then $R^2$ has a noncentral chi-squared distribution with two degrees of freedom and noncentrality parameter $v^2$.

I've also learnt that, given a data vector, it was possible to identify the population which generated it via MLE method.

Considering that the dataset has $\sigma \neq 1$

  1. What strategy should I follow for parameter estimation in $R \sim R(\nu,\sigma)$?

  2. Once I have the parameters, how can I make sure that above-mentioned transition to Noncentral $\chi^2$ applies to my dataset?

I apologize in advance if my questions are not well-structured due to my partial understanding.

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1 Answer 1

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I've figured out the solution. Here's the recipy;

  1. Use MLE in $R(\nu, \sigma)$ to obtain $(\overline{\nu}, \overline{\sigma})$
  2. Divide the data set by $ \sqrt{\overline{\sigma}}$ ( Now it has unit variance $R(\nu,1)$ )
  3. $R^2(\nu,1)$ has noncentral $\chi^2$ distribution with two degrees of freedom and noncentrality parameter $v^2$
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