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Stats - mle poisson distribution -- quick question

  1. Jan 7, 2015 #1
    This is probably a stupid question , but,

    It's easy enough to show that the mle of a poission distribution is ## \bar{x}##: ## \hat{ \lambda}= \bar{x} ##

    But,I'm then looking at the generalized ratio test section of my book, multinomial, it esitmates ## \lambda ## for some data by ## \sum \frac{( number X frequency that number occurred)}{ n} ##

    how are these 2 equivalent?

    Thanks in advance.
     
  2. jcsd
  3. Jan 7, 2015 #2

    haruspex

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    It's the same thing. Suppose you have a sample 9, 5, 7, 8, 9, 9. You can get the sum by just adding them, or you can rewrite it as 1 x 5 + 1x 7 + 1 x 8 + 3 x 9.
     
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