- #1

- 15

- 0

f(x;p)={(lnp)^x}/px! for x=0,1,...; p>1 and 0 otherwise

Find CRLB for p?

My problem is finding E[x] which is somekind of maclaurin series but can't figure out which one?

Please any suggestions?

Thanks

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In summary, the conversation is about finding the CRLB for a distribution with a given probability density function and parameter, and the difficulties in finding the expected value of the distribution. The conversation includes a suggestion to use a Maclaurin series to solve the problem. Eventually, the expected value is determined to be lnp, and the conversation ends with a thank you.

- #1

- 15

- 0

f(x;p)={(lnp)^x}/px! for x=0,1,...; p>1 and 0 otherwise

Find CRLB for p?

My problem is finding E[x] which is somekind of maclaurin series but can't figure out which one?

Please any suggestions?

Thanks

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- #2

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What expression do you have for E[x]? You need to show more work for us to see where you're getting stuck.

- #3

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Once I have the expected value E[X] of this distribution I will be able to find the CRLB as well which is defined to be in this case

1/(n*[d/dp ln f(x;p)]^2

Any help is appreciated

- #4

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- #5

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- #6

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sum of z^k/k! is e^k, so is it sum of z^k/(k-1)! will be e^(k-1)?

- #7

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neznam said:sum of z^k/k! is e^k, so is it sum of z^k/(k-1)! will be e^(k-1)?

Sum of z^k/k! is e^z. Try that again.

- #8

- 15

- 0

Ok i think i got it

E[x]=[(lnp)/p]*e(lnp)=lnp

Thanks so much

E[x]=[(lnp)/p]*e(lnp)=lnp

Thanks so much

The Cramér-Rao lower bound (CRLB) for p is a theoretical lower limit on the variance of unbiased estimators of a parameter p in a statistical model. It provides a benchmark for the best possible performance of unbiased estimators and can be used to evaluate the efficiency of different estimation methods.

The CRLB for p is typically calculated using the Fisher information, which is a measure of the amount of information that a sample of data provides about the parameter p. The CRLB is then derived by taking the inverse of the Fisher information matrix.

The CRLB is important because it helps to determine the minimum achievable variance for an unbiased estimator of a parameter. This can be used to evaluate the efficiency of different estimation methods and to compare the performance of different estimators.

The Maclaurin series is a special case of the Taylor series, which is a mathematical representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point. In the Maclaurin series, the single point is chosen to be 0.

The Maclaurin series can be used to find the expected value (E[x]) of a function by taking the first derivative of the function at 0 and multiplying it by x, and then taking the second derivative at 0 and dividing it by 2 factorial and multiplying it by x^2, and so on. The sum of these terms will give the expected value of the function at x=0.

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