Using the second moment to estimate parameter $p$ for a Geometric distribution, it is unbiased or not? If it...
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Using the second moment (method of moment) to estimate parameter $p$ for a Geometric distribution with $mu=1/p$ and $var = 1/p^2$, it is unbiased or not? If it is biased, how to compute the bias?
Here is what I did.enter image description here
probability-theory probability-distributions
asked Nov 23 at 3:59
Weile Chen
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Using the second moment (method of moment) to estimate parameter $p$ for a Geometric distribution with $mu=1/p$ and $var = 1/p^2$, it is unbiased or not? If it is biased, how to compute the bias?
Here is what I did.enter image description here
probability-theory probability-distributions
asked Nov 23 at 3:59
Weile Chen
11
There is a direct relationship between the second moment and p. The question makes sense only if the second moment is an estimate. Then you need to know the statistics that led to the estimate of the second moment.
– herb steinberg
Nov 23 at 4:35
@herbsteinbergThanks for replying me. I have edited the question and specified something, would you like to like it again? Thanks in advanced.
– Weile Chen
Nov 23 at 13:47
You approach seems to be correct. In general, an unbiased estimate of the variance uses division by N-1 rather than division by N (sample size). This approach applies to any distribution where the variance is finite. en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation
– herb steinberg
Nov 23 at 18:09
@herbsteinbergThanks for helping me!
– Weile Chen
Nov 24 at 19:46
add a comment |
up vote
0
down vote
favorite
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up vote
0
down vote
favorite
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1
Using the second moment (method of moment) to estimate parameter $p$ for a Geometric distribution with $mu=1/p$ and $var = 1/p^2$, it is unbiased or not? If it is biased, how to compute the bias?
Here is what I did.enter image description here
probability-theory probability-distributions
asked Nov 23 at 3:59
Weile Chen
11
Using the second moment (method of moment) to estimate parameter $p$ for a Geometric distribution with $mu=1/p$ and $var = 1/p^2$, it is unbiased or not? If it is biased, how to compute the bias?
Here is what I did.enter image description here
probability-theory probability-distributions
probability-theory probability-distributions
asked Nov 23 at 3:59
Weile Chen
11
asked Nov 23 at 3:59
Weile Chen
11
edited Nov 23 at 13:45
asked Nov 23 at 3:59
Weile Chen
11
asked Nov 23 at 3:59
Weile Chen
11
asked Nov 23 at 3:59
Weile Chen
11
11
There is a direct relationship between the second moment and p. The question makes sense only if the second moment is an estimate. Then you need to know the statistics that led to the estimate of the second moment.
– herb steinberg
Nov 23 at 4:35
@herbsteinbergThanks for replying me. I have edited the question and specified something, would you like to like it again? Thanks in advanced.
– Weile Chen
Nov 23 at 13:47
You approach seems to be correct. In general, an unbiased estimate of the variance uses division by N-1 rather than division by N (sample size). This approach applies to any distribution where the variance is finite. en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation
– herb steinberg
Nov 23 at 18:09
@herbsteinbergThanks for helping me!
– Weile Chen
Nov 24 at 19:46
add a comment |
There is a direct relationship between the second moment and p. The question makes sense only if the second moment is an estimate. Then you need to know the statistics that led to the estimate of the second moment.
– herb steinberg
Nov 23 at 4:35
@herbsteinbergThanks for replying me. I have edited the question and specified something, would you like to like it again? Thanks in advanced.
– Weile Chen
Nov 23 at 13:47
You approach seems to be correct. In general, an unbiased estimate of the variance uses division by N-1 rather than division by N (sample size). This approach applies to any distribution where the variance is finite. en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation
– herb steinberg
Nov 23 at 18:09
@herbsteinbergThanks for helping me!
– Weile Chen
Nov 24 at 19:46
There is a direct relationship between the second moment and p. The question makes sense only if the second moment is an estimate. Then you need to know the statistics that led to the estimate of the second moment.
– herb steinberg
Nov 23 at 4:35
There is a direct relationship between the second moment and p. The question makes sense only if the second moment is an estimate. Then you need to know the statistics that led to the estimate of the second moment.
– herb steinberg
Nov 23 at 4:35
@herbsteinbergThanks for replying me. I have edited the question and specified something, would you like to like it again? Thanks in advanced.
– Weile Chen
Nov 23 at 13:47
@herbsteinbergThanks for replying me. I have edited the question and specified something, would you like to like it again? Thanks in advanced.
– Weile Chen
Nov 23 at 13:47
You approach seems to be correct. In general, an unbiased estimate of the variance uses division by N-1 rather than division by N (sample size). This approach applies to any distribution where the variance is finite. en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation
– herb steinberg
Nov 23 at 18:09
You approach seems to be correct. In general, an unbiased estimate of the variance uses division by N-1 rather than division by N (sample size). This approach applies to any distribution where the variance is finite. en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation
– herb steinberg
Nov 23 at 18:09
@herbsteinbergThanks for helping me!
– Weile Chen
Nov 24 at 19:46
@herbsteinbergThanks for helping me!
– Weile Chen
Nov 24 at 19:46
add a comment |
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There is a direct relationship between the second moment and p. The question makes sense only if the second moment is an estimate. Then you need to know the statistics that led to the estimate of the second moment.
– herb steinberg
Nov 23 at 4:35
@herbsteinbergThanks for replying me. I have edited the question and specified something, would you like to like it again? Thanks in advanced.
– Weile Chen
Nov 23 at 13:47
You approach seems to be correct. In general, an unbiased estimate of the variance uses division by N-1 rather than division by N (sample size). This approach applies to any distribution where the variance is finite. en.wikipedia.org/wiki/Unbiased_estimation_of_standard_deviation
– herb steinberg
Nov 23 at 18:09
@herbsteinbergThanks for helping me!
– Weile Chen
Nov 24 at 19:46