The question I'm referring to comes from Stack Overflow: https://stackoverflow.com/questions/8723652/estimating-number-of-results-in-google-app-engine-query
In short: With $N$ ordered samples of a uniform distribution, how to better estimated $N$ with $k$th sample info?
How to compute the probability that the $k$th fall in a specify interval? For example, Is there a c.d.f for the order statistics?
Is there a better way to estimate the $N$? For example, use three samples 1000th, 2000th, 3000th together?
@whuber: I have read the link you provide, but I still have some question about how to use it correctly.
The probability U(k) falling in the interval [u,u+du] is equaled to
- Is this function a p.d.f or a c.d.f? If it is a p.d.f, could I integrate it to get a c.d.f?
- While N is big (for example 60000), is there any approximation I can use?
- Try to explain this issue more clearly:
We did N(unknown number) random samples for an uniform distribution [0,1]. These samples are collected and sorted (but we still don't know the exactly total number of them). How to guess the N based on the known kth value? For example, if the 10th sample is 0.1, we may guess the N is 10. If the 10th samples is 0.01, we may guess N is 100. But how accurate this guess will be? If I can have more info such as the 10th sample is 0.1 and 20th sample is 0.2, will that help to get better results?