10.09.2014
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Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. I have a large population of size $n$ from an unknown continuous random variable $X$, and I do not know the underlying distribution of $X$.
I have found the following discussion in Wikipedia which is independent of the number of population.
I have also found some methods to determine sample size for data to be analyzed by nonparametric tests.you don't have to make any assumption about the distribution of the values. There is a substantial difference between the answer to this question for a single value of $c$ and an answer that is valid for more than one value.
About your update: yes, this is what I said, if you count the sample values $x_i$ such that $x_i \leq c$ then this count has a binomial distribution.
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Is it possible to have a secondary managed DNS provider to quickly delegate to when DDOS attack on our *primary* external DNS provider happens? Given a constant number $c$, I want to determine the minimum sample size I need to estimate the probability $P(X \le c)$ given a confidence level, $p_c$, and confidence interval, $I_c$ (I am not sure if we need them!
This is a sequential method that adaptively selects sample size to guarantee a certain confidence level for a prescribed relative confidence interval.
The required sample size $b$ (I'm using $b$ to distinguish it from $n$ because you already set your population size as $n$ in the problem statement) is determined by $$b \geq \left( {1 \over 2 \epsilon^2 } \right) \mathrm{ln} \left( {2 \over \alpha} \right),$$ where $\epsilon$ is how close you want your empirical cdf to be and $1\alpha$ is the confidence level. Sorry I am not good at statistic, I have another question; Can we say ? is confidence interval?
Now I am confused if these nonparametric methods can be used to solve my problem or the method I found in Wikipedia is the correct way to solve my problem, or there exists a better solution. So, for example, this method can assure that the estimated probability does not deviate from the true probability by more than, say, 10% with 95% confidence.
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