Assuming a normal probability density function with mean = $\mu$ and standard deviation = $\sigma$, I know that if I generate randomly many times a number from this pdf, the sample that I will obtain will represent accurately the pdf. Consequently, the quantiles of my sample will describe accurately my true pdf distribution and I will be able to find back $\mu$ and $\sigma$.
However, if i decide to generate only few random numbers (let say $10$ or $20$ times), it is likely to be misleading.
Is there a way to generate NOT random numbers to be sure to create a sample that preserves the distribution specificities? How to sample the pdf to preserve the quantiles with a very small sample?
Thank you !
(I apologize, I'm far from being a mathematician, the vocabulary I use may not be appropriate)
Only if it's a bounded, discrete random variable can you construct a finite sample that reproduces the original distribution.