Finding confidence intervals is an important statistical problem because the confidence intervals provide an interval evaluation of the quantity of interest. Supose that we are interested in a certain quantile of an unknown continuous distribution, given a sample of independent observations from this distribution, we can calculate a confidence interval with a certain confidence level for the particular quantile. Sometimes we want to calculate a confidence interval for several quantiles with a certain total confidence level. We call this a simultaneous confidence interval. Since we do not have any distribution assumptions, we use non-parametric methods for calculating confidence intervals. Searching for confidence intervals for a single quantile can be calculated using the binomial method. The method searches for confidence intervals with an individual confidence level exactly $1-\alpha$. If we want to search for confidence intervals whose total confidence level is $1-\alpha$, we need different methods. Two of these methods will be presented in this work. If we search for confidence intervals for all quantiles of an unknown distribution, or if we are interested in confidence intervals for many quantiles that are scattered over the entire interval $(0,1)$, then it is best to obtain confidence intervals from confidence bands. One of the ways to search for confidence bands is using the Kolmogorov method. Simultaneous confidence intervals obtained from confidence bands are usually very wide and therefore often useless. Therefore, there is a method based on multinomial distribution that searches for simultaneous confidence intervals for only a few selected quantiles. These confidence intervals are usually narrower. To calculate the simultaneous confidence level, there is a recursive algorithm that has a computational complexity that increases linearly with the number of quantiles that interest us. For simultaneous confidence intervals we want to find a set of super-feasible boundary values values. In order to find them, we employ five criteria: symmetry, one-sidedness and two-sidedness, confidence interval spread, confidence level and inclusion. Simultaneous confidence intervals obtained by the multinomial method are usually narrower than those obtained from confidence bands and wider than the confidence intervals for individual quantile. If we are looking for simultaneous confidence intervals by means of the multinomial method, it is preferable to use nonparametric methods, since then the confidence intervals do not depend on distribution assumptions.
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