Sample Quantiles of Discrete Distributions

Sample quantiles for discrete distributions The classical definition of sample quantiles and their asymptotic properties for absolutely continuous distributions are well known. This no longer applies to discrete distributions. This thesis deals with implementing new quantiles based on the mid-distribution function, and their properties. The theoretical part shows the asymtotic properties of sample quantiles based on the mid-distribution function for both discrete and absolutely continuous distributions. In the absolutely continuous case it shows that the results are the same as those for the classical sample quantiles. In the discrete case the asymptotic distribution is normal. The practical part includes the exact distribution of these new sample quantiles for the binomial distribution. This thesis also includes a small simulation study for the standardized normal distribution and binomial distribution