@phdthesis{Sans2019,
  author    = {Sans, Wolfgang},
  title     = {Monotonic Probability Distribution : Characterisation, Measurements under Prior Information, and Application},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-175194},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2019},
  abstract  = {Statistical Procedures for modelling a random phenomenon heavily depend on the choice of a certain family of probability distributions. Frequently, this choice is governed by a good mathematical feasibility, but disregards that some distribution properties may contradict reality. At most, the choosen distribution may be considered as an approximation. The present thesis starts with a construction of distributions, which uses solely available information and yields distributions having greatest uncertainty in the sense of the maximum entropy principle. One of such distributions is the monotonic distribution, which is solely determined by its support and the mean. Although classical frequentist statistics provides estimation procedures which may incorporate prior information, such procedures are rarely considered. A general frequentist scheme for the construction of shortest confidence intervals for distribution parameters under prior information is presented. In particular, the scheme is used for establishing confidence intervals for the mean of the monotonic distribution and compared to classical procedures. Additionally, an approximative procedure for the upper bound of the support of the monotonic distribution is proposed. A core purpose of auditing sampling is the determination of confidence intervals for the mean of zero-inflated populations. The monotonic distribution is used for modelling such a population and is utilised for the procedure of a confidence interval under prior information for the mean. The results are compared to two-sided intervals of Stringer-type.},
  subject      = {Mathematik},
  language  = {en}
}