A Note on Monotonic Probability Distributions

Abstract A rational selection of a probability distribution constitutes a major problem. Often a distribution function is selected which fits well to the observed data. In other cases the availability of statistical methods determines the model. Finally, in many fields of application there are certain traditional practices concerning the selection of probability distributions. This paper treats exemplarily how a probability distribution can be selected by considering the available information about a given situation on the one hand and taking into account the amount of ignorance on the other hand.