Abstract
Characterization of probability distributions play important role in probability and statistics. Before a probability distribution is applied to a real set of data it is necessary to know the distribution that fits the data by characterization. A probability distribution can be characterized by various methods, see for example Ahsanullah et al. (2014). In this chapter we will characterize probability distributions by various properties of ordered data. We will consider order statistics, record values and generalized order statistics to characterize the probability distributions.