Progressively Type II Censored Order Statistics and Characterizations

The theory of ordered random variables is used in many fields of statistical science and inference. Some of ordered random variable models are order statistics, progressively censored order statistics, record values and generalized order statistics. Each one of these models has different interpretations and interesting applications in many fields, for example, in survival analysis, reliability theory, financial economics, etc. In this work, the joint probability density function of nonadjacent Progressively Type II censored order statistics is presented. It is proved that Progressively Type II censored order statistics are reduced to order statistics for special censoring scheme. This reduction theorem enables to extend distributional properties of order statistics into properties of Progressively Type II censored order statistics with this censoring scheme. Then by using this result, for a general class of distributions some characterizations through the properties of conditional expectations of order statistics and Progressively Type II censored order statistics are given.