Abstract
In previous chapters we have discussed some popular models of ordered random variables when the sample is arranged in increasing order. The simplest of these models is Order Statistics and is discussed in detail in Chap. 2. The comprehensive model for ordered random variables arranged in ascending order is Generalized Order Statistics and is discussed in detail in Chap. 4. The generalized order statistics produce several models for ordered random variables arranged in ascending order as special cases for various choices of the parameters involved. Often it happen that the sample is arranged in descending order for example the life length of an electric bulb arranged from highest to lowest. In such situations the distributional properties of variables can not be studied by using the models of ordered random variables discussed earlier. The study of distributional properties of such random variables is studied by using the inverse image of Generalized Order Statistics and is popularly known as Dual Generalized Order Statistics (DGOS).
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