In recent decades, studying order statistics arising from independent and not necessary identically distributed (INID) random variables has been a main remarkable for researchers. To provide the cumulative distribution function (CDF) of these random variables (Fi:n) is a complex manipulating, long time consuming and a softwareintensive tool that takes considerable time. Therefore, to obtain approximations and bounds for Fi:n and other theoretical properties of these variables, such as moments, quantiles, characteristic functions, and some related probabilities, has always been a main challenge. Recently, Bayramoglu (2018), [7], has introduced a set of CDFs (F[i]), whose definitions are based on a point to point ordering of the original CDFs (Fi), that can be used to approximate the CDF of i-th order statistics (Fi:n). Furthermore, new approximations for F1:n and Fn:n, as well as for other cases, are derived. Comparisons with respect to approximations suggested by Bayramoglu [7] are also provided.

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