Bounds for CDFs of Order Statistics Arising from INID Random Variables

In recent decades, studying order statistics arising from independent and not necessary identically distributed (inid) random variables has been a remarkable concern for researchers. 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, 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 the main challenge. recently, bayramoglu (2018), bayramoglu (2018), 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). here, by using just f[1] and f[n], we provide new upper and lower bounds for the 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 bayramoglu (2018) are also provided.