Characterization of Negative Exponential Distribution Based on Patil-Seshadri Condition

In this paper, the different characterizations of the negative exponential distribution in the context of the Patil-Seshadri (P-S) condition are analyzed. To support this conclusion, we next show in the case of several continuous probability distributions including the generalized logistic, Laplace, lognormal and more, that under certain conditions they can be seen as a damaged rendition of the negative exponential distribution. The results offer new insights into the ways to continue previous research on how damaged data may appear to follow simpler exponential forms. The paper also presents the theoretical judgments of these characterizations and practical uses in biological frameworks, fund and signal handling where exponential developments and decays are usual scenes. Our research aims to have the following implications to these fields; it provides a fresh view to exponential model.