In this note, we characterize the exponential distribution by the property, "the distribution of a function of the first order statistic and the parent distribution are the same for one specific ...

Let X₁ , X₂,..., Xn be a random sample of size n from a population with probability density function f(x), x > 0, and let X₁,n < · · · < Xn,n be the associated order statistics. Some characterizations ...