A new continuous distribution and two new families of distributions based on the exponential

Abstract

Recent work on social status led to derivation of a new continuous distribution based on the exponential. The new variate, termed the ring(2)‐exponential, in turn leads to derivation of two closely related new families of continuous distributions, the mirror‐exponential and the ring‐exponential. Both the standard exponential and the ring(2)‐exponential are special cases of both the new families. In this paper, we first focus on the ring(2)‐exponential, describing its derivation and examining its properties, and next introduce the two new families, describing their derivation and initiating exploration of their properties. The mirror‐exponential arises naturally in the study of status; the ring‐exponential arises from the mathematical structure of the ring(2)‐exponential. Both have the potential for broad application in diverse contexts across science and engineering. Within sociobehavioral contexts, the new mirror‐exponential may have application to the problem of approximating the form and inequality of the wage distribution.