A new continuous distribution and two new families of distributions based on the exponential |
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Authors: | Guillermina Jasso Samuel Kotz† |
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Institution: | Department of Sociology, New York University, 295 Lafayette Street, 4th Floor, New York, NY 10012-9605, USA; Department of Engineering Management and Systems Engineering, George Washington University, Washington, DC 20052, USA |
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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. |
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Keywords: | continuous univariate distributions Erlang distribution general Erlang distribution gamma distribution general gamma distribution folded distributions Gini coefficient social status social inequality wage function wage distribution wage inequality |
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