Abstract
The dual generalized order statistics is a unified scheme which contains the well known decreasingly ordered random variables such as (reversed) order statistics, lower record values and lower Pfeifer record values. In this article, characterization results on Gompertz-Verhulst distribution through the conditional expectation of dual generalized order statistics based on non-adjacent dual generalized order statistics are given. These relations are deduced for moments of reversed order statistics, order statistics and lower record values. Further a characterization result through the truncated moment is also derived.
Highlights
Models of ordered random variables are important and received a great attention from many researchers during the past century
The study of distributional properties of such random variables is studied by using the inverse image of gos and is popularly known as dual generalized order statistics
It appears from literature that no attention has been paid on the characterization of Gompertz –Verhulst distribution through conditional expectations of dual generalized order statistics and truncation moment
Summary
Models of ordered random variables are important and received a great attention from many researchers during the past century. The comprehensive model for ordered random variables in ascending order is generalized order statistics Often it happen that the sample is arranged in descending order for example the life length of an electric bulb arranged from highest to lowest. The study of distributional properties of such random variables is studied by using the inverse image of gos and is popularly known as dual generalized order statistics. The dual generalized order statistics (dgos) was introduced by Burkschat et al [3] as a unified model for descendingly ordered random variables like reverse order statistics, lower record values and lower Pfeifer record values. DUAL GENERALIZED ORDER STATISTICS FROM GOMPERTZ-VERHULST DISTRIBUTION. It appears from literature that no attention has been paid on the characterization of Gompertz –Verhulst distribution through conditional expectations of dual generalized order statistics and truncation moment. Throughout the paper, we consider the Case II and deduce it for Case I
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