Recurrence relations for single and product moments of k-th record values from pareto,generalized pareto and burr distributions

In this note we give recurrence relations satisfied by single and product momenrs of k-th upper-record values from the Pareto, generalized Pareto and Burr distributions. From these relations one can obtain all the single and product moments of all k-th record values and at the same time all record values ( k=1). Moreover, we see that the single and product moment of all k-th record values from these distributions can be exprrssed in terms of the moments of the minimal statistic of a k-sample from the exponential distribution may be deduced by letting the shape parameter deptend to 0. At the end we give characterizations of the three distributions considered. These results generalize, among other things, those given by Balakrishnan and Abuamllah (1994).     

Diskussionsbeitrag zur betriebswirtschaftlichen Ethik

Adam Smith as a Professor for moral philosophy didn’t intend to enforce immorality on the markets. But after a while he realized, that his concept of empathy wasn’t sufficient. Publishing his “Inquiry” he made the “Interest” to the inner movement of the “sympathy”. In this way he knitted together the personal “Interest” with the “Interest” of the society, not only economically but in morals too. And the “Interest” of society, the public welfare, had to enforce the wealth of the Nation, by being just and fair in the sense of Aristoteles. But to Deism belongs the tendency to relieve from religious beliefs as well as from virtues and values. And thus people began to think later, they had only to rely on “godless” laws of nature in economics too. That made the economic market-concept of Adam Smith drift to Manchester liberalism. At last that enforced the “selfinterest” to an unacceptable immoral “selfishness”, what Smith didn’t aim to and what would destroy the ethical foundation of his thinking. In the meantime it had become evident that markets don’t simple work after quasi laws of nature, but are in the need of a spiritual foundation. To that every market-participant must be invited on and on.