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A Unifying Method for Some Computations in Renewal Theory
Author(s) -
Hinderer K.
Publication year - 1985
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19850650603
Subject(s) - computation , renewal theory , poisson distribution , joint probability distribution , mathematics , distribution (mathematics) , risk theory , statistical physics , poisson process , residual , statistics , mathematical analysis , physics , algorithm , actuarial science , business
In renewal theory the residual life time Y t , the spent life time Z t and the total life time L t play an important role. A unifying method is presented for the computation of the (joint) probability distribution, of the (mixed) moments, of the (joint) densities and of other quantities of interest. As examples we compute, among others, for the Poisson process the probability distribution of Y t /L t and the correlation coefficient of Z t and L t .