Identification Of Multivariate Life Distribution And Its Applications

Constructing life tables are of great importance in the life insurance mathematics. As is wellknown, population data and life insurance data need be used while constructing life tables.The joint-life status data and the last-survivor status data are contained. The life data of people areseparated from these data, which is the identification problem. Many scholars and experts layemphasis on the identification of the life distributions. Based on the research achieved at home andabroad, this thesis derives new mixed type exponential distribution and discusses the identificationof the distribution, discusses the identification of two kinds of typical bivariate exponentialdistributions, studies the identification of bivariate uniform distribution, further studies theidentification of corresponding multivariate life distribution, explains simply the identification ofbivariate logarithm normal distribution and Marshall-Olkin type exponential distribution , derivesthe applications in the life insurance mathematics .The main results of the thesis are as follow:In the first part, domestic and foreign literatures are roughly introduced.In the second part, a new mixed exponential distribution is researched. The thesis derives onecharacterization of bivariate distribution, deduces the identification theorem in the maximum andthe minimum condition;In the third part, the identification of Proschan-Sullo type bivariate exponential distributionand Friday-Patil type bivariate exponential distribution are discussed.In the fourth part, the identification of bivariate uniform distribution is discussed.In the fifth part, the identification of multivariate life distribution is discussed.In the sixth part, based on the results of some scholars, the identification of bivariate Marshall-Olkin type exponential distribution and bivariate logarithm normal distribution are simplyexplained.In the seventh part, taking bivariate Marshall-Olkin type exponential distribution and bivariateuniform distribution for example , the net single premium expression is given.