The Research Of The Hospital Beds' Management Based On The Poisson Difference Distribution

With the development of medicine and the severe situation of population aging,the problem of medical resources become more and more important.Sickbed as one of the key resources got many researches for its allocation.In lots of resources,studies always simulated the hospitals' input process to model resources allocation based on the assumption of infinite capacity and using queuing theory.For input process,it is often assumed that the time interval of arrival follow the Poisson distribution,but its property(mean and variance are equal)constrained the application of the Poisson distribution.For the output process,in the simulation,the average sojourn time is often used the individual sojourn time as instead,or approximately considered that it follows the normal distribution.However,in reality,systems with limited capacity need to be considered the input and output process at the same time.Poisson difference distribution works for this situation which has the probability P(X=x),x?N.So this thesis uses PD distribution to consider both the positive number of arrivals(individuals entering the system)and the negative number of arrivals(individuals leaving the system).First of all,we introduce the distribution of the difference between two independent Poisson random variables—Poisson.The definition showed that its random variables contain negative integer.Then,through new representation of the Poisson difference distribution,the relationship between the representation of the Poisson difference distribution and Poisson distribution was discussed.Next,for estimation,this thesis showed the moment estimates and maximum likelihood estimates.And the asymptotic properties of the maximum likelihood estimates were discussed.This thesis also showed some simulation results for computing the estimates of the parameters of PD distribution using the method of moments and the maximum likelihood method.After that,the likelihood ratio test for PD distribution was introduced.Afterwards,when the data couldn't fit Poisson distribution,the changes in number of occupied beds,which included the input process and the output process,fitted the PD distribution well.By estimates method and simulation results,the estimates of parameters were obtained.Through that,we got the distribution function of the changes in number of occupied beds.Finally,using PD distribution,we designed dynamic parameters warning system to help the managements and simulated this system comparing with the actual situation to test the feasibility of the system.