Certain Chance Mechanisms Related to Birth and Death Processes Which Have Classical Discrete Distributions as Special Cases.
Abstract
The paper is a study of birth and death processes. Little known results are brought together with well known results and some new results are found. A formula for the solution of a general birth and death process is found and the case where each birth rate factors into a function of the sizes of the population components and a function of time is solved. For the r-dimensional birth and death process where the birth and death rates factor as above and where all rates are linear, the solution is found to have either the negative multinomial, independent Poisson, or the multinomial distribution. A few related processes are studied. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1971
- Accession Number
- AD0735831
Entities
People
- G. P. Patil
- M. T. Boswell
Organizations
- University of Wisconsin–Madison