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Frequency distributions from birth, death and creation processes.

Authors
Bartley-DL; Ogden-T; Song-R
Source
Biosystems 2002 Aug; 66(3):179-191
NIOSHTIC No.
20022896
Abstract
The time-dependent frequency distribution of groups of individuals versus group size was investigated within a continuum approximation, assuming a simplified individual growth, death and creation model. The analogy of the system to a physical fluid exhibiting both convection and diffusion was exploited in obtaining various solutions to the distribution equation. A general solution was approximated through the application of a Green's function. More specific exact solutions were also found to be useful. The solutions were continually checked against the continuum approximation through extensive simulation of the discrete system. Over limited ranges of group size, the frequency distributions were shown to closely exhibit a power-law dependence on group size, as found in many realizations of this type of system, ranging from colonies of mutated bacteria to the distribution of surnames in a given population. As an example, the modeled distributions were successfully fit to the distribution of surnames in several countries by adjusting the parameters specifying growth, death and creation rates.
Keywords
Models; Group-dynamics; Families; Data-processing; Statistical-analysis; Statistical-quality-control
Contact
National Institute for Occupational Safety and Health, 4676 Columbia Parkway, Cincinnati, OH 45226, USA
CODEN
BSYMBO
Publication Date
20020801
Document Type
Journal Article
Fiscal Year
2002
NTIS Accession No.
NTIS Price
Issue of Publication
3
ISSN
0303-2647
NIOSH Division
DART
Source Name
Biosystems
State
OH; GA
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