Central limit theorem for germination-growth models in Rd with non-Poisson locations

S. N. Chiu; M. P. Quine

doi:10.1239/aap/1011994026

Central limit theorem for germination-growth models in Rd with non-Poisson locations

S. N. Chiu^*, M. P. Quine

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

7 Citations (Scopus)

28 Downloads (Pure)

Abstract

Seeds are randomly scattered in R^d according to an m-dependent point process. Each seed has its own potential germination time. From each seed that succeeds in germinating, a spherical inhibited region grows to prohibit germination of any seed with later potential germination time. We show that under certain conditions on the distribution of the potential germination time, the number of germinated seeds in a large region has an asymptotic normal distribution.

Original language	English
Pages (from-to)	751-755
Number of pages	5
Journal	Advances in Applied Probability
Volume	33
Issue number	4
DOIs	https://doi.org/10.1239/aap/1011994026
Publication status	Published - Dec 2001

Scopus Subject Areas

Statistics and Probability
Applied Mathematics

User-Defined Keywords

Central limit theorem
Johnson-Mehl tessellation
m-dependent

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10.1239/aap/1011994026

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abstract = "Seeds are randomly scattered in Rd according to an m-dependent point process. Each seed has its own potential germination time. From each seed that succeeds in germinating, a spherical inhibited region grows to prohibit germination of any seed with later potential germination time. We show that under certain conditions on the distribution of the potential germination time, the number of germinated seeds in a large region has an asymptotic normal distribution.",

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AB - Seeds are randomly scattered in Rd according to an m-dependent point process. Each seed has its own potential germination time. From each seed that succeeds in germinating, a spherical inhibited region grows to prohibit germination of any seed with later potential germination time. We show that under certain conditions on the distribution of the potential germination time, the number of germinated seeds in a large region has an asymptotic normal distribution.

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KW - Johnson-Mehl tessellation

KW - m-dependent

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Central limit theorem for germination-growth models in Rd with non-Poisson locations

Abstract

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