| Project/Area Number |
12680313
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | Tokyo University of Fisheries |
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Principal Investigator |
YAMADA Sakutaro Tokyo University of Fisheries, Fisheries, Professor, 水産学部, 教授 (60017077)
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| Co-Investigator(Kenkyū-buntansha) |
KITAKADO Toshihide Tokyo University of Fisheries, Fisheries, Assistant Professor, 水産学部, 助手 (40281000)
TANAKA Eiji Tokyo University of Fisheries, Fisheries, Associate Professor, 水産学部, 助教授 (40217013)
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| Project Period (FY) |
2000 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2001: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2000: ¥500,000 (Direct Cost: ¥500,000)
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| Keywords | concentrated distribution / sampling (especially, PAS) / Probability of oversight / 見落としの確率 / adaptiveサンプリング |
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| Research Abstract |
1. Comparative study of models of concentrated distributions
We studied relation among the mean m, probability of taking positive values s, and index of concentration θ for negative binomial distribution, Polya-Aeppli distribution and Neyman type A distribution. Main results are (1) s is a monotone decreasing function of θ for fixed m. (2) s is a monotone increasing concave function of m for fixed θ. (3) m is a monotone increasing convex function of θ for fixed s.
2. Study on Probability of oversight for PAS (Presence - Absence Sampling). Suppose that observation U=1 is gotten when there are animals (or eggs), U=0 otherwise. Actual number of animal (or egg) E is supposed to have negative binomial distribution NB (m,k). (1) P(E>01U=0)=1- (k/k+m)^k/1-a+a(k/k+mU)^k, where P(U=11E=x)=a(1-e^<-bx>, w=1-e^<-b>.
This probability is a monotone decreasing function of 1/k, (2) For N stations suppose that U=0 if y_1=--=y_n=0 for n stations, U=1 otherwise. For the number E of animals in the N stations we have P(E>01U=0)=1-(k/k+m)^<k(N-n)> (k+mp/k+m)^<kn>. This is a monotone decreasing function of 1/k.
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