# 統計学 I (H25 前期 水曜 3限 & 5限） Toshihide Kitakado's Website Lec8

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### Estimating the encounter rate of XXX dolphins in the YYY Bay using a line transect method

Taro Kaiyo and Hanako Kagaku

Tokyo University of Marine Science and Technology

Abstract

INTRODUCTION

It has been widely recognized….(omission)

MATERIALS and METHODS

Data

A line transect survey was conducted using the Suisan-maru from May 22nd to 25th in 2013 to collect the information on the encounter rate of the XXX dolphins in the YYY Bay. A total of four transects were allocated in the study area and the vessel traversed along the predetermined tracklines (see Fig 1). Table 1 summarizes the data obtained through this survey.

Figure 1. The predetermined tracklines for …..

Table 1. Summary of data obtained by the survey

Estimation method

Let Li be the length of actual effort spent in the i-th transect and Yi denotes the number of individuals detected in the i-th

transect. We now assume that Yi is a random variable having a Poisson distribution Po(λLi), where the parameter λ has a

specific meaning of encounter rate of dolphins per nautical mile. For estimating the parameter of interest λ, we propose the following type of estimator,

4

1

i

i i i

=

## ∑

, (1)

where ωi is a weight to the observed encounter rate in the i-th trackline. The weights ωi (i=1,2,3,4) were determined by

the two criteria:

1) The estimator ˆ( )λ Y should be unbiased 2) The variance of ˆ( )λY should be minimized

The resultant estimator based on the conditions above is given by

4

1

i

i i i

=

## ∑

### =

(2)

The derivation of Equation (2) is shown in Appendix A.

RESULTS

The estimate of the encounter rate λ per n.mile was given by

### =

and its standard error, the standard deviation of ˆ( )λY , was assessed as

### =

DISCUSSION

In this paper ……(omission)

Trackline Actual effort (n.mile)

# individuals detected

1 50 2

2 40 0

3 60 5

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### Fictitious Article

Appendix A

The unbiasedness condition implies

ˆ( ) 0

Eλ Y  => λ for allλ

The variance of ˆ( )λY is expressed as

ˆ( )

Vλ Y  =

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