Sains Malaysiana 52(12)(2023): 3867-3877

http://doi.org/10.17576/jsm-2023-5212-18

Estimation of Population Size Based on One-Inflated, Zero-Truncated Count Distribution with Covariate Information

 (Anggaran Saiz Populasi Berdasarkan Taburan Kiraan Satu-Lambung, Sifar-Pemangkasan dengan Maklumat Kovariat)

TITA JONGSOMJIT* & RATTANA LERDSUWANSRI

Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Thailand

Received: 19 August 2023/Accepted: 12 December 2023

Abstract

In order to estimate the unknown size of the population that is difficult or hidden to enumerate, the capture-recapture method is widely used for this purpose. We propose the one-inflated, zero-truncated geometric (OIZTG) model to deal with three important characteristics of some capture–recapture data: zero-truncation, one-inflation, and observed heterogeneity. The OIZTG model is generated by two distinct processes, one from a zero-truncated geometric (ZTG) process, and the other one-count producing process. To explain heterogeneity at an individual level, the OIZTG model provides a simple way to link the covariate information. The new estimator was proposed based on the OIZTG distributions through the modified Horvitz-Thomson approach, and the parameters of the OIZTG distributions are estimated by using a maximum likelihood estimator (MLE). With regard to making inferences about the unknown size of the population, confidence interval estimations are proposed where variance estimate of population size estimator is achieved by using conditional expectation technique. All of these are assessed through simulation studies. The real data sets are provided for understanding the methodologies.

Keywords: Capture-recapture; geometric regression; observed heterogeneity

AbstraK

Dalam proses untuk menganggarkan saiz populasi yang sukar atau tersembunyi untuk dihitung, kaedah tangkap-tangkap semula digunakan secara meluas untuk tujuan ini. Kami mencadangkan model geometrik satu-lambung, geometrik sifar-pemangkasan (OIZTG) untuk menangani tiga ciri penting bagi beberapa data tangkap-tangkap semula: sifar-pemangkasan, satu-inflasi dan heterogeniti yang diperhatikan. Model OIZTG dijana oleh dua proses yang berbeza, satu daripada proses geometri terpangkas sifar (ZTG) dan satu lagi proses menghasilkan satu kiraan. Untuk menerangkan heterogeniti pada peringkat individu, model OIZTG menyediakan cara mudah untuk memautkan maklumat kovariat. Penganggar baharu telah dicadangkan berdasarkan taburan OIZTG melalui pendekatan Horvitz-Thomson yang diubah suai dan parameter taburan OIZTG dianggarkan dengan menggunakan penganggar kemungkinan maksimum (MLE). Berkenaan dengan membuat inferens tentang saiz populasi yang tidak diketahui, anggaran selang keyakinan dicadangkan dengan anggaran varians penganggar saiz populasi dicapai dengan menggunakan teknik jangkaan bersyarat. Kesemua ini dinilai melalui kajian simulasi. Set data sebenar disediakan untuk memahami metodologi.

Kata kunci: Kepelbagaian yang diperhatikan; regresi geometri; tangkap-tangkap semula

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*Corresponding author; email: tita.jong@dome.tu.ac.th