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Abstrak :
Natural mortality of trees is extremely variable due to the uncertainty and complexity of the functioning of forest ecosystems. The objective of this study was to develop a stand-level mortality model for Acacia mangium species by relating mortality to stand variables that affect the natural mortality process. The model was developed using data from l97 permanent sample plots measured periodically at 1-yr time intervals from 2-4 years until 8-11 years after planting in South Sumatra, Indonesia. The model consists of two complementary equations. The first equation is a logistic function predicting the probability of mortality incidence depending on stand density, site index and stand age. The second equation estimates the reduction in the number of surviving stems observed in a stand where natural mortality occurs. Nine equations were fitted using data from permanent sample plots where trees died over the time period and the best model was selected. Estimates from this second model were then adjusted by a factor equal to the probability of mortality applying three different approaches: probabilistic two-step, deterministic threshold and stochastic. All methods revealed no significant difference between the observed and the predicted number of surviving stems per ha. The probabilistic two-step approach, however, produced more consistent and the most accurate estimates. This method should provide reliable prediction when it is to be used in forest productivity prediction and management system for the species.

Abstrak :
Beberapa perusahaan asuransi jiwa Indonesia mengalami permasalahan keuangan karena rendahnya premi dan terlampau idealnya ekspektasi imbal hasil investasi. Hal ini tergolong semakin berisiko jika premi yang sama diberikan pula kepada calon nasabah baru tanpa melalui proses seleksi risiko. Tabel mortalitas saat ini dan asumsi keuntungan investasi terlalu ideal, sehingga asumsi yang lebih konservatif dibutuhkan untuk memeroleh rentang premi murni tahunan yang lebih realistis. Dalam penelitian ini, tabel mortalitas lengkap diestimasi dari tabel mortalitas ringkas dengan model Heligman- Pollard terpancung dan Makeham. Parameter model mortalitas diestimasi dengan metode Bayesian melalui algoritma Metropolis-Hastings. Terhadap data pada tabel mortalitas ringkas, dilakukan proses bootstrap karena ketidakcukupan jumlah untuk proses pemodelan statistika parametrik. Diperoleh akurasi baik untuk estimasi tingkat mortalitas ringkas dengan metrik koefisien korelasi Pearson dan Mean Absolute Percentage Error. Parameter yang diperoleh juga memadai untuk mengestimasi tingkat mortalitas pada tabel mortalitas lengkap dan diekstrapolasi hingga usia 99 tahun. Tingkat imbal hasil investasi diasumsikan mendekati tingkat inflasi dan tingkat inflasi bulanan diasumsikan mengikuti proses stokastik lognormal. Hasil penelitian berbasis model normal Bayesian menunjukkan bahwa terdapat peluang baik untuk terjadinya keuntungan maupun kerugian investasi. Informasi tabel mortalitas lengkap dan rentang keuntungan investasi yang diperoleh kemudian digabungkan untuk membentuk rentang premi murni tahunan yang wajar. ......Several Indonesian life insurance companies faced financial problems due to inadequate pricing and idealistic investment expectation. This condition goes riskier when equal premium rate is generalized for new customers without being underwritten. Current mortality table and investment return assumption are too ideal, so conservative assumptions are needed to get a more reasonable annual pure premium range. In this research, complete life tables are estimated from abridged life tables by truncated Heligman-Pollard and Makeham model. Parameters for mortality models are estimated by Bayesian method using Metropolis-Hastings algorithm. Data from abridged life table will be bootstrapped because of insufficient number for statistical parametric modelling. Good accuracy for estimated abridged mortality rates was reached based on Pearson correlation coefficient and Mean Absolute Percentage Error metrics. The estimated parameters were adequate to extrapolate yearly mortality rates calculation until age 99. Investment return is assumed to be close to inflation rates and monthly inflation rates are assumed to follow lognormal stochastic process. Based on Bayesian normal model, it is possible to have profitable or losing investment. Information of the complete life table and investment return range obtained are combined to form fair annual pure premium range.