Judul: Penentuan Peluang Transisi Model Select Ultimate Mortality Menggunakan Metode Matriks Force of Transition
Abstrak: Model select ultimate mortality adalah suatu model tiga state pada bidang aktuaria. Model ini diasumsikan memiliki sifat Markov yang dicirikan oleh adanya matriks peluang transisi. Dalam karya ilmiah ini dibahas salah satu metode penentuan peluang transisi, yaitu metode force of transition. Dalam metode ini, penentuan peluang transisi menggunakan nilai eigen dan vektor eigen dari matriks segi dengan entri berupa force of transition. Hasil yang diperoleh menunjukkan metode matriks force of transition yang diaplikasikan pada data penduduk negara Kanada tahun 1982-1988 yang diperoleh dari Individual Ordianary Mortality Table mempunyai nilai peluang bertahan hidup yang hampir mendekati nilai dari Individual Ordianary Mortality Table, dengan mean galat absolut sebesar 0,18%.
Keyword: rantai Markov, peluang transisi, matriks force of transition

Judul: Maximum Entropy Mortality (MEM) Model for Forecasting Mortality with Statistical Moments
Abstrak: Meramalkan mortalitas adalah inti dari ilmu aktuaria. Berbeda dengan kebanyakan model peramalan mortalitas yang menggunakan laju bahaya dan pola usia, penelitian ini meramalkan tingkat kematian pada usia tertentu dengan memanfaatkan momen statistik sebaran usia saat kematian yang merepresentasikan kematian yang terjadi dalam suatu populasi. Metode ini mempertimbangkan masalah momen berhingga di mana fungsi kepekatan positif dicari dengan pengetahuan tentang sejumlah momen dari sebaran usia saat kematian yang diramalkan dengan model deret waktu peubah banyak. Rekonstruksi sebaran ramalan menggunakan pendekatan entropi maksimum. Penelitian ini menggunakan data banyaknya kematian per usia pada tahun tertentu yang terbagi berdasarkan jenis kelamin untuk Jepang dan Taiwan pada tahun 1970-2019. Model dapat digunakan untuk data kedua negara tersebut dengan banyak momen digunakan berbeda. Kompleksitas yang diperlukan model tidak berlaku umum di mana tingkat kompleksitas yang diperlukan untuk data populasi Jepang lebih rendah daripada data populasi Taiwan., Predicting mortality is at the heart of actuarial science. Unlike many models for predicting mortality which use hazard rates and age patterns, this study forecasts the mortality rate at a certain age by utilizing the statistical moments of age-at-death distribution that represent the deaths occur in a population. This method considers the finite moment problem in which the positive density function is sought with the knowledge of a number of moments from the age-at-death distribution predicted using a multi-variable time series model. The reconstruction of the forecast distribution uses the maximum entropy approach. This study uses data on the number of deaths per age in a particular year by gender in Japan and Taiwan in 1970-2019. The model can be used for both countries’ data with difference in the number of moments used. The required model complexity does not apply in general where the level of complexity required for Japanese population data is lower than its Taiwan counterpart.
Keyword: age-at-death distribution, finite moment problem, maximum entropy, mortality forecasting, statistical moments

Judul: Characteristic of chili drying (Capsicum annum L.) as a natural dyeing cosmetic
Abstrak: Chilli (Capsicum sp.) contains carotenoids, which are a group of natural pigments consist of red, orange or yellow color. Carotenoids can be dissolved in lipid so that they can be applied to oil-based cosmetic ingredients. Therefore, chilli is potential to be developed as cosmetic colorants. However, pungency of red chili needs to be removed because it is irritating and it provides stinging sensation to skin. Red chilli was investigated as a potent material for a cosmetic colourant in this research because it has a nice uniform red color and has a pungency level less than cayenne pepper. The purpose of this research was to investigate the influence of blanching on drying characteristics of red chilli using a tray dryer, determine the proper time of chili blanching in sodium bisulfite solution, examine color changes stability of red chili powder as a cosmetic dye, and analyze the effect of oleoresin extraction on color and pungency level of red chili powder. The results showed that blanching could affect the drying characteristics. Blanching the chilli for 9 minutes prior drying could speed up the drying rate of chilli and thus the drying time, therefore, the chilli achieved the desired moisture content fast. Sodium bisulfite solution of 0.2%, used as the blanching media, could maintain the color well. However, longer time of blanching might cause several pigments soluble in the blanching media. Blanching the chilli for 9 minutes was able to maintain red color after the stability tested and after extraction of oleoresin. Therefore, blanching red chilli in a solution of 0.2% sodium bisulfite for 9 minutes prior drying is concluded as the best treatment to retain the color of red chilli powder
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