Judul: Modeling Loss Data of General Insurance Companies with Log-EIG Distribution
Abstrak: Sebaran log-EIG (Exponential Inverse Gaussian) merupakan sebaran yang dimodifikasi dari sebaran EIG yang lebih dulu diperkenalkan. Sebaran log-EIG memiliki kecondongan ke kanan dan kurtosis yang lebih besar dari sebaran normal sehingga sebaran log-EIG dapat dikategorikan sebagai sebaran berekor berat. Sebaran semacam ini bermanfaat untuk memodelkan data kerugian perusahaan asuransi umum supaya dapat meminimumkan risiko kerugian di masa yang akan datang. Simulasi menunjukkan bahwa data yang dibangkitkan dari sebaran log-EIG tidak dapat dijelaskan dengan baik oleh sebaran lognormal dan Weibull. Untuk himpunan data yang digunakan, sebaran log-EIG memiliki nilai kriteria informasi Quesenberry dan Kent (QK) lebih besar dibandingkan dengan sebaran lognormal dan Weibull. Hasil ini menunjukkan bahwa sebaran log-EIG lebih baik dalam memodelkan himpunan data dibandingkan dengan sebaran lognormal dan Weibull, The log-EIG (Exponential Inverse Gaussian) distribution is a modification of the earlier EIG distribution. It has a positive skewness and a kurtosis that is greater than a normal distribution so that the log-EIG distribution can be categorized as a heavy-tailed distribution. This kind of distribution is useful to model loss data of general insurance companies in order to minimize the risk of loss in the future. The simulation shows that data generated from a log-EIG distribution is not well-described by a lognormal and a Weibull distribution. For the dataset used, the log-EIG distribution has a greater value of Quesenberry and Kent (QK) Information Criterion than the lognormal and the Weibull distribution. These results indicate that the log-EIG distribution models the dataset better than the lognormal and the Weibull distribution.
Keyword: heavy-tailed, modeling data, QK criterion, risk, simulation

Judul: Pemodelan Peluang Risiko dengan Menggunakan Sebaran Compound Generalized Poisson
Abstrak: Insurace is a form of risk management that is used for protection against loss. In insurance companies, the pricing of insurance premium should be based on fair principles, i.e. in accordance with the value of class of risk. The higher the risk, the higher amount of insurance premium will be. The class of risk can be estimated by insurance claim. Modelling the claim frequency is one of the most important areas in risk theory. Generally, insurance claims can be modelled with Poisson or negative binomial distribution. Gossiaux and Lemaire (1981) and Willmot (1987) have considered generalized Poisson distribution as an alternative to Poisson or negative binomial disribution. Generalized Poisson distribution will be applied if there is overdispersion in data. Generalized Poisson distribution can be viewed as a compound Poisson (𝜃) and sum of Borel (𝜆) distribution. If a random variable N (the number of claims) has a generalized Poisson distribution, then the total number of claims has a compound generalized Poisson distribution. A recursive algorithm is needed to model the risk probability of this distribution. First step of this algorithm is to compute the coefficients of the moment generating function, which sum to the probability function of the compound Borel (𝜆) distribution. The next step of this algorithm is to compute the probabilities by using Panjer’s recursion formula for the Poisson (𝜃) distribution.
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Judul: Sintesis dan Pencirian Natrium Titanat (Na2Ti2O4(OH)2) Berbahan Dasar Titanium Dioksida
Abstrak: TiO2 can be utilized as basic material for synthesis of sodium titanate (Na2Ti2O4(OH)2). This research was purposed to synthesize and characterize sodium titanate from TiO2 rutile powder as a basic material. Sodium titanate was synthesized by hydrothermal process at temperature 130 °C by mixing TiO2 rutile powder with 5 M and 10 M NaOH solution, then each was calcinated at temperature 700 °C. The energy dispersive X-ray analysis showed that sodium titanate has been successfully synthesized. This result was also supported by functional group analysis with Fourier transform infrared (FTIR) spectrofotometer showing the existence of Ti-O-Na vibration band at 989.42 cm-1. The formation of sodium titanate was depend on the reaction condition such as temperature, reaction time, and NaOH concentration. Scanning electron microscope image indicated that sodium titanate synthesized at 130 °C in 20 hours reaction time with 10 M NaOH had crystal size of 99.37 nm.
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