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: Modelling General Insurance Claim Data with Composite Lognormal-Pareto Distribution
Abstrak: Salah satu tahapan penting untuk menentukan premi agar perusahaan asuransi umum dapat membayar kerugian para tertanggung yaitu dengan memodelkan data klaim. Biasanya data besarnya klaim asuransi umum dimodelkan dengan sebaran lognormal atau sebaran Pareto. Sebaran lognormal dapat memodelkan data besarnya klaim dengan baik tetapi memiliki ekor sebaran yang lebih cepat menuju nol sehingga sebaran lognormal biasa digunakan untuk memodelkan data klaim yang lebih kecil. Sebaran Pareto memiliki bentuk monoton menurun dan ekor sebaran yang lebih berat. Sebaran Pareto sering digunakan untuk memodelkan data reasuransi atau data klaim besar. Sebaran lognormal-Pareto komposit merupakan kandidat yang cocok untuk memodelkan data klaim yang frekuensi klaim lebih kecil dan klaim lebih besarnya sama-sama tinggi. Baik data yang dibangkitkan maupun data aktual dianalisis untuk mengetahui kecocokan data dengan sebaran lognormal-Pareto komposit, lognormal, dan Pareto. Sebaran lognormal-Pareto komposit adalah sebaran yang paling cocok untuk memodelkan kedua data tersebut., One of important steps to determine premiums so that general insurance companies could pay the insureds’ losses is by modelling claim data. Usually, general insurance claim severity data is modeled by lognormal distribution or Pareto distribution. Lognormal distribution could fit well the claim severity data, but it has a tail that fades away faster to zero so that the lognormal distribution is usually used to model the smaller claim data. Pareto distribution has a monotonically decreasing density shape and a heavier tail. Pareto distribution is often used to model the reinsurance data or the larger claim data. The composite lognormal-Pareto distribution is a candidate that fits to model claim data that has smaller and larger claim data with high frequencies. Both generated data and actual data are analyzed to show the data fitted to composite lognormal-Pareto, lognormal, and Pareto distributions. The composite lognormal-Pareto distribution is the most fitted distribution to model both data.
Keyword: composite lognormal-Pareto distribution, lognormal distribution, Pareto distribution, the amount of claim, general insurance

Judul: Leaf morphology and Anatomy Characters of Some Sansevieria Species
Abstrak: Penelitian ini bertujuan untuk mengkaji karakter morfologi dan anatomi daun pada lima spesies tumbuhan Sansevieria. Berdasarkan pengamatan karakter morfologi, dijumpai variasi morfologi daun meliputi ukuran panjang, lebar dan tebal daun serta pola warna pada daun ke lima spesies Sansevieria. S. sufruticosa memiliki daun berbentuk silindris berwarna hijau, dengan ujung daun berduri merah kecoklatan. S. masoniana congo memiliki daun berbentuk jorong, warna hijau tua, dengan tepi daun berwarna merah. S. samurai dwarf memiliki daun berwarna hijau dengan permukaan cekung membentuk saluran. S. trifasciata gold flame memiliki daun berbentuk lanset, tebal berwarna hijau tua bergaris hijau muda dengan tepi daun berwarna kuning, sedangkan S. kirkii brown memiliki daun berbentuk lanset, berwarna coklat dengan bercak putih, permukaannya bergelombang. Pada ke lima spesies Sansevieria daun dilapisi selapis epidermis berbentuk poligonal dengan 4 hingga 6 sisi yang berdinding tipis, kecuali spesies S. samurai dwarf sel epidermis berdinding tebal merata. Stomata dijumpai pada kedua permukaan daun, terdapat lebih banyak pada permukaan bawah daun (abaksial). S. masoniana congo memiliki stomata berukuran (panjang x lebar) terbesar, sedangkan S. kirkii brown memiliki stomata terkecil. S. masoniana congo memiliki kerapatan stomata terkecil dengan indeks stomata terbesar, sebaliknya S. sufruticosa memiliki kerapatan stomata terbesar dengan indeks stomata terkecil. Diantara kelima spesies yang diteliti, daun S. masoniana congo memiliki kutikula yang paling tebal sebaliknya S. trifasciata gold flame memiliki kutikula paling tipis., This research aims to describe leaf morphology and anatomy characters of five Sansevieria species. Based on the morphology characters, there are some variation in the length, width, thickness and leaf color pattern. S. sufruticosa has green cylindrical leaf, with auburn thorny leaf tip. S. masoniana congo has elliptical leaf, dark green with red stripe on the leaf margins. S. samurai dwarf has green leaf blade with concave surface forms thick wide channel. S. trifasciata gold flame has thick lanceolate leaf, light green striped dark green with yellow stripe in the leaf margin, while S. kirkii brown has white spotted brown lanceolate leaf with wavy surface. Sansevieria was leaf covered with a layer of epidermis. Epidermal cells are polygonal in shape with four to six thin wall sides, except S. samurai dwarf with thick cell wall. Stomata were found on both leaf sides, more stomata present on the lower epidermis than the upper epidermis. S. masoniana congo has the biggest (length x width) stomata, while S. kirkii brown has the smallest stomata. S. masoniana congo has the lowest stomatal density with the highest stomatal index, whereas S. sufruticosa has the highest stomatal density with the lowest stomatal index. Among all species, S. masoniana congo leaf has the thickest cuticula while S. trifasciata gold flame has the thinnest. Key words: Leaf anatomy, leaf morphology, Sansevieria, stomata
Keyword: Anatomi daun, morfologi daun, Sansevieria, stomata