Judul: Pendugaan Parameter Beberapa Sebaran Poisson Campuran dan Beberapa Sebaran Diskret dengan Menggunakan Algoritme EM
Abstrak: Asuransi adalah transaksi pertanggungan yang melibatkan dua pihak, yaitu tertanggung dan penanggung. Perusahaan asuransi mengeluarkan polis yang berisi kesepakatan antara pihak tertanggung dan penanggung, dan menjanjikan akan membayar pemiliknya jika terjadi kerugian sepanjang waktu kontrak belum berakhir. Pembayaran kerugian disebut klaim sedang pengasuransi diwajibkan membayar premi. Sebaran Poisson secara luas digunakan dalam masalah asuransi terutama untuk model proses klaim. Salah satu contohnya pada asuransi kendaraan bermotor, kejadian musibah seperti kecelakaan terjadi dalam waktu yang berbedabeda merupakan kejadian acak, sehingga klaim yang datang tidak dapat diprediksi.
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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: Pembentukan akar tanaman hias Cordyline fruticosa 'Hawaian flag' secara ex vitro
Abstrak: Cordyline sp. is a woody ornamental monocot, belongs to Asparagaceae family. The use of in vitro culture can support the propagation of Cordyline sp. to produce more planlets in a shorter time. In vitro root system of plantlets of Cordyline fruticosa 'Hawaian flag' is usually very weak and easily removed when washed in running tap water. Therefore, planlets were grown without roots in vitro and rooting of planlets was conducted during acclimatization period. This research was aimed to determine the influence of various types and concentrations of auxin on rooting and growth of Cordyline fruticosa plantlets during the acclimatization period. Type of auxin hormones i.e. IAA, IBA and NAA and concentrations at 20 μM, 100 μM and 500 μM did not significantly affect the rooting and growth of Cordyline fruticosa. Having compared all the treatments, it can be concluded that IAA 100 μM was the better one in inducing roots of the planlets in term of numbers of secondary roots and the growth of the shoots. Ex vitro rooting can also be done without hormones with the same results as with auxins was used in this research.
Keyword: Bogor Agricultural University, acclimatization, ex vitro rooting, Cordyline fruticosa, auxin