Judul: Penentuan Sebaran Kerugian Agregat Menggunakan Metode Fast Fourier Transform
Abstrak: Kerugian agregat adalah total kerugian yang dapat dihitung dengan pendekatan sebaran gabungan (compound distribution), baik secara analitik maupun numerik. Penentuan sebaran kerugian agregat dilakukan untuk memodelkan klasifikasi kerugian agregat yang meliputi penghitungan Value at Risk (VaR) dan Expected Shortfall (ES). Secara analitik, penentuan sebaran gabungan menggunakan metode fungsi karakteristik itu rumit. Sebagai alternatif, penentuan sebaran gabungan dihitung menggunakan metode fast Fourier transform. Dari data klaim dataCar di package R, diperoleh banyaknya klaim mempunyai sebaran Zero Truncated Negative Binomial (ZTNB) serta besarnya klaim mempunyai sebaran Inverse Gaussian (IG) dan sebaran Lognormal (LN). Sebaran compound ZTNB–IG lebih baik memodelkan besar VaR, nilai harapan, dan ragam data dibandingkan sebaran compound ZTNB–LN. Sedangkan untuk ES, kedua sebaran compound dapat digunakan untuk menghampiri ES empirik pada tingkat kepercayaan 97%., Aggregate loss is total losses that can be calculated with a compound distribution approach, both analytically and numerically. Determination of the aggregate loss distribution is carried out to model the classification of aggregate losses which includes the calculation of Value at Risk (VaR) and Expected Shortfall (ES). Analytically, the determination of the compound distribution using the characteristic function method is complicated. Alternatively, the determination of the compound distribution can be calculated using the fast Fourier transform method. From the dataCar claim data in package R, frequency claims have a Zero Truncated Negative Binomial (ZTNB) distribution and severity claims have an Inverse Gaussian (IG) distribution and a Lognormal (LN) distribution. The compound ZTNB–IG distribution better models the size of VaR, expectation value, and variance from the data compared to the compound ZTNB–LN distribution. Meanwhile for the ES, the two compound distributions can be used to approximate the empirical ES at the 97% confidence level.
Keyword: aggregate loss, characteristic function method, ES, fast Fourier transform method, VaR

Judul: Penentuan Sebaran Total Kerugian Asuransi Kendaraan
Abstrak: Kerugian agregat merupakan total kerugian pemegang polis yang harus ditanggung oleh perusahaan asuransi dalam periode waktu tertentu. Kerugian agregat dapat dihitung dengan menentukan sebaran total kerugian pada periode sebelumnya. Karya ilmiah ini menggunakan Loss Distribution Approach (LDA) yaitu metode untuk menghitung sebaran total kerugian dengan mempertimbangkan banyaknya klaim dan besarnya klaim yang dihitung dengan model sebaran compound. Metode rekursif Panjer digunakan untuk mendapatkan model sebaran compound, kemudian diperoleh nilai Value at Risk (VaR) dan Expected Shortfall (ES). Untuk data klaim asuransi kendaraan di Australia periode 2004-2005, diperoleh banyaknya klaim menyebar Zero Truncated binomial negatif dan besarnya klaim menyebar invers Gauss, lognormal, dan Pareto. Untuk menghitung VaR dan ES, sebaran yang paling baik untuk besar klaim adalah sebaran invers Gauss karena paling mendekati VaR dan ES empiris., Aggregate loss is the total loss of the policyholder that must be paid by the insurance company within a certain period of time. Aggregate losses can be calculated by determining the distribution of total losses in the previous period. This scientific work uses the Loss Distribution Approach (LDA), which is a method for calculating the distribution of total losses by considering the number of claims and the amount of claims calculated using the compound distribution model. Panjer recursive method is used to obtain a compound distribution model, and then the Value at Risk (VaR) and Expected Shortfall (ES) values are obtained. For vehicle insurance claims data in Australia for the period 2004-2005, the number of claims have a Zero Truncated negative binomial distribution and the amount of claims have inverse Gaussian, lognormal, and Pareto distribution. To calculate VaR and ES, the best distribution for the amount of claims is the inverse Gaussian distribution because it is closest to the empirical VaR and ES.
Keyword: Expected Shortfall, kerugian agregat, metode rekursif Panjer, , Value at Risk

Judul: Respiratory Quoti<mt of Duck (Anas platyrhynchos), Muscovy (Cairina moschata) and Mule Ducic.
Abstrak: Duck, muscovy and mule duck are water jowl that have a great prospect to be developed. Duck is a good water fowl layer. Muscovy can be developed as a m(.;at water fowl and it produces less eggs compared DY duck so that muscovy has a lov..er reproduction ability. Mule duck can be used is a solution for that problem. The additional information for the advancement of mule duck reproduction nowadays still being searched and developed. The information of oxygen consumption of animal can be used as the indicator for knowinB. the metabolism activity and also for estimating the energy metabolism need of animal. This study was done in Poultry Animal Production Laboratory, Faculty of Animal Science, Bogor Agricultural University from January until March 2003. The material that have been used were 12 ducks, 12 muscovies and 12 mule ducks. The entire material were 36 Day Old Ducks that have been kept for eight weeks. The oxygen consumption and carbon dioxide production data were gained by locating the ducks inside the respiration chamber which were supplied by pure oxygen. The first week measurement was used 12 animal for eaGh species. The forth and eight week were used respectively 4 ducks. Respiratory Quotient have been measured based on the oxygen consumption and C(h production fwm each animal.
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