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 Kerugian Agregat dengan Metode Rekursif Panjer
Abstrak: Perhitungan kerugian agregat diperlukan dalam mengukur modal risiko operasional suatu perusahaan asuransi. Kerugian agregat merupakan total kerugian pemegang polis yang harus ditanggung oleh perusahaan pada periode waktu tertentu. Loss Distribution Approach (LDA) merupakan metode untuk menghitung sebaran kerugian agregat berdasarkan data kerugian operasional di periode sebelumnya. Data tersebut terdiri atas data severity klaim (besarnya klaim) dan frequency klaim (banyaknya klaim). Sebaran kerugian agregat tersebut dapat dihitung dengan model sebaran compound. Dalam karya ilmiah ini digunakan metode Rekursif Panjer untuk menduga ukuran risiko Value at Risk (VaR) dan Expected Shortfall (ES) untuk data klaim Perusahaan Asuransi A tahun 2017. Metode Rekursif Panjer dapat digunakan apabila sebaran severity klaim merupakan sebaran diskret, sehingga sebaran severity klaim yang biasanya merupakan sebaran kontinu perlu didiskretisasi terlebih dahulu. Penghitungan sebaran kerugian agregat dengan Metode Rekursif Panjer mudah diimplementasikan dan hanya melibatkan galat diskretisasi saja.
Keyword: sebaran kerugian agregat, sebaran compound, metode rekursif Panjer

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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