Judul: Karakteristik Kelas Sebaran (𝑎�, 𝑏�, 1).
Abstrak: Penentuan model frekuensi klaim yang dilakukan pihak tertanggung pada pengajuan klaim asuransi dapat dimodelkan dengan berbagai macam sebaran diskret. Sebaran-sebaran diskret ini dapat dikelompokkan ke dalam berbagai kelas. Kelas sebaran yang dipelajari pada karya tulis ini adalah kelas sebaran (𝑎��, 𝑏��, 1) . Misalkan 𝑁�� adalah peubah acak diskret frekuensi klaim dan 𝑝��𝑘�� = 𝑃��(𝑁�� = 𝑘��) adalah fungsi massa peluang frekuensi klaim sebanyak 𝑘�� . Kelas sebaran (𝑎��, 𝑏��, 1) adalah hasil modifikasi kelas sebaran (𝑎��, 𝑏��, 0) pada nilai 𝑝��𝑘�� yaitu saat 𝑘�� = 0 (𝑝��0), yaitu nilai peluang ketika tidak ada frekuensi klaim atau dengan kata lain nilai peluang saat tidak terjadi klaim. Terdapat dua jenis modifikasi yang digunakan, yaitu ketika peluang terjadinya kerugian sangat kecil sehingga peluang awalnya sangat besar (𝑝��0 > 0) dan modifikasi untuk peluang tidak terjadi klaim bernilai nol (𝑝��0 = 0). Tujuan dari karya tulis ini adalah menentukan karakteristik sebaran-sebaran anggota kelas sebaran (𝑎��, 𝑏��, 1) di antaranya fungsi massa peluang, fungsi pembangkit peluang, dan nilai harapan serta ragam masingmasing sebaran. Fungsi massa peluang sebaran gabungan dari kelas sebaran (𝑎��, 𝑏��, 1) dengan sebaran lain juga ditunjukkan dalam simulasi grafik pada karya tulis ini. Dengan menentukan parameter-parameter dari masing-masing sebaran dapat ditunjukkan pola frekuensi klaim yang terjadi.
Keyword: frekuensi klaim, kelas sebaran (𝑎�, 𝑏�, 1)

Judul: Pemodelan Sebaran Total Klaim pada Asuransi Sosial dengan Metode Compound Dua Peubah Acak Bebas
Abstrak: Salah satu cara untuk menentukan cadangan klaim asuransi adalah dengan menentukan sebaran dari total klaim. Total klaim merupakan total pengeluaran dalam satu periode yang harus ditanggung oleh suatu perusahaan asuransi. Total klaim dibentuk dari sebaran banyak klaim dan sebaran besar klaim. Untuk menghitung total klaim dibutuhkan model sebaran compound. Dalam karya ilmiah ini digunakan metode compound dua peubah acak bebas untuk memodelkan sebaran total klaim dari data BPJS Ketenagakerjaan Kota Pekalongan tahun 2020. Data tersebut terdiri dari data program Jaminan Kecelakaan Kerja, Jaminan Pensiun, dan Jaminan Kematian. Hasil Uji Khi Kuadrat menunjukkan bahwa sebaran binomial negatif merupakan sebaran yang cocok untuk memodelkan sebaran banyak klaim, sedangkan hasil Uji Anderson Darling menunjukkan bahwa dari masing-masing program jaminan memiliki sebaran yang berbeda untuk sebaran besar klaim. Dari hasil sebaran total klaim tersebut dapat ditentukan nilai harapan dan ragam dari sebaran agregat pada masing-masing program jaminan., One way to determine the reserve for insurance claims is to determine the distribution of aggregate claims. Aggregate claims are total losses within one period that must be borne by an insurance company. Aggregate claims are formed from the distribution of the number of claims and amount of claims. To calculate aggregate claims, a compound distribution model is used. In this manuscript, the compound of two independent random variables method is used to model the distribution of aggregate claims from BPJS Ketenagakerjaan participants in Pekalongan City in 2020. The data consists of data on work accident insurance, pension security, and death benefits programs.The Chi-Square Test results show that the negative binomial distribution is a suitable distribution to model the claim frequency distribution. Meanwhile, the results of the Anderson Darling test show that each guarantee program has a different distribution for the distribution of claim severity. From the results of the distribution of the aggregate claims, it can be determined the expected value and the variance of the aggregate distribution in each guarantee program.
Keyword: aggregate claims, amount of claims, compound distribution, number of claims

Judul: Utilization of hydrolized duckweed (Lemna minor) meal as a soybean replacement in Nile tilapia (Oreochromis niloticus) diet,
Abstrak: Tilapia is a fast growing fish widely cultured in many tropical and sub tropical countries. The recent production figures reported our global production estimates for 2015 is 5,576.8 metric tons. In developing countries the major challenges facing aquaculture industry is high cost of production associated with fish feeds. Feed represents 40-70% of operating costs for aquaculture operations, increasing expenses and potential declining supplies soybean meal have led scientists to search for less expensive but compatible alternative protein sources for fish feed; most of which are based on animal or plant protein sources. The objectives of study was to determine the incubation period for hydrolysis of duckweed and to evaluate the use of hydrolized duckweed as aprotein source for the growth performance of Nile tilapia Three experiments were conducted to determine the composition and digestibility of hydrolyzed duckweed meal by sheep rumen liquor as the replacement of soybean meal in the diet of Nile tilapia. The first trial examined the effectivity of sheep rumen liquor enzyme to decrease crude fiber contents of (DWM), the added volume of sheep rumen liquor was 100 ml/kg DWM and then it was incubated for 0, 12, 24 hr . The second trial was to evaluate the apparent digestibility of hydrolyzed DWM for Nile Tilapia, apparent digestibility were determined using chromic oxide indicator added to both reference diet and test diets. The feed ingredients used in the trial were hydrolyzed DWM (HDWM) and unhydrolyzed DWM (DWM). Ten fish with an average weight of 18±0.36g were used in the trial and reared in the aquarium of size 30×40×50cm for 15 days; feces were collected from three replicates using a fecal collection column attached to the aquarium. Third trial was to evaluate the growth performance of Tilapia fed test diet with hydrolyzed Duckweed meal (HDWM). The experimental design was set according to completely randomized design with four treatments and three replicates of HDWM inclusion levels that is 0%, 15%, 30% and 45%. Nile tilapia fish with initial body weight of 18±0.36g was kept in 12 units aquarium size of 30×40×50cm at stocking density of 10fish/aquarium, the fish were fed two times a day at 08:00am and 16:00pm to apparent satiation for a period of 60 days. The results indicated that duckweed meal (DWM) hydrolyzed with 100 mL/kg and incubated for 24 hrs showed the lowest crude fiber contents of 13.68% compared to other treatments. Total digestibility of hydrolyzed duckweed (HDWM) meal was 87.3% compared with unhydrolyzed duckweed (DWM) which was 66.8%. Total final weight (TFW), survival rate (SR), specific growth rate (SGR), feed conversional rate (FCR) and protein retention (PR) shows growth performance at 15% inclusion. The results of this study showed that 100mL/kg sheep rumen liquor at incubation period of 24 hr can be suitable for hydrolysis of duckweed to reduce crude fiber also hydrolyzed duckweed can substitute soybean meal at an incubation rate of 15% in the diet of Nile tilapia and had the same growth and FCR with control diet
Keyword: Digestibility, Duckweed meal, Growth performance, Sheep rumen