Judul: Sebaran Negative Binomial-Generalized Exponential dan Aplikasinya pada Data Kecelakaan Kendaraan Tunggal
Abstrak: Pemodelan frekuensi kecelakaan kendaraan tunggal dapat berguna bagi beberapa pihak salah satunya pihak asuransi. Pada tugas akhir ini dijelaskan sebaran Negative Binomial-Generalized Exponential yang merupakan sebaran campuran antara sebaran Binomial Negatif dengan sebaran Generalized Exponential. Sebaran Negative Binomial-Generalized Exponential dapat digunakan untuk memodelkan data yang mengalami overdispersion serta yang memiliki nilai peluang frekuensi nol besar. Sebaran ini diaplikasikan pada data kecelakaan tunggal di Texas antara tahun 2003 hingga 2008. Parameter sebaran diduga menggunakan metode kemungkinan maksimum dengan software R 4.0.3. Pada hasil perhitungan menunjukkan bahwa sebaran Negative Binomial-Generalized Exponential cocok untuk menduga frekuensi kecelakaan kendaraan tunggal., Frequency modeling of single-vehicle collisions could be useful for several parties, one of which is the insurance company. In this paper, the Negative Binomial-Generalized Exponential distribution is explained as a mixture distribution of the Negative Binomial and the Generalized Exponential distribution. Negative Binomial-Generalized Exponential distribution can be used to model overdispersion data with a large zero frequency probability value. This distribution is applied to single-vehicle crash data in Texas between 2003 and 2008. The distribution parameters are estimated using maximum likelihood method. The numerical calculation was done by using R 4.0.3 software. The result shows that the Negative Binomial-Generalized Exponential distribution is suitable for estimating the single-vehicle crash data.
Keyword: collision, frequency of crashes, maximum likelihood method, negative binomial-generalized exponential distribution

Judul: Sebaran Gabungan Binomial Negatif-Eksponensial
Abstrak: Total kerugian yang harus ditanggung oleh perusahaan asuransi pada periode waktu tertentu disebut risiko total. Penghitungan sebaran risiko total dapat dilakukan dengan sebaran gabungan (compound) dari sebaran banyaknya klaim (claim frequency) dan sebaran besarnya klaim (claim severity). Sebaran banyaknya klaim yang digunakan ialah sebaran binomial negatif dan sebaran binomial. Sebaran besarnya klaim yang digunakan ialah sebaran eksponensial. Penghitungan sebaran gabungan binomial negatif-eksponensial secara analitik menggunakan metode konvolusi melibatkan deret tak hingga yang sukar dihitung. Jika parameter skala dari sebaran binomial negatif adalah bilangan bulat positif, maka sebaran gabungan binomial negatif-eksponensial ekuivalen dengan sebaran gabungan binomial-eksponensial dengan parameter yang disesuaikan. Akibatnya, sebaran gabungan binomial negatif-eksponensial dapat dihitung melalui sebaran gabungan binomial-eksponensial yang hanya melibatkan deret berhingga yang mudah dihitung. Pada tugas akhir ini, diberikan contoh implementasi untuk data yang dibangkitkan melalui software Mathematica 11.3. Kemudian dihitung Value at Risk (VaR) dan Expected Shortfal (ES) menggunakan metode konvolusi dan metode Monte Carlo., The total loss that must be covered by the insurance company is called total risk. The total risk distribution can be calculated using compound distribution of the distribution of the number of claims (claim frequency) with the distribution of the amount of claims (claim severity). The distributions of the number of claims used are negative binomial distribution and binomial distribution. The distribution of the amount of claims used is exponential distribution. The analytical calculation of compound distribution of negative binomial-exponential using the convolution method is involving an infinite series that is difficult to calculate. If the scale parameter of the negative binomial distribution is a positive integer, then the compound distribution of negative binomial-exponential is shown to be equivalent to the compound distribution of binomial-exponential with adjusted parameters. As a result, the compound distribution of negative binomial-exponential can be calculated through the compound distribution of binomial-exponential in which involving only a finite series that is easy to calculate. In this final project, an implementation example for data generated through Mathematica 11.3 software is given. Then, Value at Risk (VaR) and Expected Shortfall (ES) are calculated using the convolution method and the Monte Carlo method.
Keyword: risiko total, sebaran binomial negatif-eksponensial, metode konvolusi, penghitungan tak hingga, sebaran binomial-eksponensial, penghitungan berhingga, total risk, negative binomial-exponential distribution, convolution method, infinite total risk, binomial-exponential distribution, finite total risk

Judul: The Fern of West Timor  East Nusa Tenggara
Abstrak: Based on this study there are 58 species belonging to 36 genera. They are Achrosticum (1 species), Adiantum (5 species), Amphineuron (3 species), Asplenium (4 species), Athyrium (1 species), Belvisia (1 species), Botrycium (1 species), Ceratopteris (1 species), Christella (4 species), Ctenitis (1 species), Ctenopteris (1 species), Cyathea (1 species), Davallia (2 species), Dennstaedtia (1 species), Diplazium (2 species), Doryopteris (1 species), Drynaria (2 species), Dryopteris (1 species), Gleichenia (1 species), Heterogoniurn (1 species), Humata (1 species), Lycopodium (1 species), Microlepia (1 species), Microsorium (1 species), Nehprolepis (2 species), Oleandra (1 species), Platycerium (1 species), Pleocnemia (1 species), Pteris (5 species), Pyrrosia (1 species), Sellaginela (1 species), Selliguea (1 species), Sphaerostephanos (2 species), Tectaria (1 species), Trichomanes (1 species), and Vittaria (1 species).
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