Judul: Uji kebebasan pada sebaran eksponensial bivariat
Abstrak: Masalah uji kebebasan diasumsikan terjadi pada dua komponen dalam sistem seri. Sebaran bersama dari lama hidup komponen dimodelkan dengan sebaran eksponensial bivariat Pickands, yang secara luas menggunakan sebaran Marshall dan Olkin. Komponen identik akan dibahas lebih dahulu. Uji takbias paling kuasa seragam (UMPU) dan uji rasio kemungkinan diperoleh. Uji UMPU yang diperoleh ialah takbersyarat dan uji ini sama dengan uji yang diperoleh dengan menggunakan uji rasio kemungkinan. Kasus komponen takidentik juga dibahas dan Uji UMPU dan rasio kemungkinan diperoleh. Uji UMPU diperoleh untuk menguji kebebasan pada komponen yang diperluas menjadi censoring scheme tipe II. Uji UMPU takbersyarat diperoleh pada pengujian apakah dua komponen identik atau tidak.
Keyword: Ruang contoh, Peubah acak, Momen

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: Morphofunction changes of gonadal and mandibular glands of the cave swiflets (Collocalia linchi) during nesting and reproductive period
Abstrak: The present study aimed to study the morphological and histochemical changes and possible correlation between the gonads and mandibular glands of the cave swiflets (Collocalia linchi) during reproductive and nesting period. A total of seventy two adult birds were used in this study. The birds, three males and three females, were collected each month during a period of one year. After being sacrificed, samples of gonads and mandibular salivary glands were taken out and processed routinely for light microscopy. The present result showed that the gonads were active during the period of February - June. In the testis, the size of the testicle were similar throughout the year, but the testis had different color according to month. The testis in June - January were black in color, and were white and black in February, March, May and were all white in April. The size and structure of the ovaries were also increase towards February - May. Therefore the period of February - June was regarded as reproductive period of the cave swiftlet. The size and structure of mandibular glands were also clearly increased and the glands were more active during the nesting and reproductive period. Histochemically, the bindings of some lectins in the gonad and mandibular glands were also increase in the number of reactive cells and in the intensities of the positive reactions during the nesting and reproductive period, suggested that certain carbohydrates were involved and may play important roles in the reproductive function of the cave swiftlet. The present result showed that there were clear signs on the functional and structural changes of the gonads and mandibular glands of the cave swiftlets during the active nesting and reproductive period, suggested a possible regulatory mechanism of the mandibular gland through gonadal hormones pathway.
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