Judul: Sebaran Bivariate Inverse Weibull
Abstrak: Sebaran baru dapat dibangun dari sebaran lain yang telah ada. Salah satu cara yang umum digunakan adalah menggabungkan dua atau lebih sebaran untuk mendapatkan sebaran baru. Pada karya ilmiah ini akan dibahas suatu sebaran baru yaitu sebaran bivariate inverse Weibull yang dibangun dari dua pasang sebaran inverse Weibull yang saling bebas. Menggunakan definisi sebaran maksimum, fungsi sebaran kumulatif bersama dan fungsi kepekatan peluang bersama dari sebaran bivariate inverse Weibull dapat dirumuskan dari fungsi sebaran inverse Weibull. Pendugaan parameter dilakukan dengan metode penduga kemungkinan maksimum dan metode Newton-Raphson. Pembangkitan serangkaian data dengan jumlah yang berbeda menunjukkan data dengan jumlah besar memberikan dugaan yang lebih akurat bagi parameter., A new distribution can be built from already existing distributions. One of the common method is compounding two or more distributions to obtain a new one. This paper will discuss a new distribution that is a bivariate inverse Weibull distribution. This new distribution is built from two pairs of independent inverse Weibull distributions. Using the definition of maximum distribution, the joint cumulative distribution function and the joint probability density function of a bivariate inverse Weibull can be formulated from the inverse Weibull distribution function. Parameter estimation was done using the maximum likelihood method and Newton-Raphson method. Generating several sets of data with different amounts pointed out that a large number data gave more accurate estimates for parameters.
Keyword: bivariate inverse Weibull distribution, maximum distribution, inverse Weibull distribution, maximum likelihood method, Newton-Raphson method

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: Mercury Toxicity and It’s Effect on Histopathology Change of Nile Tilapia (Oreochromis niloticus).
Abstrak: Nile tilapia (Oreochromis niloticus) is one of fish species that oportunity to contaminated with mercury. The effects of pollutants can damage living organisms organs and can cause death. The effects caused mercury had acute or chronic character. The aims of this study are to determine threshold and acute toxicity of mercury chloride (HgCl2) of Nile tilapia (Oreochromis niloticus), to assess the effect of mercury chloride (HgCl2) on several biometric parameters (survival, growth rate of average daily weighted, liver condition, bile and reproductive variability of Nile tilapia (Oreochromis niloticus), assess the level of damage to the histological structure of the gills, liver and kidney of Nile tilapia (Oreochromis niloticus) caused mercury chloride (HgCl2) exposure. This study was conducted from February to June 2013. Nile Tilapia (Oreochromis niloticus) were used in this study were female with average weight 20 grams or 11-13 cm length range. Toxicant materials used in this study was mercury chloride (HgCl2). Fish were reared in each aquarium 60x40x30 containing 48 liters of water. This study consists of three stages: a preliminary test, acute test, and sub-chronic test. To determine the changes in biometric condition of tilapia approximated by measuring the survival rate (SR), the growth rate of average daily weight , the content of mercury in the fish organs, hepatosomatic index (HSI), the relative bile volume (VER), gonadal soamtic index (IKG), fecundity and oocit diameter, tissue damage caused by mercury in fish organs by making histological preparations stained with hematoxylin and eosin. The median lethal concentration (96 hr, LC50) of Mercury Chloride was calculated as 1,64 mgL--1.The survival rate was highest in the control treatment (46,67 %) . Mercury chloride with concentration 0.196 mgL--1 show significant effect to changes HSI and relative bile volume, and oocyte diameter of Nile tilapia (p < 0,05). Mercury chloride with a concentration of 0,164 mgL-1 and 0,196 mgL-1 have not a significant effect on the growth rate of weight, gonadal somatic index and fecundity of Nile tilapia (p > 0,05). Mercury chloride cause damage to gills (hyperplasia, hypertrophy, proliferation and neukrosis), liver (hyperplasia, hemorhage, shrinkage of hepatocytes, proliferation and neukrosis) and kidney (hyperplasia, hemorrhage, shrinkage of the glomerulus, proliferation and neukrosis).
Keyword: Nile tilapia, Hepatosomatic indexs (HSI), histopathology