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"Distribusi Beta-Pareto merupakan distribusi kontinu yang dapat memodelkan data yang unimodal dan heavy-tailed. Distribusi Beta-Pareto merupakan hasil pengkombinasian antara distribusi Pareto dan distribusi Beta menggunakan distribusi Beta-Generated. Pada tugas akhir ini akan dibahas mengenai pembentukan distribusi Beta-Pareto, fungsi kepadatan probabilitas, dan karakteristik-karakteristik distribusi Beta-Pareto lainnya. Penaksiran parameter dari distribusi Beta-Pareto menggunakan metode maksimum likelihood. Sebagai ilustrasi, akan digunakan data debit aliran air sungai Sunter selama setahun pada tahun 1995 yang akan dimodelkan dengan distribusi Beta-Pareto.

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Beta-Pareto distribution is a continuous distribution which can model unimodal and heavy-tailed data. Beta-Pareto distribution is derived from Pareto distribution and Beta distribution using the Beta-Generated distribution. It will be explained how to construct the Beta-Pareto distribution, probability density function, and other characteristics of Beta-Pareto distribution. Maximum likelihood method is used for estimating Beta-Pareto?s parameters. Discharge rates of the Sunter River in 1995 are used to illustrate the applicability of Beta-Pareto distribution."

"Tugas akhir ini membahas tentang distribusi Weibull-Pareto yang merupakan distribusi probabilitas kontinu yang dibangun dengan menggunakan metode Transformed-Transformer. Distribusi Weibull-Pareto dapat menggambarkan data yang menceng kanan, menceng kiri, atau simetris serta dapat menggambarkan data yang mempunyai light-tailed maupun heavy-tailed. Pembahasan meliputi fungsi kepadatan probabilitas, fungsi distribusi, fungsi survival, dan fungsi hazard. Kemudian dicari karakteristik-karakteristik dari distribusi Weibull-Pareto yang meliputi modus, persentil, dan fungsi pembangkit momen. Terakhir dicari taksiran parameter dari distribusi ini dengan menggunakan metode Alternative Maximum Likelihood (AML). Simulasi data juga dilakukan sebagai ilustrasi.

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This paper discusses about Weibull-Pareto distribution, the continuous probability distribution which arised by Transformed-Transformer method. The Weibull-Pareto distribution gives a good fit to right skew, left skew, or symmetric. In particular, Weibull-Pareto distribution can solve light tailed or heavy tailed problem. At first, we study about probability density function, cumulative distribution function, survival function, and hazard function. Then, we find the characteristic of Weibull-Pareto distribution, that is mode, percentile, and moment generating function. Finally, we estimate the parameters of Weibull-Pareto distribution using Alternative Maximum Likelihood (AML) method. Simulation data is used as illustration."

"ABSTRAKTugas akhir ini membahas mengenai distribusi Gamma-Pareto yang merupakandistribusi probabilitas kontinu yang diperoleh dengan melakukan metodetransformed-transformer pada distribusi Gamma dan distribusi Pareto. Metode inidiperkenalkan oleh Alzaatreh. Distribusi Gamma-Pareto dapat mengatasi masalahkemencengan dan heavy-tail. Beberapa karakteristik distribusi akan dipelajari,seperti fungsi kepadatan probabilitas, fungsi distribusi, fungsi survival, fungsihazard, modus, dan momen ke-r. Kemudian, dicari estimasi parameter denganmenggunakan metode alternatif maksimum likelihood. Pada akhirnya, dataBirnbaum dan Saunders (1969) digunakan sebagai ilustrasi.

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ABSTRACTThis paper discusses about Gamma-Pareto distribution, the continued probabilitydistribution which is obtained by using transformed-transformer method inGamma and Pareto distribution. This method is introduced by Alzaatreh. Gamma-Pareto distribution can solve skewness and heavy-tail problem. First, somecharacteristics of distribution will be studied, such as probability density function,distribution function, survival function, hazard function, mode, and rth moment.Then, parameter estimation will also be studied by using alternative maximumlikelihood. Finally, a set of data Birnbaum dan Saunders (1969) will be used asillustration."

"Pada kondisi tertentu, harga saham dapat mengalami fluktuasi yang cukup tajam (lompatan). Jika model harga saham tidak memperhatikan kemungkinan terjadinya lompatan, prediksi harga saham kurang dapat mencerminkan kondisi yang sebenarnya. Karena itu dibutuhkan model Jump-Diffusion (JD) yang dapat menangkap lompatan tersebut. Salah satu model JD adalah model Pareto-Beta Jump- Diffusion (PBJD). Model yang diusulkan oleh C.A Ramezani dan Y. Zeng (1998) ini merupakan perluasan model Merton Jump-Diffusion (MJD) (1976). Waktu muncul lompatan ke atas dan ke bawah masing-masing direpresentasikan oleh suatu proses Poisson, sedangkan besar lompatan ke atas berdistribusi Pareto(ηu), dan besar lompatan ke bawah berdistribusi Beta(ηd,1). Model PBJD memiliki koefisien difusi s konstan yang menyatakan volatilitas model. Pada tesis ini volatilitas konstan s diganti menjadi volatilitas stokastik mengikuti model Heston (1993). Model PBJD dengan volatilitas stokastik selanjutnya disebut sebagai model PBJDVS, dan model PBJDVS ini berbentuk sebuah sistem Persamaan Diferensial Stokastik (PDS). Tesis ini membahas bagaimana menentukan solusi analitik model PBJDVS. Berdasarkan solusi analitik tersebut, ditentukan probability density function (pdf) log-return saham satu periode model PBJDVS. Selain itu, berdasarkan solusi analitik, dilakukan simulasi lintasan (sample path) harga saham dan simulasi bentuk pendekatan kurva pdf log-return saham satu periode model PBJDVS. Hasil simulasi lintasan harga saham model PBJDVS dengan parameter tertentu dapat menunjukkan adanya lompatan.

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In certain conditions, stock price can fluctuate highly (jump). If a stock price model ignores the possiblity of jump, the stock price prediction can?t adequately reflect the real condition. That is why Jump-Diffusion (JD) model that can catch the jump is needed. One of the JD models is Pareto-Beta Jump-Diffusion (PBJD) model. The model, proposed by C.A Ramezani and Y. Zeng (1998), is an extension of Merton Jump-Diffusion (MJD) (1976) model. Each of the up and down jump occurence times are represented by a Poisson process, while the up-jump magnitudes are distributed Pareto(ηu), and the down-jump magnitudes are distributed Beta(ηd,1). PBJD model has constant diffusion coeficient s that means volatility of the model. In this thesis the constant volatility s is replaced by a stochastic volatility following Heston model (1993). PBJD model with stochastic volatility will be called PBJDVS model, and this PBJDVS model has the form of Stochastic Differential Equation (SDE) system. This thesis discusses how to determine analytic solution of PBJDVS model. Based on this analytic solution, probability density function (pdf) for one-period stock log-returns of PBJDVS model is determined. In addition, based on analytic solution, sample path of stock price and approximate curve of pdf for one-period stock log-returns of PBJDVS model are simulated. The simulation of sample path of stock price with certain parameters can show jump."

"This book offers definitive coverage of the sea beet, the wild ancestor of all cultivated beets, which grows mainly on Mediterranean shores. The editors have collected both scientific and historical source material, illustrations and references."

"Risiko klaim merupakan salah satu risiko operasional yang harus dikelola oleh perusahaan asuransi. Pada penelitian ini akan dihitung besar perkiraan risiko klaim yang akan terjadi dengan menggunakan pendekatan Loss Distribution Approach-Aggregation Method dan Extreme Value Theory-Generalized Pareto Distribution. Selanjutnya akan dibandingkan metode mana yang lebih cocok dalam pengukuran risiko operasional untuk klaim kecelakaan kerja. Berdasarkan hasil perhitungan dan back testing didapat bahwa kedua metode valid digunakan untuk menghitung perkiraan risiko klaim operasional pada klaim kecelakaan kerja. Akan tetapi metode Loss Distribution Approach-Aggregation Method lebih cocok untuk mengukur risiko klaim kecelakaan kerja berdasarkan data yang ada.

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The risk of claims is one of the operational risks that must be managed by the insurance company. This research will calculate the estimates of the risk of claims that will occur using Loss Distribution Approach Aggregation Method and Extreme Value Theory Generalized Pareto Distribution. Furthermore, these two methods will be compared and chosen which is more suitable for the measurement of operational risk for work accident claims.

Based on the calculations and back testing, both of the methods are valid to calculate the estimates operational risk of claim for work accident claims but the Loss Distribution Approach Aggregation Method is more suitable to measure the risk of work accident claims based on existing data."

"Tujuan dari tesis ini adalah melihat bagaimana hubungan antara beta CAPM dengan beta Multifactor Models. Yang menjadi variabel dependen ialah beta CAPM. Dan variabel independennya ialah beta inflasi, beta nilai tukar, dan beta suku bunga. Sampel yang dipilih merupakan saham-saham yang termasuk kategori LQ45 selama periode 2005-2007 yaitu sebanyak 12 saham. Hasil penelitian ini menunjukkan bahwa hanya variabel beta inflasi yang mempunyai pengaruh signifikan terhadap beta CAPM, sedangkan variabel beta nilai tukar dan beta suku bunga tidak

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The purpose of this thesis is to see how the relationship between beta CAPM and beta Multifactor Models. The dependent variable is the CAPM beta. And the independent variables are inflation beta, exchange rate beta, and interest rate beta. The sample selected is stocks that are included in the LQ45 category during the period 2005-2007, which are 12 stocks. The results of this study indicate that only the inflation beta variable has a significant effect on the CAPM beta, while the exchange rate beta and interest rate beta do not. Keywords."

"This publication reviews most of the available literature on the fatigue properties of β annealed Ti-6Al-4V and titanium alloys with similar microstructures. The focus is on β processed and β heat-treated alloys because β annealed Ti-6Al-4V has been selected for highly loaded and fatigue-critical structures, including the main wing-carry-through bulkheads and vertical tail stubs, of advanced high-performance military aircraft. An important aspect of the review is a concise survey of fatigue life assessment methods and the required types of fatigue data. This survey provides the background to recommendations for further research, especially on the fatigue behaviour of β annealed Ti-6Al-4V under realistic fatigue load histories, including the essential topic of short/small fatigue crack growth. Such research is required for independent fatigue life assessments that conform to the aircraft manufacturer?s design requirements, and also for life reassessments that most probably will have to be made during the service life of the aircraft."