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"Gaussian processes can be viewed as a far-reaching infinite-dimensional extension of classical normal random variables. Their theory presents a powerful range of tools for probabilistic modelling in various academic and technical domains such as Statistics, Forecasting, Finance, Information Transmission, Machine Learning, to mention just a few. The objective of these Briefs is to present a quick and condensed treatment of the core theory that a reader must understand in order to make his own independent contributions. The primary intended readership are PhD/Masters students and researchers working in pure or applied mathematics. The first chapters introduce essentials of the classical theory of Gaussian processes and measures with the core notions of reproducing kernel, integral representation, isoperimetric property, large deviation principle. The brevity being a priority for teaching and learning purposes, certain technical details and proofs are omitted. The later chapters touch important recent issues not sufficiently reflected in the literature, such as small deviations, expansions, and quantization of processes. "

"Dalam pengenalan objek pada sistem pengawasan lalu lintas dibutuhkan sebuah metode yang mampu membedakan antara objek dan non objek. Salah satu metode umum yang biasa digunakan adalah background subtraction. Background subtraction menjadi bagian awal yang penting dari sebuah aplikasi dalam metode computer vision. Hasil dari background subtraction biasanya digunakan dalam proses pada level yang lebih tinggi. Kami mengajukan sebuah metode Gaussian Mixture Model (GMM) dengan algoritma Hole Filling(HF). Ide utama dari pendekatan yang diajukan karena hasil dari GMM menghasilkan noisy image yang berasal dari kesalahan klasifikasi. Hal ini terjadi karena berbagai situasi (waving trees, rippling water dan illumination change). Metode HF yang sederhana mampu meningkatkan akurasi hingga 97,9% dan Kappa statistic hingga 0,74 dengan mengurangi kesalahan klasifikasi dari GMM. Hasil eksperimen and evaluasi pada pixel level menunjukkan bahwa GMMHF mampu unggul dari metode yang lain. Dengan peningkatan kinerja deteksi kendaraan menggunakan GMMHF, estimasi kecepatan kendaraan mendapatkan perbaikan. GMMHF yang dipadukan dengan Pin Hole model menghasilkan estimasi kecepatan terbaik dibandingkan skenario lainnya, dimana simpangan ratarata sebesar 7,4 Km/jam.

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.There is a necessity in traffic control system using camera to have the capability to discriminate between an object and non-object in the image. One of the procedure to discriminate between those two is usually performed by background subtraction. Gaussian Mixture Model (GMM) is popular method that has been employed to tackle the problem of background subtraction. However, the output of GMM is a rather noisy image which comes from false classification. This situation may arise because several conditions in the video input such as, waving trees, rippling water, and illumination changes. In this paper, a version of GMM technique which is combined with Hole Filling Algorithm (HF) classifier is proposed to alleviate those has problems. The experimental result shows that the proposed method improved the accuracy up to 97.9% and Kappa statistic up to 0.74. This result has outperformed many similar methods that is used for evaluation. With improvement of vehicles detection performance using GMMHF, vehicle?s speed estimation also improved. GMMHF that combined with Pin Hole Model produce the best speed estimation compared with other scenarios, where standard deviation is 7,4 Km/hr."

"Pada skripsi ini dibuat perangkat lunak simulasi modulator dan demodulator GMSK ( Gaussian faltered Minimum Shift Keying) yang bertujuan untuk mengetahui proses modulasi yang terjadi pada modulator serta unjuk kerja demodulator dalam menerjemahkan sinyal GMSK termodulasi yang telah dipengaruhi oleh faktor pengganggu, yaitu Additive White Gaussian Noise (AWGN) dan fading Rayleigh. Demodulator yang digunakan adalah demodulator deteksi differensial Z bit. Simulasi ini dibuat dengan bahasa pemrograman Borland Delphi for Windows. Analisa proses modulasi dan demodulasi dilakukan dengan mengamati bentuk-bentuk sinyal yang terjadi pada setiap tahapan proses. Dari uji cobs simulasi maka dapat dianahsa karakteristik unjuk kerja demodulator deteksi differensial Z bit, yaitu berupa laju kesalahan bit atau Bit Error Rate (BER) sebagai fungsi dari perbandingan energi tiap bit terhadap kepadatan noise, EblN. Selain itu dianalisa juga perbandingan unjuk kerja demodulator antara kanal yang tidak dipengaruhi fading Rayleigh dengan kanal yang dipengaruhi fading Rayleigh. Dan pada simulasi ini diperlihatkan juga pengaruh perubahan konstanta BcT terhadap unjuk kerja demodulator. Dari anahsa hasil simulasi tersebut dapat diketahui bahwa fading Rayleigh mengakibatkan penurunan unjuk kerja demodulator, dan dari analisa hash simulasi dapat diketahui jugs bahwa semakin besar harga konstanta BtT, semakin baik unjuk kerja demodulator."

"Statistika inferensi merupakan metode penarikan kesimpulan tentang keseluruhan informasi dalam populasi berdasarkan data sampel. Statistika inferensi sangat erat kaitannya dengan distribusi probabilitas. Distribusi invers Gaussian merupakan salah satu distribusi probabilitas kontinu yang memfasilitasi masalah kemencengan dan long-tail. Distribusi ini memiliki dua parameter yaitu dan . Dalam tugas akhir ini dibahas beberapa inferensi parameter dari distribusi invers Gaussian antara lain taksiran titik terbaik, taksiran interval, pengujian hipotesis parameter. Bagian akhir dari tugas ini membahas pengujian one-way Analysis of Reciprocal (ANORE).

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Inference statistics is the method to draw conclusion about information of population based on sample. Inference statistcs has close relationship with the probability distribution. Inverse Gaussian distribution is one of the distribution probability that can facilitate skewed and long-tail data. The distribution has two parameters, and .This paper discusses some parameter inference of inverse Gaussian distribution, such as best point estimator, interval estimation, and hypotesis test. The last part of this paper explains detail of one-way Analysis of Reciprocal (ANORE)."

"Tugas akhir ini membahas mengenai distribusi invers gaussian yang merupakan distribusi probabilitas kontinu yang dapat mengatasi masalah kemencengan dan long-tail. Pembahasan meliputi fungsi kepadatan probabilitas, fungsi distribusi, fungsi survival, fungsi hazard, serta membentuk fungsi pembangkit momen. Kemudian, dicari bentuk mode, mean, variansi, kemencengan, dan kurtosis distribusi invers gaussian. Terakhir, dicari taksiran parameter dan distribusi dari taksiran parameter menggunakan MLE. Data Jug Bridge mengenai drainase digunakan sebagai ilustrasi.

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This paper discusses about Inverse Gaussian Distribution, the continued probability distribution which can solve skew and long tail problem. At first, we study about probability density function, cumulative distribution function, survival function, hazard function, and form moment generating function. Then, we seek mode, mean, variance, skewness, and kurtosis of inverse gaussian distribution. Finally, we try to discover parameter estimation and distribution of parameter estimation using MLE. Jugde Bridge data about drianage will be used as illustration."

"The Birnbaum-Sanders (BS) distribution was first introduced in 1969 by Birnbaum and Saunders as a combination of inverse Gaussian distributions with a length-biased inverse Gaussian distribution. Later, in 2008, Ahmed et al. introduced a new parametrization of the BS distribution based on Birnbaum-Sanders, and they also proposed a parameter estimation using the method of moments and regression-quantile estimation. In this paper, we emphasize the Birnbaum-Sanders distribution presented by Ahmed et al., and we develop an EM-algorithm to estimate two unknown parameters of this distribution. The EM-algorithm is a general method used to estimate the parameters when the probability density function is complicated and it is the best alternative for the estimation of a mixture distribution. We assumed that this problem has a missing value, and maximized complete data log-likelihood function instead log-likelihood function because it is analytically easier. Moreover, some simulation experiments were conducted in order to examine the performance of the proposed parameter estimation, and it was observed that the performances were quite satisfactory. Specifically, the MSE, variance and bias tend to decrease as n increases."