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Abstrak :
ABSTRAK Count data tidak selalu bersifat ekuidispersi. Sehingga, distribusi Poisson tidak dapat digunakan untuk memodelkan count data tersebut. Beberapa distribusi alternatif dari distribusi Poisson telah dikenalkan untuk memodelkan data overdispersi. Namun, distribusi tersebut memiliki kompleksitas yang lebih tinggi dalam jumlah parameter distribusi. Perlu dilakukan modifikasi pada distribusi Poisson agar distribusi yang terbentuk bisa merepresentasikan data overdispersi. Salah satu caranya yaitu dengan melakukan pencampuran distribusi antara distribusi Poisson dengan distribusi Lindley. Distribusi yang terbentuk yaitu distribusi Poisson-Lindley. Namun, distribusi Poisson-Lindley belum dapat mengatasi data underdispersi. Selain itu terdapat data asli yang tidak memiliki observasi bernilai nol. Dengan demikian, untuk mendapatkan distribusi yang lebih fleksibel agar lebih cocok dengan count data tersebut, perlu dilakukan modifikasi pada distribusi Poisson-Lindley dengan menerapkan metode zero-truncated. Distribusi baru yang terbentuk yaitu distribusi Zero-truncated Poisson-Lindley. Distribusi baru tersebut dapat mengatasi data yang tidak memiliki observasi bernilai nol dalam kondisi overdispersi maupun underdispersi. Dalam skripsi ini, didapat karakteristik dari distribusi Zero truncated Poisson-Lindley dan penaksiran parameter distribusi menggunakan metode maximum likelihood.

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ABSTRACT Not every count data has equal-dispersion. As a result, Poisson distribution is no longer appropriate to be used for count data modelling. Several distributions have been introduced to be used as an alternative to Poisson distribution on handling the over-dispersion in data. In general, the alternative distributions have higher complexity in the number of parameters. Modification needs to be done in Poisson distribution so that the distribution can represent the condition of the over-dispersion in data. By doing mixing Poisson and Lindley distribution, a new distribution called Poisson-Lindley is developed. However, Poisson-Lindley distribution cannot handle data that exhibits under-dispersion. On the other hand, there is real data that has no zero-count. Therefore, in order to obtain a more flexible distribution to fit count data that has no zero count, a modification needs to be done in Poisson Lindley distribution by applying a zero truncated method in Poisson-Lindley distribution. The newly formed distribution is named Zero-truncated Poisson Lindley distribution. It can handle the condition when the data has no zero-count both in over-dispersion and under-dispersion. In this paper, characteristics of Zero truncated Poisson Lindley distribution are obtained and estimate distribution parameters using the maximum likelihood method.

Abstrak :
Distribusi Weibull-Poisson merupakan distribusi kontinu yang dapat memodelkan beberapa macam bentuk hazard yaitu monoton naik, monoton turun dan increasing upside-down bathtub shape yang mempunyai bentuk bathtub shape terbalik dan monoton naik. Distribusi ini merupakan suatu distribusi lifetime yang dapat memodelkan kegagalan dalam suatu sistem seri dan merupakan pengembangan dari distribusi EksponensialPoisson. Distribusi ini diperoleh dengan melakukan metode compounding terhadap distribusi Weibull dan distribusi ZT-Poisson. Untuk mendapatkan bentuk akhir dari distribusi tersebut digunakan beberapa sifat matematis seperti order statistik dan ekspansi deret taylor. Selain pembentukan distribusi Weibull-Poisson, skripsi ini menjelaskan fungsi kepadatan peluang, fungsi distribusi, momen ke-r, momen sentral ke-r, mean, dan variansi. Sebagai ilustrasi, dibahas pula aplikasi distribusi Weibull-Poisson pada data survival marmut setelah terinfeksi virus Turblece Bacilli. ......The Weibull-Poisson distribution is a continuous distribution that can be modeled various forms of hazard namely monotone up, monotone down and upside-down down bathtub shape which is shaped up. This distribution is a lifetime-distribution that can model failures in a series system and is development of the Exponential-Poisson distribution. This distribution is obtained by perform the compounding method on the Weibull distribution and the ZT-Poisson distribution. To obtain the final form of the distribution, several mathematical properties are used such as statistical order and Taylor's number expansion. In addition to the formation of Weibull-Poisson distribution, this thesis includes the probability density function, distribution function, moment rth, rth central moment, mean, and variance. As an illustration, Weibull-Poisson distribution is applied on guinea pig survival data after being infected with Turblece virus Bacilli.

Abstrak :
ABSTRACT
Count data are often described by the Poisson distribution, which requires identical mean and variance, namely equi dispersion. However, in practical situations, count data usually exhibit either over dispersion with variance larger than mean, or under dispersion with variance smaller than mean. Therefore, traditional approaches that focus on only mean shifts, such as the c chart, cannot monitor count data with over/under dispersion efficiently.To monitor mean and dispersion of count data simultaneously, this paper adopts Conway MaxwelI Poisson (COMPoisson) distributions to ht count data with over/under dispersion, and constructs a control chart based on the likelihood ratio test. The proposed chart is powerful in detecting both mean and dispersion shifts of count data with either over dispersion or under dispersion. Numerical simulations have demonstrated its performance in various cases.

Abstrak :
Tugas akhir ini membahas mengenai penentuan distribusi dari banyaknya 'hit' kerandoman barisan bilangan biner pada metode Overlapping Template Mathcing Test. Metode ini merupakan suatu metode yang terfokus pada sering atau tidaknya muncul 'pola' acak pada tiap blok barisan bilangan biner dengan menggunakan suatu template. Penentuan distribusi ini dimulai dengan menggunakan distribusi Compound Poisson , lebih khusus lagi menggunakan distribusi Geometric Poisson. Lebih lanjut lagi digunakan transformasi Confluent Hypergeometric Function (Kummer's Function). Selain itu, dalam tugas akhir ini juga diberikan ilustrasi dalam menguji kerandoman barisan bilangan biner dengan menggunakan metode Overlapping Template Mathcing Test. ......This paper discusses about determining distribution number of hit of bit sequence randomness in Overlapping Template Matching Test. This method focusses on how often the pattern appears in each blok of bit sequence by using a template. This determining distribution starts by using Compound Poisson distribution, specifically by using Geometric Poisson distribution. Moreover, Confluent Hypergeometric Function is used as transformation's method. Besides, this paper also gives illustration about how to test the randomness of bit sequence using Overlapping Template Matching Test.