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"Pemodelan jumlah klaim mengklaim salah satu topik paspor adalah praktik lapangan. masalah ini sering ditemukan dalam model ingthataatais persebaran. Poisson dributiontion yang digunakan dalam pemodelan sumber klaim tidak dapat digunakan sebagai fakta overproperti penyebaran.Oleh karena itu, distribusi yang distandarisasi di luar negeri dapat dimanfaatkanjumlah klaim yang mengklaim pengungkapan properti yang dibutuhkan. Dalam tulisan ini, analternatif menerima distribusi yang dihasilkan, yaitu Distribusi Umum Biomial Negatif-Negatif Distribusi adalah distribusi distribusi negatif negatif dan distribusi Membalik Gaussie dan distribusi metameterisasi pada parameter negatif Distribusi binomial yaitu p = exp (), di mana nilai variabel acak acak yang didistribusikan Inverse Gaussian. Distribusi eksternal ini adalah unimodal, hasa tebal thailand hasa positif menghasilkan kewajiban koefisien. Dalam tesis tingkat bawah, kemungkinan serangan dan komitmen faktorial dari distribusi NB-IG yang didistribusikan. Berarti, varians, skewness danurturtasthasic properties ofNB-IG distribusi disajikan dan parameter pengujian diperlakukan melalui survival maksimum maksimum metode estimasi. Kepenuhan distribusi NB-IG diilustrasikan oleh data nyata set.

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One topic of passports is field practice. this problem is often found in modeling the data distribution. tion used in modeling claims sources cannot be used as a fact of overproperty distribution. Therefore, standardized distributions abroad can be used the number of claims claimed In this paper, accept the resulting distribution, namely General Negative-Negative Biomial Distribution, Distribution is negative negative distribution and Gaussie Reverse distribution and metameterization distribution on negative parameters, binomial distribution ie p = exp (), where the variable value Varies Published InverseGaussian. This external distribution is immunodal, Thailand has a positive potential to produce the coefficient obligation. In the lower-level thesis, attacks and factorial commitments from the distributed NB-IG distribution are published. Means, variants, skewness and strictness of the properties of NB-IG distribution are presented and test parameters are approved through maximum maximum survival estimation method. The fullness of the NB-IG distribution is illustrated by real data sets."

"Analisis regresi digunakan untuk mengetahui hubungan antara satu variabel respon dan satu atau lebih variabel penjelas. Ketika variabel respon berupa data count yaitu data yang berupa bilangan bulat non-negatif, analisis regresi yang sering digunakan adalah analisis regresi Poisson. Pada regresi Poisson terdapat asumsi kesamaan nilai mean dengan nilai variansinya. Dalam data count sering didapati kondisi dimana nilai variansi lebih besar dari nilai meannya atau disebut overdispersi. Pada data yang overdispersi, regresi Poisson kurang tepat jika digunakan karena nilai standard error dari taksiran parameter yang dihasilkan akanunderestimate sehingga beresiko memberikan kesimpulan yang tidak tepat. Model regresi Poisson-Inverse Gaussian dapat digunakan pada data count yang overdispersi dan memiliki tail panjang. Penaksiran parameter model regresi Poisson-Inverse Gaussian menggunakan metode maksimum likelihood dan solusi dari fungsi log -likelihood-nya menggunakan pendekatan numerik yaitu Newton-Raphson. Uji kesesuaian model yang digunakan mencakup statistik pseudo R-Squared, uji rasio likelihood, dan Uji Wald.

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Regression analysis is used to investigate the relationship between one response variable and one or more regressor variables. If the response variable is count data, that has non negative integer value, the regression analysis that usually used is Poisson Regression. Poisson regression has an assumption that mean of response variable equal to its variance. On count data frequently found that the variance is greater than mean, or called overdispersion. On overdispersion case, poisson regression is inconvenient to used because it may underestimate the standard error of regression parameters and consequently it risk to give misleading inference. Poisson Inverse Gaussian regression model can be used on overdispersion and long tail count data. Parameter estimation of Poisson Inverse Gaussian Regression Model can be obtained through the maximum likelihood method and the solution of log likelihood function may be solved by using numerical method called Newton Raphson. Goodness of fit testing of this model includes pseudo R Squared, rasio likelihood test, and Wald test."

"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."

"Seringkali analisis statistik beranggapan suatu data hanya berasal dari satu populasi saja. Padahal pada kenyataannya terdapat kondisi dimana suatu data bisa dibagi menjadi beberapa sub-populasi. Gaussian Finite Mixture Model adalah salah satu metode untuk memodelkan data heterogen yang memungkinkan berasal dari sub-populasi yang berbeda. Model ini berbentuk superposisi dari beberapa distribusi Gaussian. Jumlah distribusi akan ditentukan dengan menggunakan Akaikes Information Criterion dan model diagnostik. Estimasi parameter pada model ini menggunakan metode Bayesian, yaitu dengan menentukan distribusi prior untuk parameter model, digabungkan dengan likelihood yang akan menghasilkan distribusi posterior. Kemudian, Markov chain Monte Carlo-Gibbs Sampler digunakan untuk menarik sampel pada parameter dari distribusi poteriornya masing-masing.

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Commonly statistical analysis assume data comes from one population. But there are conditions where data might be generated from several sub-populations. Gaussian Finite Mixture Model (GFMM) is one of the methods to model heterogeneous data that might come from different sub-populations. This model was formed as a superposition of several Gaussian distribution, with different location parameter. Number of distributions will be determined using Akaike`s Information Criterion and model diagnostic. Parameter estimation is conducted using Bayesian method, that is by specifying the prior distribution for the models parameters, combined with the likelihood to produce the posterior distribution. Finnally, Markov chain Monte Carlo-Gibbs Sampler is implemented to withdraw sampel of parameters from the corresponding posterior distributions."

"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)."

"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."

"Distribusi Negative Binomial-Generalized Exponential (NB-GE) merupakan distribusi yang mampu memodelkan data overdispersi dengan extreme excess zeros yaitu lebih dari 80% angka nol dalam data. Distribusi Negative Binomial-Generalized Exponential (NB-GE) merupakan distribusi campuran hasil dari mixing antara distribusi Negative Binomial (NB) dengan distribusi Generalized Exponential (GE). Pembentukan distribusi Negative Binomial-Generalized Exponential (NB-GE) serta karakteristik-karakteristik distribusi Negative Binomial-Generalized Exponential (NB-GE) seperti fungsi kepadatan peluang, momen ke-, mean, variansi, koefisien skewness dan koefisien kurtosis dibahas pada pada skripsi ini. Penaksiran parameter-parameter dari distribusi Negative Binomial-Generalized Exponential (NB-GE) menggunakan metode maximum likelihood. Sebagai ilustrasi, digunakan data kecelakaan fatal yang memiliki lebih dari 80% angka nol yang dimodelkan dengan distribusi Negative Binomial-Generalized Exponential (NB-GE).

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Negative Binomial-Generalized Exponential (NB-GE) distribution is a distribution that capable for modeling overdispersion data with extreme excess zeros, which is more than 80% zeros in a data. The distribution is a mixture distribution that obtained by mixing the Negative Binomial (NB) distribution with the Generalized Exponential (GE) distribution. The formation of the Negative Binomial-Generalized Exponential (NB-GE) distribution and the characteristics of the Negative Binomial-Generalized Exponential (NB-GE) distribution such as the probability density function, kth moment, mean, variance, skewness and kurtosis are discussed in this paper. Estimation of the parameters from the Negative Binomial-Generalized Exponential (NB-GE) distribution using the maximum likelihood method. As an illustration, Negative Binomial-Generalized Exponential (NB-GE) distribution used to model the data of fatal crash that has more than 80% zeros."