Modeling data count is an important thing in various fields. For this purpose, Poisson regression models are often used. However, in this model there is an assumption of equidispersion data where the mean value equals the value of the variance. In fact, this assumption is often violated in the observed data. In real data, the value of variance actually exceeds the mean (overly dispersed) value with the cause of the overdispersion depending on many situations. When the overdispersion source is exceeds zero (excess zero), then a more suitable model to use is the Zero-inflated Poisson regression model. In this paper, after the framework of Poisson regression and the Zero-inflated Poisson regression is reviewed then the model is adjusted to the claim frequency data in a private health insurance scheme where the frequency of claims is overly dispersed because of the number of zeros in the data set. Then Vuong's test is done to compare the two models and obtain the result that the Zero-inflated Poisson regression is more suitable for modeling the frequency data of PT.

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<p><em>Abstraksi</em> <strong>-  Penelitian ini secara umum bertujuan memperoleh fakta empiris tentang pendapatan keluarga dan kaitannya dengan prestasi akademik mahasiswa, khususnya pada mahasiswa sastra Arab UAI. Prestasi akademik merujuk pada indeks prestasi kumulatif per semester atau pertahun. Secara teoritis prestasi akademik dipandang sebagai <em>output</em> dari koleksi investasi dalam pendidikan. Namun, Meskipun prestasi akademik siswa dianggap sebagai <em>output</em> langsung dari input alokasi investasi dalam pendidikan yang diusahakan oleh orang tua, tingkat keberhasilannya dianggap bergantung pada sejumlah faktor eksogen yang melekat pada siswa, keluarga, atau sekolah. Faktor-faktor eksogen ini antara lain adalah kumpulan karakteristik anak atau siswa, seperti jenis kelamin, usia dan kemampuan bawaan. Dengan menggunakan analisa deskriptif dan analisa <em>inference</em>, diperoleh hasil penelitian yang menyatakan bahwa prestasi akademik mahasiswa menurut kelompok pendapatan orang tua, tidak bisa terlihat secara nyata, pada masing-masing tahun masuk atau angkatan di UAI. Hal yang sama juga ditemukan pada analisa perbedaan prestasi akademik mahasiswa menurut kelompok pendapatan orang tua, pada masing-masing kelompok jenis kelamin, status beasiswa, dan pendidikan terakhir sebelum memasuki UAI. Ini menunjukkan bahwa karakteristik siswa belum cukup kuat untuk mendukung kita membedakan perbedaan prestasi akademik mahasiswa berdasarkan pendapatan orang tua mereka.</strong></p><p><strong> </strong><strong> </strong></p><p><em>Abstract</em><strong> - The aim of this reseach is to empirically investigate the relation between academic achievement and parent’s income  of students  in the department of arabic at the University of Al-Azhar Indonesia. The arabic department students that has been admitted to the University from  2008 to 2011 academic year are selected to be a sample in this study. Using the student’s first year grade point average (GPA), as the proxy of student’s academic achievement,  and his/her ordinal scaled monthly parent’s income as independent variable, as well as other student’s characteristic variables as additional exogenous variables, the study reveals that the arabic students academic achievement are on average not signficantly different based on their parent’s income, especially for those students with motnhly parents equals to or gretaer than ten million rupiahs (high income level). For those wiht parents income less than ten million rupiahs, there is slightly the negative relation between students academic achievement and their parents income, but the result of testing hypothesis do not support this descriptive statistics. Similar results are found when student’s chracteristics such as gender, admission year into the University, and the type of pre-university eduacation, are included in the analysis. There is no significantly differences in general in academic achievement between students in different parents income level. However if we group students based on their characteristics, there are some differences significantly found in the academic achievement of students in different particular characteristic, especially in different entry academic year, gender or the type of their last education. </strong></p><p> </p>

This study aims to calculate the allowance for losses by applying Gaussian Process regression to estimate future claims. Modeling is done on motor vehicle insurance data. The data used in this study are historical data on PT XYZ's motor vehicle insurance business line during 2017 and 2019 (January 2017 to December 2019). Data analysis will be carried out on the 2017 - 2019 data to obtain an estimate of the claim reserves in the following year, namely 2018 - 2020. This study uses the Chain Ladder method which is the most popular loss reserving method in theory and practice. The estimation results show that the Gaussian Process Regression method is very flexible and can be applied without much adjustment. These results were also compared with the Chain Ladder method. Estimated claim reserves for PT XYZ's motor vehicle business line using the chain-ladder method, the company must provide funds for 2017 of 8,997,979,222 IDR in 2018 16,194,503,605 IDR in 2019 amounting to Rp. 1,719,764,520 for backup. Meanwhile, by using the Bayessian Gaussian Process method, the company must provide funds for 2017 of 9,060,965,077 IDR in 2018 amounting to 16,307,865,130 IDR, and in 2019 1,731,802,871 IDR for backup. The more conservative Bayessian Gaussian Process method. Motor vehicle insurance data has a short development time (claims occur) so that it is included in the short-tail type of business.

In a non-life insurance business, an insurer often needs to build up a reserve to ensure the company can fulfill its obligation. Chain ladder is one of the most widely used methods in claim reserving. However, the chain ladder method is very vulnerable to an outlier. This study focused on claim reserving that was resistant to outlier data by using a robust chain ladder. There are two steps to robustify the chain ladder method. The first step is to detect outlier by using the median as a development factor to compute the residual and adjust the outlying values. The second step is to apply a classic chain ladder method to the adjusted data. This study shows that a robust chain ladder has a better result than a standard chain ladder method.