Judul: Modelling General Insurance Claim Data with Composite Lognormal-Pareto Distribution
Abstrak: Salah satu tahapan penting untuk menentukan premi agar perusahaan asuransi umum dapat membayar kerugian para tertanggung yaitu dengan memodelkan data klaim. Biasanya data besarnya klaim asuransi umum dimodelkan dengan sebaran lognormal atau sebaran Pareto. Sebaran lognormal dapat memodelkan data besarnya klaim dengan baik tetapi memiliki ekor sebaran yang lebih cepat menuju nol sehingga sebaran lognormal biasa digunakan untuk memodelkan data klaim yang lebih kecil. Sebaran Pareto memiliki bentuk monoton menurun dan ekor sebaran yang lebih berat. Sebaran Pareto sering digunakan untuk memodelkan data reasuransi atau data klaim besar. Sebaran lognormal-Pareto komposit merupakan kandidat yang cocok untuk memodelkan data klaim yang frekuensi klaim lebih kecil dan klaim lebih besarnya sama-sama tinggi. Baik data yang dibangkitkan maupun data aktual dianalisis untuk mengetahui kecocokan data dengan sebaran lognormal-Pareto komposit, lognormal, dan Pareto. Sebaran lognormal-Pareto komposit adalah sebaran yang paling cocok untuk memodelkan kedua data tersebut., One of important steps to determine premiums so that general insurance companies could pay the insureds’ losses is by modelling claim data. Usually, general insurance claim severity data is modeled by lognormal distribution or Pareto distribution. Lognormal distribution could fit well the claim severity data, but it has a tail that fades away faster to zero so that the lognormal distribution is usually used to model the smaller claim data. Pareto distribution has a monotonically decreasing density shape and a heavier tail. Pareto distribution is often used to model the reinsurance data or the larger claim data. The composite lognormal-Pareto distribution is a candidate that fits to model claim data that has smaller and larger claim data with high frequencies. Both generated data and actual data are analyzed to show the data fitted to composite lognormal-Pareto, lognormal, and Pareto distributions. The composite lognormal-Pareto distribution is the most fitted distribution to model both data.
Keyword: composite lognormal-Pareto distribution, lognormal distribution, Pareto distribution, the amount of claim, general insurance

Judul: Modeling Loss Data of General Insurance Companies with Log-EIG Distribution
Abstrak: Sebaran log-EIG (Exponential Inverse Gaussian) merupakan sebaran yang dimodifikasi dari sebaran EIG yang lebih dulu diperkenalkan. Sebaran log-EIG memiliki kecondongan ke kanan dan kurtosis yang lebih besar dari sebaran normal sehingga sebaran log-EIG dapat dikategorikan sebagai sebaran berekor berat. Sebaran semacam ini bermanfaat untuk memodelkan data kerugian perusahaan asuransi umum supaya dapat meminimumkan risiko kerugian di masa yang akan datang. Simulasi menunjukkan bahwa data yang dibangkitkan dari sebaran log-EIG tidak dapat dijelaskan dengan baik oleh sebaran lognormal dan Weibull. Untuk himpunan data yang digunakan, sebaran log-EIG memiliki nilai kriteria informasi Quesenberry dan Kent (QK) lebih besar dibandingkan dengan sebaran lognormal dan Weibull. Hasil ini menunjukkan bahwa sebaran log-EIG lebih baik dalam memodelkan himpunan data dibandingkan dengan sebaran lognormal dan Weibull, The log-EIG (Exponential Inverse Gaussian) distribution is a modification of the earlier EIG distribution. It has a positive skewness and a kurtosis that is greater than a normal distribution so that the log-EIG distribution can be categorized as a heavy-tailed distribution. This kind of distribution is useful to model loss data of general insurance companies in order to minimize the risk of loss in the future. The simulation shows that data generated from a log-EIG distribution is not well-described by a lognormal and a Weibull distribution. For the dataset used, the log-EIG distribution has a greater value of Quesenberry and Kent (QK) Information Criterion than the lognormal and the Weibull distribution. These results indicate that the log-EIG distribution models the dataset better than the lognormal and the Weibull distribution.
Keyword: heavy-tailed, modeling data, QK criterion, risk, simulation

Judul: Removal of Hexavalent Chromium with Scrap Iron Filling.
Abstrak: Chromium is a transition element commonly found in the environment as trivalent and hexavalent forms. Apparently, the hexavalent form is much more toxic than the trivalent form. Textile wastewater treatment is required in order to prevent hexavalent chromium to contaminate the environment. The methods of this research consisted of effect of pH determination, effect of agitating rate determination, effect of agitating time determination, and effect of iron level determination; and its application in textile wastewater sample. The methods used in textile wastewater application are: determination of textile wastewater hexavalent chromium concentration, determination of textile wastewater hexavalent chromium concentration with standard addition method, and removal of hexavalent chromium in textile wastewater with scrap iron filling. Concentration of hexavalent chromium was determined using visible light spectrophotometry method. Optimum conditions of pH, agitating rate, iron amount, and agitating time obtained were pH 3, 450 rpm, 5 grams, and 10 minutes giving concentrations of hexavalent chromium 16.98 ppm, 15.96 ppm, 0.24 ppm, and 0.14 ppm, respectively. Iron filling could effectively remove hexavalent chromium ions from textile wastewater in a relatively short time. Absorbance of hexavalent chromium in textile coloring process wastewater after the addition of iron filling was 0.002, whereas in textile final wastewater was 0.000.
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