# การแจกแจงมูลค่าปัจจุบันของความสูญเสียรวมภายใต้ข้อสมมติความไม่เป็นอิสระกันโดยวิธีจำลองมอนติคาร์โล

## Abstract

Abstract

The purpose of this research is to find the distribution of the present value from aggregate loss taken in one year and to find the descriptive statistics of the present value of aggregate loss in one year; e.g., mean, 2.5th percentile, 97.5th percentile, and the coefficient of variation. It also compares the distributions of the present value from the aggregate loss in one year with various payment’s distribution under dependence assumption by Monte Carlo simulations. Since In insurance practice, the actual compensation payment time depends on the amount of payment paid. The results show that the distributions of the present value of aggregate loss in 1 year period is positively skewed curve and means of the present value from the aggregate loss doesn’t depend on payment’s distribution, regardless the amount of payment’s distribution. When mean of the payment equals 250 Baht, the present value of the aggregate loss in 1 year with the payment’s distribution are Pareto, Weibull, gamma, and lognormal equal to 1,206.55, 1,205.95, 1,202.36 and 1,205.94 respectively. The 2.5th percentile and 97.5th percentile are [131.39,3652.34], [181.20,2937.48], [280.77,2646.60] and [22.25,3356.39] respectively. The coefficient of variation are 86.82, 60.16, 51.61 and 70.88 % respectively. When mean of the payment equals 500 Baht, the present value of the aggregate loss in 1 year with the payment’s distribution are Pareto, Weibull, gamma, and lognormal equal to 2,410.68, 2,399.82, 2,391.63 and 2,397.85 respectively. The 2.5th percentile and 97.5th percentile are [260.73,7391.71], [364.45,5879.31], [556.05,5267.05] and [373.42,6687.62] respectively. The coefficient of variation are 88.35, 60.47, 51.65 and 70.96 % respectively. When mean of the payment equals 1,000 Baht, the present value of the aggregate loss in 1 year with the payment’s distribution are Pareto, Weibull, gamma, and lognormal equal 4,774.85, 4,749.47, 4,757.49 and 4,768.87 respectively. The 2.5th percentile and 97.5th percentile are [516.37,14662.89], [713.29,11635.1], [1104.64,10478.44] and [740.34,13291.13] respectively. The coefficient of variation are 86.49, 60.36, 51.71 and 71.03 % respectively. Furthermore, the distribution of the present value from aggregate loss depends on it’s coefficient of variation.

Keywords: Pareto distribution; Weibull distribution; Gamma distribution; Lognormal distribution

## Article Details

Section
วิทยาศาสตร์กายภาพ
Author Biographies

### กฤษกร อาชววาณิชกุล

สาขาวิชาคณิตศาสตร์และสถิติ คณะวิทยาศาสตร์และเทคโนโลยี มหาวิทยาลัยธรรมศาสตร์ ศูนย์รังสิต ตำบลคลองหนึ่ง อำเภอคลองหลวง จังหวัดปทุมธานี 12120

### กมล บุษบา

สาขาวิชาคณิตศาสตร์และสถิติ คณะวิทยาศาสตร์และเทคโนโลยี มหาวิทยาลัยธรรมศาสตร์ ศูนย์รังสิต ตำบลคลองหนึ่ง อำเภอคลองหลวง จังหวัดปทุมธานี 12120

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