E jurnal Matematika

7-13

Authors: Ni Wayan Nining Ismiranti, I Putu Eka N. Kencana, I Komang Gde Sukarsa

The aim of this research is to find the alternative solutions that could be used to handle the traffic congestions in the Denpasar City and the priorities of each alternative. The main problem of this research is determining the appropriateness of alternatives and its criterias that could be used to set the priorities of the alternatives. Based on the interview with the transport experts of Denpasar City, there are three main factors that affect the traffic congestion i.e (1) the ratio of the volume of vehicles on the road capacity, (2) the existing traffic management, and the traffic regulation . The interviewee also suggest that there are six alternatives that can be used to handle traffic congestion. These alternatives are (1)improve the public transport system, (2) use technology to monitor and enforce the rules,(3) create a 3 in 1 rule, (4) create road pricing rule,(5) optimize the existing management in the road, and (6) create rule of road zoning. Based on the calculations by Analytic Network Process (ANP) method, improving the public transport system is the best alternative among others that is appropriate to handle traffic congestion in the Denpasar City.

22-26

Authors: Ni Putu Iin Vinny Dayanti, Ni Luh Putu Suciptawati, Made Susilawati

Ordinary Least Squares (OLS) Method is a good method to estimate regression parameters when there is no violation in classical assumptions, such as the existence of outlier. Outliers can lead to biased parameters estimator, therefore we need a method that can may not affected by the existence of outlier such as Minimum Covariance Determinant (MCD) and Least Median of Squares (LMS). However, the application of this method is less accurate when it is used for small data. To overcome this problem, it was aplicated bootstrap method in MCD and LMS to determine the comparison of bias in parameters which were produced by both methods in dealing outlier in small data. The used bootstrap method in this study was the residual bootstrap that works by resampling the residuals. By using 95% and 99% confidence level and 5%, 10% and 15% outlier percentage, MCD-bootstrap and LMS-bootstrap give value of parameter estimators which were unbias for all percentage of outlier. We also found that the widht of range which produced by MCD-bootstrap method was shorter than LMS-bootstrap method produced. This indicates that MCD-bootstrap method was a better method than LMS-bootstrap method. Keywords: outliers, bias, robust, Minimum Covariance Determinant, Least Median of Squares, bootstrap residual

32-37

Authors: Ni Luh Putu Ratna Dewi, I Nyoman Widana, Desak Putu Eka Nilakusmawati

Premium reserve is a number of fund that need to be raised by insurance company in preparation for the payment of claims. This study aims to get the formula of premium reserve as well as the value of the premium reserve for joint life insurance by using retrospective calculation method. Joint life insurance participants in this study are limited to 2 people. Calculations in this study is using Indonesian Mortality Table (TMI) 2011, joint life mortality tables, commutation tables, value of annuities, value of single premiums and constant annual premium and using constant interest rates of 5%. The results showed that by using age of the participant insurance joint life of x = 50 and y = 45 years and the premium payment period of t = 10 years, we obtained that the value of premium reserve from the end of the first year until the end of the 11th year has increased every year, while the value of premium reserves from the end of the 12th year and so on until a lifetime has decreased every year. Keywords: Joint Life Insurance, Premium Reserve, Retrospective