Binomial Negative-Lindley Distribution in the Frequency Data of Automotive Motor Vehicles Claim in Indonesia
Abstract
In this thesis is explained about the testing of the new distribution fit that is the negative-Lindley binomial distribution proposed by Zamani and Ismail (2010) on the frequency data of motor vehicle insurance claims in Indonesia. Lindley's negative-binomial distribution depends on two parameters: r> 0 and θ> 0. This distribution has the highest Pr (X = 0) value of each parameter value r and θ so it is assumed to be able to handle overdispersion problems and solve the problem if the number of frequencies (X = 0) is very large. The parameters of Lindley's negative-binomial distribution can only be estimated using numerical methods, such as the Newton-Raphson method. The distribution fit test was performed using chi-square test. The data used is secondary data of motor vehicle insurance result of recording obtained from the Ministry of Finance in 2009-2010. The results show that Lindley's binomial distribution is suitable for modeling the frequency data of motor vehicle category 1 insurance claims in Indonesia.
Keywords
Motor Vehicle Insurance, Negative Binomial Distribution-Lindley, Chi Square Test, Newton-Raphson Method
Full Text:
PDF (Bahasa Indonesia)References
Gençtürk, Y., & Yiğiter, A., 2015. Modelling Claim Number Using a New Mixture Model: Negative Binomial Gamma Distribution. Journal Of Statistical Computation and Simulation, Vol 86, pp. 1829-1839.
Klugman, S. A., Panjer, H. H., Willmot, G. E. (2004). Loss Models: From Data to Decisions. Wiley Interscience, New York.
Lord, D., and S.R. Geedipally (2011) The Negative Binomialâ€Lindley Distribution as a Tool for Analyzing Crash Data Characterized by a Large Amount of Zeros. Accident Analysis & Prevention, Vol. 43, No. 5, pp. 1738-1742.
Zamani, H., Ismail, N., 2010. Negative binomialâ€Lindley distribution and Its Application. Journal of Mathematics and Statistics 6 (1), 4â€9.
DOI: http://dx.doi.org/10.29313/.v0i0.8581
   Â