Estimation the number of road traffic accidents in Indonesia with a non-homogeneous compound poisson process

Abstract

One goal of development land transportation system is to build a safe and well organized land transportation system. A safety and well organized system referred to the number of traffic accidents that occur. A small number of traffic accidents that occurs show a good quality of land transportation system. This research will estimate the number of traffic accidents on land transportation in Indonesia by using a non-homogeneous compound Poisson process. The Poisson process {N(t),t≥0} is called a non-homogeneous Poisson process when the parameter λ is not a constant function. It is notated as λ(t). The sum of independent and identical random variables to their indices following the Poisson process is a compound Poisson process. A compound Poisson can be expressed as Y(t)=∑i=1N(t)Xi,t≥0. where {Xi,i≥1} is a set of random variables. In this paper, the function λ(t) = a + bX, with a and b coefficient values, can be determined using a linear model Yi = a + bX. The non-homogeneous compound Poisson process is explained by determining the assumptions, variables, and intensity function needed. As the result, it is obtained that the Poisson process is not homogeneous compound with rank compilation function is E(Y(t))=(at+b2t2)μ1. The mean of the Poisson and homogeneous compound process is 144t + 0,016t2 as an estimation of the number of traffic accidents in Indonesia.