Kolmogorov-Smirnov Goodness-of-Fit test for identifying distribution of the number of earthquakes and the losses due to earthquakes in Indonesia

Abstract

Earthquakes of high magnitude often result in large casualties and huge economic losses in Indonesia. An earthquake risk assessment must be carried out. The risk assessment process requires a structured approach. This paper is containing of the first step of risk assessment using actuarial-statistical method. The data used as research variables in this paper are the number of earthquakes and the losses due to earthquakes. The earthquakes data used are earthquakes with magnitude > 5 Richter Scale. Data is collected within the last 40 years, from 1980 to 2019. Data is collected from Indonesian Disaster Data and Information, and NOAA National Centers for Environmental Information (NCEI). Descriptive statistics analysis obtains that the most frequently earthquakes with magnitude > 5 Richter Scale occurred in Indonesia in 2004, where as it is known that at the end of 2004 an earthquake with a magnitude of 9.1 Richter Scale occurred in Aceh which caused the highest loss, which was around 147485.500 billion rupiah. Normality test of the variables results that the number of earthquakes and the losses due to earthquakes are not normally distributed. Kolmogorov-Smirnov Goodness-of-Fit test results that the number of earthquakes follows Gamma Distribution with shape parameter α = 1.800 and scale parameter β = 2.236; while the losses due to earthquakes follows Power Function Distribution with shape parameter α = 0.072, and boundary parameter a = 0, b = 2.810 x 105.

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“…dimana 𝑁𝑁 adalah banyak data dan 𝑖𝑖 adalah urutan data. Keputusan diambil dengan membandingkan 𝐷𝐷 dengan 𝑑𝑑 tabel Kolmogorov-Smirnov [9].…”

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“…The Kolmogorov-Smirnov (KS) test is used to determine whether the data sample is originated from population with certain probability distribution (Oktaviana, 2021). Given 𝑁 is ordered sample points 𝑌 1 , 𝑌 2 , … , 𝑌 𝑁 with certain empirical cumulative distribution function (ECDF) is defined in Eq.…”

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