METODE JACKKNIFE DAN METODE BOOTSTRAP DALAM ESTIMASI KURTOSIS DAN SKEWNESS

Authors

  • Riadil Jannah Sihombing Universitas Negeri Medan
  • Elmanani Simamora . Universitas Negeri Medan

DOI:

https://doi.org/10.24114/jmk.v8i2.34206

Keywords:

ootstrap, Jackknife, Skewness, Kurtosis

Abstract

Hal yang harus diperhatikan untuk melakukan uji statistik sebagai proses analisis yaitu uji asumsi klasik, salah satunya adalah uji normalitas. Data yang tidak berdistribusi normal disebabkan terlalu banyak nilai-nilai ekstrim dalam satu set data sehingga menghasilkan distribusi skewness dan distribusi kurtosis. Untuk mengatasi masalah tersebut, dapat menggunakan metode bootstrap dan metode jackknife. Tujuan dari penelitian ini yaitu menentukan hasil estimasi dari metode bootstrap dan metode jackknife, serta menentukan estimator terbaik dengan cara membandingan nilai MSE kedua metode tersebut. Data yang digunakan dalam penelitian ini yaitu data kekuatan gempa bumi di Indonesia tahun 2020 dengan kekuatan magnitudo di atas 5. Berdasarkan simulasi dengan menggunakan bantuan program Matlab R2015a dilakukan resampling sebanyak 50, 100, 200, 500, dan 1000. Jika  dilihat  secara  keseluruhan  diperoleh nilai MSE terkecil yaitu dengan metode bootstrap. Dapat disimpulkan bahwa metode bootstrap merupakan metode yang efisien dibandingkan metode jackknife, hal ini didukung dengan kecilnya tingkat MSE yang dihasilkan.  AbstractThe thing that must be considered in carrying out statistical tests as an analytical process is the classical assumption test, one of which is the normality test. Data that are not normally distributed are caused by too many extreme values in one data set, resulting in a skewness distribution and a kurtosis distribution. To solve this problem, you can use the bootstrap method and the jackknife method. The purpose of this study is to determine the estimation results from the bootstrap method and the jackknife method, and to determine the best estimator by comparing the MSE values of the two methods. The data used in this study is data on the strength of the earthquake in Indonesia in 2020 with a magnitude above 5. Based on the simulation using the help of the Matlab R2015a program, resampling of 50, 100, 200, 500, and 1000 was obtained. The smallest MSE is the bootstrap method. It can be concluded that the bootstrap method is an efficient method compared to the jackknife method, this is supported by the small level of MSE generated.

Author Biographies

Riadil Jannah Sihombing, Universitas Negeri Medan

Jurusan Matematika

Elmanani Simamora ., Universitas Negeri Medan

Jurusan Matematika

References

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Published

2022-07-03

Issue

Vol. 8 No. 2 (2022): Karismatika

Section

Articles

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Copyright (c) 2022 KARISMATIKA: Kumpulan Artikel Ilmiah, Informatika, Statistik, Matematika dan Aplikasi

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