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Submitted
April 11, 2016
Published
December 17, 2015
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Abstract

Kajian mengenai distribusi dari suatu fungsi peubah acak, khususnya mengenai distribusi dari jumlah dua atau lebih peubah acak, sudah banyak dilakukan. Sedangkan kajian mengenai distribusi dari selisih dua peubah acak masih jarang dilakukan, terlebih pada peubah acak-peubah acak diskrit. Penelitian ini berfokus pada penurunan distribusi selisih dua peubah acak Poisson yang saling bebas. Metode yang digunakan untuk menentukan distribusi tersebut adalah metode fungsi pembangkit momen dan metode fungsi massa peluang. Karakteristik-karakteristik dari distribusi diturunkan melalui sifat-sifat dari momen ke- k ; khususnya dari momen pertama hingga momen keempat. Selanjutnya, distribusi dari selisih dua peubah acak Poisson yang saling bebas ini akan dibandingkan dengan distribusi Poisson Difference (PD) yang diturunkan oleh Alzaid dan Omair (2010) atau dikenal juga dengan nama distribusi Skellam. Parameter-parameter dari distribusi diestimasi menggunakan metode momen dan maksimum likelihood. Aplikasi pada data penduduk melek huruf dilakukan untuk mendapatkan pemahaman yang lebih baik mengenai distribusi tersebut.

Keywords

distribusi Poisson distribusi Poisson Difference fungsi pembangkit momen fungsi massa peluang metode momen metode maksimum likelihood

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Author Biography

Atina Ahdika, Program Studi Statistika, Universitas Islam Indonesia


How to Cite
Ahdika, A. (2015). Distribution Of The Difference Of Two Independent Poisson Random Variables And Its Application To The Literate Population Data. EKSAKTA: Journal of Sciences and Data Analysis, 15(1-2), 61–74. https://doi.org/10.20885/eksakta.vol15.iss1-2.art7
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References

  1. Alzaid, A., Omair, M. 2010. On The Poisson Difference Distribution Inference and Applications. Bull. Malays. Math. Sci. Soc. (2) 33(1), 17-45.
  2. Badan Pusat Statistik (BPS). http://www.bps.go.id/Subjek/view/id/28#subjekViewTab3|accordion-daftar-subjek1. Diakses pada 15 Desember 2015.
  3. Irwin, M. 2006. Moment Generating Function. Statistics 110. Harvard : Summer 2006.
  4. Karlis, D., Ntzoufras, I. 2000. Discrete Distribution with Applications in Sports. Department of Statistics Athena University of Economics and Bussiness, Technical Report.
  5. Karlis, D., Ntzoufras, I. 2006. Bayesian Analysis of The Differences of Count Data. Wiley InterScience.
  6. Ross, S. 2007. Introduction to Probability Models, 9th Edition. Berkeley California: University of California. Hal. 32, 51, 53, 66, 307.
  7. Vernic, R. 1997. On The Bivariate Generalized Poisson Distribution. ASTIN Bulletin, Vol. 27, Issue 01, May 1997, pp 23-32.
  8. Walpole, R., Myers, R. 1995. Ilmu Peluang dan Statistika untuk Insinyur dan Ilmuwan, Edisi ke-4 (Terjemah). Bandung: Penerbit ITB.
  9. Hwang, Y., et al. 2007. Sensor Noise Modeling Using the Skellam Distribution: Application to the Color Edge Detection. IEEE Conference on Computer Vision and Patern Recognition, pp 1 – 8.