Kajian Generalisasi Distribusi Binomial yang Bertipe COM-Poisson dan Sifat-Sifatnya

Marselly Dian Saputri
Submission Date: 2015-08-05 12:49:20
Accepted Date: 2016-01-20 15:21:47

Abstract


Distribusi Binomial dan Poisson digunakan untuk menganalisis data diskrit. Karena distribusi Poisson berlaku equidispersi, sehingga dilakukan generalisasi terhadap distribusi Poisson menjadi distribusi COM-Poisson untuk menganalisis data diskrit yang equidispersi, overdispersi dan underdispersi. Generalisasi dari distribusi Binomial yang dapat menganalisis data dengan kejadian overdispersi dan underdispersi adalah distribusi COM-Poisson-Binomial. Pdf nya diperoleh dari  distribusi COM-Poisson bersyarat dari penjumlahan dua distribusi COM-Poisson. Selain itu, dalam Tugas Akhir ini juga dilakukan estimasi terhadap parameter-parameter dari COM-Poisson-Binomial dengan menggunakan Maximum Likelihood Estimation (MLE). Selanjutnya hasil estimasi ini dicoba pada data asosiasi sekunder dari kromosom di Brassika. Karena Maximum Likelihood Estimation menghasilkan persamaan non-linier yang hasilnya digunakan untuk mencari nilai estimasi parameter dan parameter persamaan non-linier tersebut diselesaikan dengan menggunakan metode Newton-Raphson. Hasil dari proses tersebut didapatkan nilai estimasi parameter dan nilai estimasi parameter

Keywords


Distribusi Binomial; Distribusi COM-Poisson; Overdispersi; Underdispersi; Maximum Likelihood Estimation

References


Shmueli, G., T. P. Minka, J. B. Kadane, Borle, and P. Boatwright. 2005. “A Useful Ditribution for Fitting Discrete Data: Revival of The Conway-Maxwell-Poisson Distribution”. Applied Statistics, Journal of Royal Statistical Society 54 no. 1, hal.127-142.

Altham, P.M.E. 1978. ”Two generalizations of the binomial distribution”. J. Roy. Statist. Soc. Ser. C 27, hal. 162-167.

Kupper, L.L., Haseman, J.K. 1978. “The use of a correlated binomial model for the analysis of certain toxicological experiments”. Biometrics 34, hal. 69-76.

Borges, P., Rodrigues, J., Balakrishnan, N., and B. Jorge. 2014. “A COM-Poisson Type Generalization of the Binomial Distribution and its Properties and Applications”. Statistics and Probability Letters 87, hal.158-166.

Walpole, R.E. “Pengantar Statistika Edisi ke-3”. Jakarta: PT. Gramedia Pustaka Utama.

Bain, L.J., and Engelhardt, Max. 1991. “Introduction to Probability and Mathematical Statistics 2nd edition”. Belmont, California: Duxbury Press.

Agresti, A. 2002. “Categorical Data Analysis 2nd edition”. John Wiley and Sons, New York.

Skellam, J.G. 1948. “A probablility distribution derived from the binomial distribution by regarding the probability of success as variable between the sets of trials”. J.Roy. Statist.Soc.Ser. B 10, hal.257-261.


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