Jurnal Gantang
Vol 1 No 1 (2016): "Matematika, Permasalahan, dan Solusinya dalam Meningkatkan Kualitas Pembelajaran

ANALISA FUNGSI KARAKTERISTIK SEBAGAI PENCIRI DISTRIBUSI PELUANG

Alona Dwinata (Universitas Maritim Raja Ali Haji)



Article Info

Publish Date
11 Oct 2016

Abstract

Fungsi karakteristik dari sebuah peubah acak mempunyai peranan penting dalam mengkaji kekonvergenan suatu fungsi distribusi. Salah satu teorema penting dalam kekonvergenan suatu fungsi distribusi adalah Teorema Limit Pusat Le’vy. Teorema Limit Pusat Le`vy menjelaskan bahwa jumlah dari peubah acak yang saling bebas, berdistribusi identik, dan mempunyai variansi akan mendekati distribusi Normal untuk n yang cukup besar. Jika (?n) merupakan barisan fungsi karakteristik dari barisan fungsi distribusi (Fn) yang saling bebas dan berdistribusi identik dan ? merupakan fungsi karakteristik dari fungsi distribusi F, maka apakah jika barisan (Fn) konvergen ke F akan diikuti kekonvergenan (?n) ke ??. Berdasarkan kajian pustaka diperoleh jawaban bahwa kekonvergenan barisan fungsi distribusi (Fn) ke fungsi distribusi F akan diikuti kekonvergenan (?n) ke ? dengan syarat : FnF syarat perlu ? kontinu pada t = 0 syarat cukup. Kata Kunci : Fungsi distribusi, Fungsi Karakteristik, Kekonvergenan Characteristics function from a random variable has a crucial role in examining the convergence of a particular distribution function. One of important theorems in convergence of a distribution function is theorem of Le’vy’s central limit. It implies that sum of some independently random variables, identically distributed, and having variance, will approach normal distribution for great enough value of n. Given as series of characteristics function from series of distribution function which is independent each other and identically distributed and as characteristics function of distribution function F, then if given series convergent to F, will it be implied by convergence of to ?. Based on literature study, it is obtained that the convergence of series of distribution function to distribution function F will be followed by the convergence of to under these following conditions: FnF necessary condition ? continue on t = 0 sufficient condition. Keywords: distribution function, characteristics function, convergence

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Journal Info

Abbrev

gantang

Publisher

Subject

Education Mathematics

Description

Jurnal Gantang is a peer-reviewed journal. Jurnal Gantang is published two numbers per year by Raja Ali Haji Maritime University, Tanjungpinang, Riau Islands, Indonesia. The articles written for Jurnal Gantang are state-of-the-art research articles in the field of Mathematics Education. Starting in ...