, Warsono and Kurniasari, Dian (2014) Approximations of the Generalized LogLogistic Distribution to the ChiSquare Distribution. IPTEK, The Journal for Technology and Science, 25 (1).

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Abstract
The main purpose of this article is to do approximations graphically and mathematically the fourparameter generalized loglogistic distribution, denoted by G4LL (α,β,m1,m2,to the oneparameter Chisquare distribution with υ degrees of freedom. In order to achieve this purpose, this article creates graphically the probability density functions of both distribution and derives mathematically the MGF of the both distributions. To prove the MGF of Chisquare as a special case of the MGF of G4LL distribution, we utilized an expansion of the MacLaurin series. The results show that graphically, the Chisquare distribution can be approximated by the generalized loglogistic distribution. Moreover, by letting α=1, β= In(2m2), m1= v/2 dan m2→∞, the MGF of the G4LL distribution can be written in the form of the MGF of the Chisquare distribution. Thus, the Chisquare distribution is a limiting or special case distribution of the generalized loglogistic distribution. Keywordschisquare distribution, generalized loglogistic distribution, moment generating function, MacLaurin series
Item Type:  Article 

Divisions:  Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA) > Prodi Matematika 
Depositing User:  Marbiyah . Siti 
Date Deposited:  11 Aug 2016 02:49 
Last Modified:  11 Aug 2016 02:49 
URI:  http://repository.lppm.unila.ac.id/id/eprint/293 
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