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All Journal IPTEK The Journal for Technology and Science JSI: Jurnal Sistem Informasi (E-Journal) JURNAL E-DUMATH Journal of Information Systems Engineering and Business Intelligence KLIK (Kumpulan jurnaL Ilmu Komputer) (e-Journal) Jurnal Komputasi Indonesian Journal of Artificial Intelligence and Data Mining Prosiding Seminar Nasional Teknoka Jurnal Teknik Informatika (JUTIF) Jurnal Pengabdian Kepada Masyarakat (JPKM) Tabikpun Jurnal Siger Matematika SWARNA: Jurnal Pengabdian Kepada Masyarakat
Dian Kurniasari
Matematika, Fakultas Matematika Dan Ilmu Pengetahuan Alam, Universitas Lampung, Indonesia
Religion Arts Humanities Chemical Engineering, Chemistry & Bioengineering Chemistry Civil Engineering, Building, Construction & Architecture Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Engineering Health Professions Languange, Linguistic, Communication & Media Library & Information Science Mathematics Other

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Journal : IPTEK The Journal for Technology and Science

 1 
Approximations of the Generalized Log-Logistic Distribution to the Chi-Square Distribution Kartika Candra Buana; Warsono Warsono; Dian Kurniasari
IPTEK The Journal for Technology and Science Vol 25, No 1 (2014)
Publisher : IPTEK, LPPM, Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/j20882033.v25i1.478

Abstract

The main purpose of this article is to do approximations graphically and mathematically the four-parameter generalized log-logistic distribution, denoted by G4LL(α,β,m_1,m_2), to the one-parameter Chi-square 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 Chi-square as a special case of the MGF of G4LL distribution, we utilized an expansion of the MacLaurin series. The results show that graphically, the Chi-square distribution can be approximated by the generalized log-logistic distribution. Moreover, by letting α=1,β=-ln⁡(2m_2 ),m_1=v/2 and m_2→∞, the MGF of the G4LL distribution can be written in the form of the MGF of the Chi-square distribution. Thus, the Chi-square distribution is a limiting or special case distribution of the generalized log-logistic distribution.The main purpose of this article is to do approximations graphically and mathematically the four-parameter generalized log-logistic distribution, denoted by G4LL(α,β,m_1,m_2), to the one-parameter Chi-square 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 Chi-square as a special case of the MGF of G4LL distribution, we utilized an expansion of the MacLaurin series. The results show that graphically, the Chi-square distribution can be approximated by the generalized log-logistic distribution. Moreover, by letting α=1,β=-ln⁡(2m_2 ),m_1=v/2 and m_2→∞, the MGF of the G4LL distribution can be written in the form of the MGF of the Chi-square distribution. Thus, the Chi-square distribution is a limiting or special case distribution of the generalized log-logistic distribution.
On the Moments, Cumulants, and Characteristic Function of the Log-Logistic Distribution Dian Ekawati; Warsono Warsono; Dian Kurniasari
IPTEK The Journal for Technology and Science Vol 25, No 3 (2014)
Publisher : IPTEK, LPPM, Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/j20882033.v25i3.574

Abstract

This research examine about the moments, cumulants, and characteristic function of the log-logistic distribution. Therefore, the purposes of this article are (1) finding moments of the log-logistic distribution by using moment generating function and by definition of expected values of the log-logistic random variable and (2) finding the cumulants and characteristic function of the log-logistic distribution. Log-logistic distribution has two parameters: the shape parameter α and β as a parameter scale. Moments of the log-logistic distribution can be determined by using the moment generating function or the definition of expected value. Cumulants determined by the moments that have been found previously. Furthermore, skewness and kurtosis can be determined from the log-logistic distribution. While the characteristic function is the expected value of e^itx, which I as an imaginary number
Co-Authors . Wamiliana Aang Nuryaman Ahmad Faisol Amanto Amanto Amelia Fallizia Putri Anis Mahfud Al’afi Anisa Fitriyani Asmiati Asmiati Dalfa Habibah Nurul Aini Dian Ekawati Dolly Yudhistira, Dolly Evita Fitriasari Fatkur Rokhman Fitriani Indah Suciati Jevri Setia Nugraha Kartika Candra Buana Kurnia Muludi Muhammad Taufiq Sofrizal Mustofa Usman Mustofa Usman Mustofa Usman Noferdis Setiawan Notiragayu Notiragayu Notiragayu Notiragayu Notiragayu Nur Alifiah Rahman Cahyadi, Rahman Ranti Vidia Mahyunis Siti Laelatul Chasanah Sulistian Oskavina Wamiliana Wamiliana Warsono Warsono Warsono Warsono Warsono Warsono Warsono Warsono Wenty Okzarima Widiarti Widiarti Widiarti Widiarti Yeftanus Antonio