Estimasi Parameter Distribusi Loglogistik pada Data Tersensor Progressive Tipe II dengan Menggunakan Algoritma EM
Abstract: The Loglogistic
distribution is a commonly used distribution in lifetime data analysis because
natural logarithm of the lifetime variables are logistically distributed.
Loglogistic distribution has two parameters, that are the scale parameter 𝛼
and shape parameter 𝛽. The main objective of this paper is to get
parameter estimator of the Loglogistic distribution based on Progressive
type-II censoring. The method that used in this paper is Maximum Likelihood
method with EM Algorithm. EM Algorithm is consist of two steps, that are E-step
and Mstep. E-step requires the algorithm to calculate conditional expectation
of log-likelihood function and M-step calculation to maximize the conditional
expectation of log-likelihood function until get a convergen value. Software
that used to get the parameter estimator of the Loglogistic distribution easily
is Mathematica. On natural logarithm case from the time of disintregation of
the isolator fluid at 34 kV voltage with 𝑛 sample observations and 𝑚
observed failure are given respectively by 19 and 8, then the censored scheme
is 𝑅𝑗
={0,0,3,0,3,0,0,5} where 𝑗=1,2,…,𝑚
then obtained the estimator value of parameter for 𝛼� is 6,526 and for 𝛽̂is 1,108.
Keywords: Loglogistic distribution, Progressive Type II Censored, Maximum
Likelihood Estimator, EM Algorithm
Penulis: Annas Riezki
Romadhoni, Toha Saifudin, Eko Tjahjono
Kode Jurnal: jpmatematikadd130071
