Estimasi Parameter Distribusi Exponentiated Eksponensial Pada Data Tersensor Tipe II
Abstract: In this
undergraduate theses, we discuss about Exponentiated Exponential distribution which
is the general form of an exponential distribution with one parameter and we
will apply to ensored data type II which is one of the censoring methods based
on the failure.
The writing undergraduate theses purposes to determine the better
estimation method for parameter of exponentiated exponential distribution on
censored data type II. The estimation process uses Maximum Likelihood method
and Ordinary Least Square (OLS) to obtain the point estimator. Exponentiated
exponential distribution on censored data type II has the form of distribution function
is given:
𝐹(𝑡;𝛼,𝜆)=�1−𝑒−𝜆𝑡�𝛼
where 𝛼 is the shape parameter, λ is the scale
parameter, and t is data censored type II i.e data up to r failures. Estimation
parameter of exponentiated exponential distribution on censored data type II
using MLE and OLS cannot be solve analytically because the obtained estimator
is still implicit form. Therefore we need a numeric method to solve and this
final project uses Newton-Raphson method to find numeric solution. To determine
is better estimation method in this final project uses MSE criteria with the
smallest value. After doing test in data Leukimia patients, we can know that
method Ordinary Least Square (OLS) is better. The value MSE of ordinary least
square (OLS) =0.09842778 and The value of maximum likelihood estimator (MLE) =
0.3210319.
Keyword: Exponetiated
exponential distribution, lifetime data for censored type II, Ordinary Least Square
(OLS), Maximum Likelihood Estimator (MLE), Newton-Raphson, Mean square error
Penulis: Ahmad Zuda Kumala
Sani,Toha Saifudin,Eko Tjahjono
Kode Jurnal: jpmatematikadd130071
