ESTIMASI PARAMETER PADA DISTRIBUSI EKSPONENSIAL

Abstract

Point estimation of a population parameter is a value obtained from related
sample and used as an estimator of the parameter whose value is unknown. Point
estimator can be determined by using two methods: classical method (moment
method and maximum likelihood) and Bayes method. The purpose of this research
is to determine the point estimation of an exponential distribution with one
parameter using Moment method, Maximum Likelihood method and Bayes
method and determine the point estimation of an exponential distribution with two
parameters Moment method and Maximum Likelihood method.
The method of this research is a literature study from various sources that
support and relevant to the topic.
The result shows that the point estimation of Exponential distribution for
one parameter by using Moment method and Maximum Likelihood Method is
x , while the Bayes estimator of Exponential distribution for one parameter with
prior konjugate Gamma distribution is  
 x  n p
n p
n
i
i    
  


1
1 and Chi Square is




  




 




  
 2 2
1
1
2
1
k
x n
k
n
n
i
i
. The point Estimation of exponential distribution for two
parameters by using the Moment method is 1 2
2
ˆ X
n
x
n
i
i
 

 and
1 2
2
ˆ X
n
x
X
n
i
i
  

 , whereas by using the Maximum Likelihood method is
 
n
x x
n
i
n i 


 1
1:
ˆ
and n x 1: ˆ  .