Reliability Estimation For Exponential Distribution with Two Parameters

Abstract

The exponential distribution have an important role in the applications of industrial and engineering .It have
been used when the average of failure constant with time .
Sometime the need to find parameter which start in specific time and not from the zero .
In this specific time represent (time of guaranteed) . So it appeared the important need which contain the
reliability of exponential distribution, also the estimation methods for two parameter as shifting parameter &
scale parameter.
The comparative between the different estimation methods for reliability function . The methods are :
1- The First Modification Maximum Likelihood Method (M.M.L.E-I).
2- The Second Modification Maximum Likelihood Method (M.M.L.E-II) .
3- The First Modification Moments Method (M.M.E-I) .
4- Least Squares Method (L.S) .
5- Quantile Method (Q.E) .
6- Nonlinear Least Squares Method (N.L.S).
which leads two methods the second modification maximum likelihood method (M.M.L.E-II) & the first
modification moments method (M.M.E-I) .
The best two methods between estimation depending on the measures :-
1- Integral mean squared Error (IMSE) .
2- Integral mean Absolute percentage error (IMAPE) .