(untitled) (مجلة المنصور, 2022)
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) .