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@article{Reliability Estimation For Exponential Distribution with Two Parameters_2022, volume={15}, url={https://journal.muc.edu.iq/journal/article/view/322}, abstractNote={
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) .
}, number={1}, journal={Al-Mansour Journal}, year={2022}, month={Dec.}, pages={131–159} }