1.30

Impact Factor

2.10

CiteScore

# Using Simulation to Estimate Reliability Function for Transmuted Exponential Distribution

Makki A. Mohammed Salih1, Jaafer Hmood Eidi1, and Eman F. Mohommed This email address is being protected from spambots. You need JavaScript enabled to view it.1

1Department of Mathematics, College of Education, Almustansiriyah University-Baghdad-Iraq

Accepted: November 14, 2021
Publication Date: December 17, 2021

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

## ABSTRACT

Several methods were used to estimate the two parameters of the transformed exponential distribution, which are the scale and the transmuted parameters, as well as its reliability function, namely, the moments method, modified moments, percentile, least squares, weighted least squares, and the maximum likelihood estimation, where the simulation method was used to generate the required data, where a sample size (n= 10, 30, 70 and 100), repeated sample (N= 1000), and the real value of the parameters for three experiments. The obtained results were compared by mean square error, and the results showed that, in general, the method of moments is the best in estimating the scale parameters, while the maximum likelihood estimation method is the best in estimating the transmuted parameter. Regarding reliability estimation, the method of moments is the most precise in the first experiment, while for the second and third experiments the percentile method is the best.

Keywords: Exponential Distribution, Estimation methods, Simulation, Mean square error

## REFERENCES

1. [1] N. B. Khoolenjani and F. Shahsanaie, (2016) “Estimating the parameter of Exponential distribution under Type-II censoring from fuzzy data." J. Stat. Theory Appl. 15(2):181–195.
2. [2] E. A. Owoloko, P. E. Oguntunde, and A. O. Adejumo, (2015) “Performance rating of the transmuted exponential distribution: an analytical approach" SpringerPlus 4(1):1–15.
3. [3] M. A. M. Salih and J. H. Eidi. “Using Simulation to Estimate Reliability Function for Transmuted Kumaraswamy Distribution”. In: IOP Conference Series: Materials Science and Engineering. 928. 4. IOP Publishing. 2020, 042046.
4. [4] M. A. M. Salih and J. H. Eidi, (2022) “New White Method of Parameters and Reliability Estimation for Transmuted Power Function Distribution" Baghdad Science Journal 19(1): 0077–0077.
5. [5] N. S. Karam and A. H. Khaleel. “Generalized inverse Rayleigh reliability estimation for the (2+ 1) cascade model”. In: AIP Conference Proceedings. 2123. 1. AIP Publishing LLC. 2019, 020046.
6. [6] M. Abazid and D. Alkoud, (2018) “A least-squares approach to prediction the future sales of pharmacy" Int. J. Innov. Technol. Explor. Eng 7: 1–4.
7. [7] O. Sulaimon Mutiu, (2015) “Application of weighted least squares regression in forecasting" Int. J. Recent. Res. Interdiscip. Sci 2(3): 45–54.
8. [8] F. Yang, H. Ren, and Z. Hu, (2019) “Maximum likelihood estimation for three-parameter Weibull distribution using evolutionary strategy" Mathematical Problems in Engineering 2019:

2.1
2023CiteScore

69th percentile