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## A novel differential evolution algorithm approach for estimating the parameters of Gamma distribution: An application to the failure stresses of single carbon fibres

#### Aynur YONAR YONAR [1] , Nimet YAPICI PEHLİVAN YAPICI [2]

Three-parameter (3-p) Gamma distribution is widely used to model for skewed data in the reliability field. Thus, the problem of parameter estimation for the Gamma distribution has remained significant and interesting in all times. The maximum likelihood (ML) and the least square (LS) are the most popular methods in the parameter estimation. In this study, a novel Differential Evolution (DE) algorithm is proposed for the ML and LS estimation of the parameters of the 3-p Gamma distribution. This approach overcomes the problem of how to determine the search space of the DE by utilizing a new search space based on the confidence interval. The modified maximum likelihood and the profile likelihood methods are considered to constitute the confidence interval. In order to examine the performance of the proposed approach, an extensive Monte Carlo simulation study and a real data application are performed. The results show that this proposed approach is effective for estimating the parameters of the 3-p Gamma distribution with respect to mean square error and deficiency criteria.
Differential evolution, Gamma distribution, Maximum Likelihood, Least Square, Monte Carlo simulation, Parameter Estimation
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Primary Language en Statistics and Probability Statistics Orcid: 0000-0003-1681-9298Author: Aynur YONAR YONARInstitution: SELÇUK UNIVERSITY, SCIENCE FACULTYCountry: Turkey Orcid: 0000-0002-7094-8097Author: Nimet YAPICI PEHLİVAN YAPICI (Primary Author)Institution: SELÇUK UNIVERSITY, SCIENCE FACULTYCountry: Turkey Selçuk University 2016-OYP-063. Publication Date : August 6, 2020
 Bibtex @research article { hujms689381, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1493 - 1514}, doi = {10.15672/hujms.689381}, title = {A novel differential evolution algorithm approach for estimating the parameters of Gamma distribution: An application to the failure stresses of single carbon fibres}, key = {cite}, author = {Yonar, Aynur and Yapıcı Pehli̇van, Nimet} } APA Yonar, A , Yapıcı Pehli̇van, N . (2020). A novel differential evolution algorithm approach for estimating the parameters of Gamma distribution: An application to the failure stresses of single carbon fibres . Hacettepe Journal of Mathematics and Statistics , 49 (4) , 1493-1514 . DOI: 10.15672/hujms.689381 MLA Yonar, A , Yapıcı Pehli̇van, N . "A novel differential evolution algorithm approach for estimating the parameters of Gamma distribution: An application to the failure stresses of single carbon fibres" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1493-1514 Chicago Yonar, A , Yapıcı Pehli̇van, N . "A novel differential evolution algorithm approach for estimating the parameters of Gamma distribution: An application to the failure stresses of single carbon fibres". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1493-1514 RIS TY - JOUR T1 - A novel differential evolution algorithm approach for estimating the parameters of Gamma distribution: An application to the failure stresses of single carbon fibres AU - Aynur Yonar , Nimet Yapıcı Pehli̇van Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.689381 DO - 10.15672/hujms.689381 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1493 EP - 1514 VL - 49 IS - 4 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.689381 UR - https://doi.org/10.15672/hujms.689381 Y2 - 2020 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics A novel differential evolution algorithm approach for estimating the parameters of Gamma distribution: An application to the failure stresses of single carbon fibres %A Aynur Yonar , Nimet Yapıcı Pehli̇van %T A novel differential evolution algorithm approach for estimating the parameters of Gamma distribution: An application to the failure stresses of single carbon fibres %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 4 %R doi: 10.15672/hujms.689381 %U 10.15672/hujms.689381 ISNAD Yonar, Aynur , Yapıcı Pehli̇van, Nimet . "A novel differential evolution algorithm approach for estimating the parameters of Gamma distribution: An application to the failure stresses of single carbon fibres". Hacettepe Journal of Mathematics and Statistics 49 / 4 (August 2020): 1493-1514 . https://doi.org/10.15672/hujms.689381 AMA Yonar A , Yapıcı Pehli̇van N . A novel differential evolution algorithm approach for estimating the parameters of Gamma distribution: An application to the failure stresses of single carbon fibres. Hacettepe Journal of Mathematics and Statistics. 2020; 49(4): 1493-1514. Vancouver Yonar A , Yapıcı Pehli̇van N . A novel differential evolution algorithm approach for estimating the parameters of Gamma distribution: An application to the failure stresses of single carbon fibres. Hacettepe Journal of Mathematics and Statistics. 2020; 49(4): 1493-1514.

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