Topp–Leone odd log-logistic exponential distribution: Its improved estimators and applications
Abstract In this paper, a new three-parameter lifetime model called the Topp–Leone odd log-logistic exponential distribution is proposed. Its density function can be expressed as a linear mixture of exponentiated exponential densities and can be reversed-J shaped, skewed to the left and to the right...
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Published in | Anais da Academia Brasileira de Ciências Vol. 93; no. 4; p. e20190586 |
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Main Authors | , , |
Format | Journal Article |
Language | English Portuguese |
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Abstract | Abstract In this paper, a new three-parameter lifetime model called the Topp–Leone odd log-logistic exponential distribution is proposed. Its density function can be expressed as a linear mixture of exponentiated exponential densities and can be reversed-J shaped, skewed to the left and to the right. Further, the hazard rate function of the new model can be monotone, unimodal, constant, J-shaped, constant-increasing-decreasing and decreasing-increasing-decreasing and bathtub-shaped. Our main focus is on estimation from a frequentist point of view, yet, some statistical and reliability characteristics for the proposed model are derived. We briefly describe different estimators namely, the maximum likelihood estimators, ordinary least-squares estimators, weighted least-squares estimators, percentile estimators, maximum product of spacings estimators, Cramér-von-Mises minimum distance estimators, Anderson-Darling estimators and right-tail Anderson-Darling estimators. Monte Carlo simulations are performed to compare the performance of the proposed methods of estimation for both small and large samples. We illustrate the performance of the proposed distribution by means of two real data sets and both the data sets show the new distribution is more appropriate as compared to some other well-known distributions. |
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AbstractList | Abstract In this paper, a new three-parameter lifetime model called the Topp–Leone odd log-logistic exponential distribution is proposed. Its density function can be expressed as a linear mixture of exponentiated exponential densities and can be reversed-J shaped, skewed to the left and to the right. Further, the hazard rate function of the new model can be monotone, unimodal, constant, J-shaped, constant-increasing-decreasing and decreasing-increasing-decreasing and bathtub-shaped. Our main focus is on estimation from a frequentist point of view, yet, some statistical and reliability characteristics for the proposed model are derived. We briefly describe different estimators namely, the maximum likelihood estimators, ordinary least-squares estimators, weighted least-squares estimators, percentile estimators, maximum product of spacings estimators, Cramér-von-Mises minimum distance estimators, Anderson-Darling estimators and right-tail Anderson-Darling estimators. Monte Carlo simulations are performed to compare the performance of the proposed methods of estimation for both small and large samples. We illustrate the performance of the proposed distribution by means of two real data sets and both the data sets show the new distribution is more appropriate as compared to some other well-known distributions. |
Author | DEY, SANKU AL-MOFLEH, HAZEM AFIFY, AHMED Z. |
AuthorAffiliation | Department of Statistics Department of Mathematics |
AuthorAffiliation_xml | – name: Department of Statistics – name: Department of Mathematics |
Author_xml | – sequence: 1 givenname: AHMED Z. orcidid: 0000-0002-6723-6785 surname: AFIFY fullname: AFIFY, AHMED Z. organization: Department of Statistics, Egypt – sequence: 2 givenname: HAZEM orcidid: 0000-0003-3430-2464 surname: AL-MOFLEH fullname: AL-MOFLEH, HAZEM organization: Department of Mathematics, Jordan – sequence: 3 givenname: SANKU orcidid: 0000-0001-8523-8189 surname: DEY fullname: DEY, SANKU organization: Department of Statistics, India |
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Cites_doi | 10.1155/2016/8727951 10.1016/j.ress.2005.05.008 10.1080/03610918.2015.1118503 10.1080/00949655.2017.1351972 10.2991/jsta.2018.17.2.3 10.3390/math8010135 10.1080/02664763.2016.1268571 10.6339/JDS.201604_14(2).0004 10.1111/j.2517-6161.1971.tb00884.x 10.1080/03610918.2016.1267752 10.1080/03610926.2017.1414254 10.3390/math8081276 10.18187/pjsor.v16i1.3129 10.1080/03610926.2013.851221 10.1007/BF02602999 10.1080/00949658808811068 10.1016/S1568-4946(02)00059-5 10.1002/1521-4036(200102)43:1<117::AID-BIMJ117>3.0.CO;2-R 10.1080/00949650802552402 10.1016/j.spl.2009.05.026 10.1080/03610926.2015.1130839 10.1016/j.cam.2018.08.008 10.1016/j.cam.2017.12.001 |
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Keywords | exponential distribution Bathtub failure rate simulation maximum likelihood skewed data |
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213 year: 2018 end-page: 229 article-title: The extended exponential distribution and its applications publication-title: J Stat Theory Appl contributor: fullname: AFIFY, AZ; ZAYED, M; AHSANULLAH, M – volume: 46 start-page: 4377 year: 2017 end-page: 4398 article-title: Transmuted generalized exponential distribution: a generalization of the exponential distribution with applications to survival data publication-title: Commun Stat Simul Comput contributor: fullname: KHAN, MS; KING, R; HUDSON, IL – volume: 44 start-page: 3486 year: 2015 end-page: 3502 article-title: The Harris extended exponential distribution publication-title: Commun Stat Theory Methods contributor: fullname: PINHO, LG – volume: 13 year: 2021 article-title: The flexible Burr X-G family: properties, inference, and applications in engineering science publication-title: Symmetry contributor: fullname: AL-BABTAIN, AA; ELBATAL, I; AL-MOFLEH, H; GEMEAY, AM; AFIFY, AZ; SARG, AM – volume: 13 start-page: 1 year: 2004 end-page: 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Snippet | Abstract In this paper, a new three-parameter lifetime model called the Topp–Leone odd log-logistic exponential distribution is proposed. Its density function... |
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SubjectTerms | Bathtub failure rate exponential distribution maximum likelihood MULTIDISCIPLINARY SCIENCES simulation skewed data |
Title | Topp–Leone odd log-logistic exponential distribution: Its improved estimators and applications |
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