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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| Format: | Article |
| Language: | English |
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Academia Brasileira de Ciências
2021-09-01
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| Series: | Anais da Academia Brasileira de Ciências |
| Subjects: | |
| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652021000700302&tlng=en |
| _version_ | 1819005275562049536 |
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| author | AHMED Z. AFIFY HAZEM AL-MOFLEH SANKU DEY |
| author_facet | AHMED Z. AFIFY HAZEM AL-MOFLEH SANKU DEY |
| author_sort | AHMED Z. AFIFY |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-20T23:50:12Z |
| format | Article |
| id | doaj.art-0b67fe71c62b46068f857121422c185e |
| institution | Directory Open Access Journal |
| issn | 1678-2690 |
| language | English |
| last_indexed | 2024-12-20T23:50:12Z |
| publishDate | 2021-09-01 |
| publisher | Academia Brasileira de Ciências |
| record_format | Article |
| series | Anais da Academia Brasileira de Ciências |
| spelling | doaj.art-0b67fe71c62b46068f857121422c185e2022-12-21T19:22:51ZengAcademia Brasileira de CiênciasAnais da Academia Brasileira de Ciências1678-26902021-09-0193410.1590/0001-3765202120190586Topp–Leone odd log-logistic exponential distribution: Its improved estimators and applicationsAHMED Z. AFIFYhttps://orcid.org/0000-0002-6723-6785HAZEM AL-MOFLEHhttps://orcid.org/0000-0003-3430-2464SANKU DEYhttps://orcid.org/0000-0001-8523-8189Abstract 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.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652021000700302&tlng=enBathtub failure rateexponential distributionmaximum likelihoodskewed datasimulation |
| spellingShingle | AHMED Z. AFIFY HAZEM AL-MOFLEH SANKU DEY Topp–Leone odd log-logistic exponential distribution: Its improved estimators and applications Anais da Academia Brasileira de Ciências Bathtub failure rate exponential distribution maximum likelihood skewed data simulation |
| title | Topp–Leone odd log-logistic exponential distribution: Its improved estimators and applications |
| title_full | Topp–Leone odd log-logistic exponential distribution: Its improved estimators and applications |
| title_fullStr | Topp–Leone odd log-logistic exponential distribution: Its improved estimators and applications |
| title_full_unstemmed | Topp–Leone odd log-logistic exponential distribution: Its improved estimators and applications |
| title_short | Topp–Leone odd log-logistic exponential distribution: Its improved estimators and applications |
| title_sort | topp leone odd log logistic exponential distribution its improved estimators and applications |
| topic | Bathtub failure rate exponential distribution maximum likelihood skewed data simulation |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652021000700302&tlng=en |
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