Harmonic Mixture Fréchet Distribution: Properties and Applications to Lifetime Data
In this study, we propose a four-parameter probability distribution called the harmonic mixture Fréchet. Some useful expansions and statistical properties such as moments, incomplete moments, quantile functions, entropy, mean deviation, median deviation, mean residual life, moment-generating functio...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2022/6460362 |
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| _version_ | 1832568185085231104 |
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| author | Selasi Kwaku Ocloo Lewis Brew Suleman Nasiru Benjamin Odoi |
| author_facet | Selasi Kwaku Ocloo Lewis Brew Suleman Nasiru Benjamin Odoi |
| author_sort | Selasi Kwaku Ocloo |
| collection | DOAJ |
| description | In this study, we propose a four-parameter probability distribution called the harmonic mixture Fréchet. Some useful expansions and statistical properties such as moments, incomplete moments, quantile functions, entropy, mean deviation, median deviation, mean residual life, moment-generating function, and stress-strength reliability are presented. Estimators for the parameters of the harmonic mixture Fréchet distribution are derived using the estimation techniques such as the maximum-likelihood estimation, the ordinary least-squares estimation, the weighted least-squares estimation, the Cramér–von Mises estimation, and the Anderson–Darling estimation. A simulation study was conducted to assess the biases and mean square errors of the estimators. The new distribution was applied to three-lifetime datasets and compared with the classical Fréchet distribution and eight (8) other extensions of the Fréchet distribution. |
| format | Article |
| id | doaj-art-ee3d939d2299493fb33d5fa48dd20020 |
| institution | Kabale University |
| issn | 1687-0425 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ee3d939d2299493fb33d5fa48dd200202025-02-03T00:59:36ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252022-01-01202210.1155/2022/6460362Harmonic Mixture Fréchet Distribution: Properties and Applications to Lifetime DataSelasi Kwaku Ocloo0Lewis Brew1Suleman Nasiru2Benjamin Odoi3Department of Mathematical SciencesDepartment of Mathematical SciencesDepartment of StatisticsDepartment of Mathematical SciencesIn this study, we propose a four-parameter probability distribution called the harmonic mixture Fréchet. Some useful expansions and statistical properties such as moments, incomplete moments, quantile functions, entropy, mean deviation, median deviation, mean residual life, moment-generating function, and stress-strength reliability are presented. Estimators for the parameters of the harmonic mixture Fréchet distribution are derived using the estimation techniques such as the maximum-likelihood estimation, the ordinary least-squares estimation, the weighted least-squares estimation, the Cramér–von Mises estimation, and the Anderson–Darling estimation. A simulation study was conducted to assess the biases and mean square errors of the estimators. The new distribution was applied to three-lifetime datasets and compared with the classical Fréchet distribution and eight (8) other extensions of the Fréchet distribution.http://dx.doi.org/10.1155/2022/6460362 |
| spellingShingle | Selasi Kwaku Ocloo Lewis Brew Suleman Nasiru Benjamin Odoi Harmonic Mixture Fréchet Distribution: Properties and Applications to Lifetime Data International Journal of Mathematics and Mathematical Sciences |
| title | Harmonic Mixture Fréchet Distribution: Properties and Applications to Lifetime Data |
| title_full | Harmonic Mixture Fréchet Distribution: Properties and Applications to Lifetime Data |
| title_fullStr | Harmonic Mixture Fréchet Distribution: Properties and Applications to Lifetime Data |
| title_full_unstemmed | Harmonic Mixture Fréchet Distribution: Properties and Applications to Lifetime Data |
| title_short | Harmonic Mixture Fréchet Distribution: Properties and Applications to Lifetime Data |
| title_sort | harmonic mixture frechet distribution properties and applications to lifetime data |
| url | http://dx.doi.org/10.1155/2022/6460362 |
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