A Four-Parameter Extension of Burr III Distribution with Applications
Abstract In this paper, we defined and studied a new distribution called the odd exponentiated half-logistic Burr III distribution. Properties such as the linear representation of the probability density function (PDF) of the distribution, quantile function, ordinary and incomplete moments, moment g...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
UIN Syarif Hidayatullah
2021-05-01
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| Series: | InPrime |
| Subjects: | |
| Online Access: | https://journal.uinjkt.ac.id/index.php/inprime/article/view/18850 |
| _version_ | 1797293146579664896 |
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| author | Emmanuel W. Okereke Johnson Ohakwe |
| author_facet | Emmanuel W. Okereke Johnson Ohakwe |
| author_sort | Emmanuel W. Okereke |
| collection | DOAJ |
| description | Abstract
In this paper, we defined and studied a new distribution called the odd exponentiated half-logistic Burr III distribution. Properties such as the linear representation of the probability density function (PDF) of the distribution, quantile function, ordinary and incomplete moments, moment generating function and distribution of the order statistic were derived. The PDF and hazard rate function were found to be capable of having various shapes, making the new distribution highly flexible. In particular, the hazard rate function can be nonincreasing, unimodal and nondecreasing. It can also have the bathtub shape among other non- monotone shapes. The maximum likelihood procedure was used to estimate the parameters of the new model. We gave two numerical examples to illustrate the usefulness and the ability of the distribution to provide better fits to a number of data sets than several distributions in existence.
Keywords: Burr III distribution; maximum likelihood procedure; moments; odd exponentiated half-logistic-G family; order statistics.
Abstrak
Pada artikel ini akan didefinisikan dan dipelajari mengenai distribusi baru yang disebut distribusi Burr III setengah logistik tereksponen ganjil. Kami menurunkan beberapa sifat dari distribusi tersebut yaitu representasi linier dari fungsi kepadatan peluang (FKP), fungsi kuantil, momen biasa dan momen tidak lengkap, fungsi pembangkit momen dan distribusi statistik terurut. Fungsi FKP dan fungsi tingkat hazard diperoleh memiliki bermacam-macam bentuk, membuat distribusi baru ini sangat fleksibel. Secara khusus, fungsi tingkat hazard dapat berupa fungsi taknaik, bermodus tunggal, bisa juga tidak turun. Selain itu, fungsi ini juga dapat berbentuk seperti bak mandi di antara bentuk-bentuk tak monoton lainnya. Prosedur kemungkinan maksimum digunakan untuk mengestimasi parameter model yang baru. Kami memberikan dua contoh numerik untuk mengilustrasikan kegunaan dan kemampuan distribusi untuk menghasilkan kesesuaian yang lebih baik pada sejumlah kumpulan data dibandingkan beberapa distribusi yang ada.
Kata kunci: distribusi Burr III; prosedur kemungkinan maksimum; momen; keluarga setengah logistik-G teresponen ganjil; statistic terurut. |
| first_indexed | 2024-03-07T20:08:39Z |
| format | Article |
| id | doaj.art-1872ce73cb7647ad8476e6c822b69c8a |
| institution | Directory Open Access Journal |
| issn | 2686-5335 2716-2478 |
| language | English |
| last_indexed | 2024-03-07T20:08:39Z |
| publishDate | 2021-05-01 |
| publisher | UIN Syarif Hidayatullah |
| record_format | Article |
| series | InPrime |
| spelling | doaj.art-1872ce73cb7647ad8476e6c822b69c8a2024-02-28T02:16:03ZengUIN Syarif HidayatullahInPrime2686-53352716-24782021-05-013171910.15408/inprime.v3i1.188507926A Four-Parameter Extension of Burr III Distribution with ApplicationsEmmanuel W. Okereke0Johnson Ohakwe1Department of Statistics, Michael Okpara University of Agriculture, PMB, 7267, Umudike, Abia State, NigeriaDepartment of Mathematics and Statistics, Faculty of Sciences, Federal of Sciences, Federal University, Otuoke, PMB, 126, Yenogoa, Bayelsa State, NigeriaAbstract In this paper, we defined and studied a new distribution called the odd exponentiated half-logistic Burr III distribution. Properties such as the linear representation of the probability density function (PDF) of the distribution, quantile function, ordinary and incomplete moments, moment generating function and distribution of the order statistic were derived. The PDF and hazard rate function were found to be capable of having various shapes, making the new distribution highly flexible. In particular, the hazard rate function can be nonincreasing, unimodal and nondecreasing. It can also have the bathtub shape among other non- monotone shapes. The maximum likelihood procedure was used to estimate the parameters of the new model. We gave two numerical examples to illustrate the usefulness and the ability of the distribution to provide better fits to a number of data sets than several distributions in existence. Keywords: Burr III distribution; maximum likelihood procedure; moments; odd exponentiated half-logistic-G family; order statistics. Abstrak Pada artikel ini akan didefinisikan dan dipelajari mengenai distribusi baru yang disebut distribusi Burr III setengah logistik tereksponen ganjil. Kami menurunkan beberapa sifat dari distribusi tersebut yaitu representasi linier dari fungsi kepadatan peluang (FKP), fungsi kuantil, momen biasa dan momen tidak lengkap, fungsi pembangkit momen dan distribusi statistik terurut. Fungsi FKP dan fungsi tingkat hazard diperoleh memiliki bermacam-macam bentuk, membuat distribusi baru ini sangat fleksibel. Secara khusus, fungsi tingkat hazard dapat berupa fungsi taknaik, bermodus tunggal, bisa juga tidak turun. Selain itu, fungsi ini juga dapat berbentuk seperti bak mandi di antara bentuk-bentuk tak monoton lainnya. Prosedur kemungkinan maksimum digunakan untuk mengestimasi parameter model yang baru. Kami memberikan dua contoh numerik untuk mengilustrasikan kegunaan dan kemampuan distribusi untuk menghasilkan kesesuaian yang lebih baik pada sejumlah kumpulan data dibandingkan beberapa distribusi yang ada. Kata kunci: distribusi Burr III; prosedur kemungkinan maksimum; momen; keluarga setengah logistik-G teresponen ganjil; statistic terurut.https://journal.uinjkt.ac.id/index.php/inprime/article/view/18850burr iii distributionmaximum likelihood proceduremomentsodd exponentiated half-logistic-g familyorder statistics. |
| spellingShingle | Emmanuel W. Okereke Johnson Ohakwe A Four-Parameter Extension of Burr III Distribution with Applications InPrime burr iii distribution maximum likelihood procedure moments odd exponentiated half-logistic-g family order statistics. |
| title | A Four-Parameter Extension of Burr III Distribution with Applications |
| title_full | A Four-Parameter Extension of Burr III Distribution with Applications |
| title_fullStr | A Four-Parameter Extension of Burr III Distribution with Applications |
| title_full_unstemmed | A Four-Parameter Extension of Burr III Distribution with Applications |
| title_short | A Four-Parameter Extension of Burr III Distribution with Applications |
| title_sort | four parameter extension of burr iii distribution with applications |
| topic | burr iii distribution maximum likelihood procedure moments odd exponentiated half-logistic-g family order statistics. |
| url | https://journal.uinjkt.ac.id/index.php/inprime/article/view/18850 |
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