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 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.
Keywords
References
A. E. Gomes, C. Q. da-Silva, G. M. Cordeiro and E. M. M. Ortega, "The Beta Burr III Model for Lifetime Data," Brazilian Journal of Probability and Statistics, vol. 27, no. 4, pp. 502-543, 2013.
A. E. A. E. Gomes, C. Q. da-Silva and G. M. Cordeiro, "Two Extended Burr Models: Theory and Practice," Communication in Statistics-Theory and Methods, vol. 44, no. 8, pp. 1706-1734, 2015.
A. Ali, S. A. Hasnain and M. Ahmad, "Modified Burr III Distribution, Properties and Applications," Pakistan Journal of Statistics, vol. 31, no. 6, pp. 697-708, 2015.
I. B. Abdul-Moniem, "Transmuted Burr type III Distribution," Journal of Statistics: Advances in Theory and Applications, vol. 14, no. 1, pp. 37-47, 2015.
A. Y. Al-Saiari , S. A. Mousa and L. A. Bahairith, "Marshal-Olkin Extended BIII Distribution," International Mathematical Forum, vol. 11, no. 13, pp. 631-642, 2016.
F. Jamal, M. A. Nasir, M. H. Tahir and N. H. Monta, "The Odd Burr III Family of Distributions," Journal of Statistical Applications and Probability, vol. 6, no. 1, pp. 105-122, 2017.
G. M. Cordeiro, A. G. Gomes, C. Q. da-Silva and E. M. M. Ortega, "A Useful Extension of the Burr III Distribution," Journal of Statistical Distributions and Applications, vol. 4, pp. 1-15, 2017.
A. Z. Afify, E. Altun, M. Alizadeh, G. Ozel and G. G. Hamedani, "The Odd Exponentiated Half-Logistic-G family: Properties, Characterizations and Applications," Chilean Journal of Statistics, vol. 8, no. 2, pp. 65-71, 2017.
M. A. D. Aldahlan and A. Z. Afify, "The Odd Exponentiated Half-Logistic Burr XII Distribution," Pakistan Journal of Statistics and Operation Research, vol. XIV, no. 2, pp. 305-317, 2018.
B. Y. Jeong, M. S. Murshed, Y. Am Seo and J. S. Park, "A Three-Parameter Kappa Distribution with Hydrologic Application: A Generalized Gumbel Distribution," Stochastic Environmental Research and Risk Assessment, vol. 28, pp. 2063-2074, 2014.
M. Mansoor, M. H. Tahir, A. Alzaatreh and G. M. Corde, "An Extended Frechet Distribution: Properties and Applications," Journal of Data Science, vol. 14, pp. 167-188, 2016.
I. E. Okorie, A. C. Akpanta, J. Ohakwe and D. C. Chikezie, "The Extended Erlang-Truncated Exponential Distribution: Properties and Application to Rainfall Data," Heliyon, vol. 3, pp. 1-24, 2016.
I. E. Okorie, A. C. Akpanta, J. Ohakwe, Chikezie and D. C., "Marshall-Olkin Generalized Erlang-Truncated Exponential Distribution: Properties and Application," Cogent Mathematics, vol. 4, pp. 1-19, 2017.
S. Nadarajah and K. S., "On the Alternative to the Weibull Function," Engineering Fracture Mechanics, vol. 74, pp. 577-579, 2007.
S. M. Behairy, G. R. Al-Dayian and A. A. El-Helbawy, "The Kumaraswamy-Burr Type III Distribution: Properties and Estimation," British Journal of Mathematics and Computer Science, vol. 14, no. 2, pp. 1-21, 2016.
DOI: 10.15408/inprime.v3i1.18850
Refbacks
- There are currently no refbacks.
.
