On a new family of Kies Burr III distribution: Development, properties, characterizations, and applications

Document Type : Article

Authors

National College of Business Administration and Economics, Lahore, Pakistan.

Abstract

In this paper, a flexible lifetime distribution with increasing, decreasing, increasing-decreasing-increasing and bathtub hazard function, called New Family of Kies Burr III (NFKBIII) distributions is proposed. The density function of the NFKBIII is arc, J, reverse-J, U, bimodal, left-skewed, right-skewed and symmetrical shaped. The NFKBIII distribution is developed on the basis of the T-X family technique. The NFKBIII distribution is also obtained from compounding mixture distributions. Some structural and mathematical properties including moments, inequality measures, order statistics and reliability measures are theoretically established. The NFKBIII distribution is characterized via different techniques. Parameters of the NFKBIII distribution are estimated using maximum likelihood method. A simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). The potentiality of the NFKBIII distribution is demonstrated via its application to real data sets.

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References

References:
1.    Burr, I.W. “Cumulative frequency distributions”, Ann. Math. Stat., 13, pp.215-232 (1942). 
2.    Mielke, P.W. “Another family of distributions for describing and analyzing precipitation data”, J. Appl. Meterol., 12, pp.275-280 (1973). 
3.    Kleiber, C. and Kotz, S. “Statistical size distribution in economics and actuarial sciences”. New York, John Wiley & Sons, (2003). 
4.    Gove, J.H., Ducey, M.J., Leak, W.B. and Zhang, L. “Rotated sigmoid structures in managed uneven-aged northern hardwork stands: a look at the Burr Type III distribution”, Foresty, 81(2), pp. 161-176 (2008).
5.    Shao, Q., Chen, Y.D. and Zhang, L. “An extension of three-parameter Burr III distribution for low-flow frequency analysis”, Comput. Stat. Data Anal., 52, pp.1304-1314 (2008). 
6.    Benjamin, S.M., Humberto, V.H. and Arnold, B.C. “Use of the Dagum Distribution for Modeling Tropospheric Ozone levels”, J. Env. Stat., 5(6) pp. 1-11(2013). 
7.    Ali, A. Husnain, S. A., and Ahmad, M.  “Modified Burr III distribution, Properties and Applications”,  Pak. J. Statist., 31(6), pp.697-708 (2015).
8.    Gomes, A. E., da-Silva, C. Q., and Cordeiro, G. M. “Two extended Burr models: Theory and   practice”, Communications in Statistics-Theory and Methods, 44(8), pp.1706-1734(2015).
9.    Sinner, C., Dominicy, Y., Ley, C., Trufin, J., and Weber, P. “An Interpolating Family of Size Distributions”, (2016)." arXiv preprint arXiv: 2016; 1606.04430.
10.    Moisheer A. S. A. “A mixture of two Burr Type III distributions: Identifiability and estimation under type II censoring”. Mathematical Problems in Engineering, (2016).
11.    Olobatuyi, K. I., Asiribo, O. E., and Dawodu, G. A., “A New Class of Generalized Burr III Distribution for Lifetime Data” (2017).  https://arxiv.org/pdf/1701.00403.
12.    Cordeiro G.M., Gomes, A. E., da-Silva, C. Q., Ortega E.M.M. “A useful extension of the Burr III distribution”, Journal of Statistical Distributions and Applications”, 4(1), pp.24 (2017).
13.    Jamal, F., Nasir, M. A., Tahir, M. H., & Montazeri, N. H. “The odd Burr-III family of distributions”, Journal of Statistics Applications and Probability, 6(1), pp.105-122 (2017).
14.    Nasir, A., Bakouch, H. S., & Jamal, F. “Kumaraswamy odd Burr G family of distributions with applications to reliability data”, Studia Scientiarum Mathematicarum Hungarica, 55(1), pp.94-114 (2018).
15.    Kehinde, O., Osebi, A., & Ganiyu, D. “A New Class of Generalized Burr III Distribution for Lifetime Data”, International Journal of Statistical Distributions and Applications, 4(1), pp. 6 (2018).
16.    Marshall, A. W. and Olkin, I. “A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families”, Biometrika, 84(3), pp. 641-652 (1997). 
17.    Cordeiro, G. M. and Castro, M. “A new family of generalized distributions”, Journal of statistical computation and simulation, 81(7), pp. 883-898 (2011). 
18.    Alizadeh, M., Cordeiro, G. M., Nascimento, A. D., Lima, M. D. C. S., and Ortega, E. M. “Odd-Burr generalized family of distributions with some applications”, Journal of Statistical Computation and Simulation, 87(2), pp.367-389 (2017). 
19.    Cordeiro, G. M., Alizadeh, M., Ozel, G., Hosseini, B., Ortega, E. M. M. and Altun, E. “The generalized odd log-logistic family of distributions: properties, regression models and applications”, Journal of Statistical Computation and Simulation, 87(5), pp.908-932 (2017). 
20.    Haghbin, H., Ozel, G., Alizadeh, M. and Hamedani, G. G. “A new generalized odd log-logistic family of distributions”, Communications in Statistics-Theory and Methods, 46(20), pp. 9897-9920 (2017). 
21.    Korkmaz, M. Ç., & Genç, A. İ. “Two-sided generalized exponential distribution”, Communications in Statistics-Theory and Methods, 44(23), pp. 5049-5070 (2015).
22.    Korkmaz, M. Ç. and Genç, A. I. “A new generalized two-sided class of distributions with an emphasis on two-sided generalized normal distribution”, Communications in Statistics - Simulation and Computation, 46 (2), pp.1441-1460 (2017). 
23.    Cordeiro, G. M., Yousof, H. M., Ramires, T. G. and Ortega, E. M. M. “The Burr XII system of densities: properties, regression model and applications”, Journal of Statistical Computation and Simulation, 88(3), pp. 432-456 (2018). 
24.    Alizadeh, M., Korkmaz, M. Ç., Almamy, J. A., & Ahmed, A. A. E. “Another odd log-logistic logarithmic class of continuous distributions”, Journal of Statisticians: Statistics and Actuarial Sciences, 11(2), pp.55-72 (2018).
25.    Yousof, H. M., Altun, E., Ramires, T. G., Alizadeh, M. And Rasekhi, M. “A new family of distributions with properties, regression models and applications”, Journal of Statistics and Management Systems, 21(1), pp. 163-188 (2018).
26.    Korkmaz, M. Ç., Cordeiro, G. M., Yousof, H. M., Pescim, R. R., Afify, A. Z., & Nadarajah, S. “The Weibull Marshall–Olkin family: Regression model and application to censored data”, Communications in Statistics-Theory and Methods, (Accepted). (2019). DOI: 10.1080/03610926.2018.1490430.
27.    Gurvich, M. R., Dibenedetto, A. T., & Ranade, S. V. “A new statistical distribution for characterizing the random strength of brittle materials”, Journal of Materials Science, 32(10), pp. 2559-2564 (1997).
28.    Alzaatreh, A., Mansoor, M., Tahir, M. H., Zubair, M., & Ali, S. “The Gamma Half-Cauchy Distribution: Properties and Applications”, Hacettepe Journal of Mathematics and Statistics, 45 (4), pp.1143-1159 (2016). 
29.    Bourguignon, M., Silva, R.B. and Cordeiro, G.M. “The Weibull-G Family of Probability Distributions”, Journal of Data Science, 12, pp.53-68 (2014).
30.    Kies, J.A. “The strength of glass performance”, Naval Research Lab Report No. 5093, Washington, D.C., (1958).
31.    Kumar, C. Satheesh; Dharmaja, S. H. S. “On some properties of Kies distribution”, Metron, 72(1),pp. 97-122 (2014).
32.    Kotz S, Lai CD, Xie M. “On the Effect of Redundancy for Systems with Dependent Components”, IIE Trans, 35, pp.1103-1110 (2003). 
33.    Bhattacharyya, G. K., & Johnson, R. A. “Estimation of reliability in a multicomponent stress-strength model”. Journal of the American Statistical Association, 69(348), pp.966-970 (1974).
34.    Glänzel, W. A. Characterization theorem based on truncated moments and its application to some distribution families, Mathematical Statistics and Probability Theory (Bad Tatzmannsdorf, 1986), Vol. B, Reidel, Dordrecht, pp.75-84 (1987). 
35.    Aarset, M. V. “How to identify a bathtub hazard rate”, IEEE Transactions on Reliability, 36(1), pp.106-108 (1987). 
36.    Chen, G. and Balakrishnan N. “A general purpose approximate goodness-of-fit test”, J. Qual. Technol. 27, pp.154-161 (1995). 
Scientia Iranica
Volume 27, Issue 5 - Serial Number 5
Transactions on Industrial Engineering (E)
September and October 2020
Pages 2555-2571

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