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Abstract

A flexible lifetime distribution with increasing, decreasing, inverted bathtub and modified bathtub hazard rate called Modified Burr XII-Inverse Weibull (MBXII-IW) is introduced and studied. The density function of MBXII-IW is exponential, left-skewed, right-skewed and symmetrical shaped.  Descriptive measures on the basis of quantiles, moments, order statistics and reliability measures are theoretically established. The MBXII-IW distribution is characterized via different techniques. Parameters of MBXII-IW distribution are estimated using maximum likelihood method. The simulation study is performed to illustrate the performance of the maximum likelihood estimates (MLEs). The potentiality of MBXII-IW distribution is demonstrated by its application to real data sets: serum-reversal times and quarterly earnings.

Keywords

Moments Reliability Characterizations Maximum Likelihood Estimation

Article Details

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Author Biographies

Fiaz Ahmad Bhatti, National College of Business Administration and Economics , Lahore Pakistan

Deptt. of Statistics,

G. G. Hamedani, Marquette University, Milwaukee, WI 53201-1881, USA

MSCS, Professor
How to Cite
Bhatti, F. A., Hamedani, G. G., Yousof, H. M., Ali, A., & Ahmad, M. (2020). On Modified Burr XII-Inverse Weibull Distribution: Development, Properties, Characterizations and Applications. Pakistan Journal of Statistics and Operation Research, 16(4), 721-735. https://doi.org/10.18187/pjsor.v16i4.2622

References

  1. Abbas, S., Hameed, M., Cakmakyapan, S., & Malik, S. (2010). On gamma inverse Weibull distribution. Journal of the National Science Foundation of Sri Lanka, 47(4).
  2. Abbas, S., Taqi, S. A., Mustafa, F., Murtaza, M., & Shahbaz, M. Q. (2017). Topp-Leone inverse Weibull distribution: theory and application. European Journal of Pure and Applied Mathematics, 10(5), 1005-1022.
  3. Alzaatreh, A., Mansoor, M., Tahir, M. H., Zubair, M., & Ali, S. (2016). The Gamma Half-Cauchy Distribution: Properties and Applications. Hacettepe Journal of Mathematics and Statistics, 45 (4), 1143 -1159.
  4. Bhattacharyya, G. K., & Johnson, R. A. (1974). Estimation of reliability in a multicomponent stress-strength model. Journal of the American Statistical Association, 69(348), 966-970.
  5. Elbatal, I., Condino, F., & Domma, F. (2016). Reflected generalized beta inverse Weibull distribution: definition and properties. Sankhya B, 78(2), 316-340.
  6. Fayomi, A. (2019). The odd Frechet inverse Weibull distribution with application. Journal of Nonlinear Sciences and Applications, 12, 165-172.
  7. Glänzel, W. A. (1987). 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, 75-84.
  8. Glänzel, W. A. (1990). Some consequences of a characterization theorem based on truncated moments, Statistics 21 (1990) ; 613 - 618:
  9. Keller, A. Z., AZ, K., & ARR, K. (1982). Alternate reliability models for mechanical systems.
  10. Khan, M. S. (2010). The beta inverse Weibull distribution. International Transactions in Mathematical Sciences and Computer, 3(1), 113-119.
  11. Khan, M. S., & King, R. (2016). New generalized inverse Weibull distribution for lifetime modeling. Communications for Statistical Applications and Methods, 23(2), 147-161.
  12. Kotz S, Lai CD, Xie M. (2003).”On the Effect of Redundancy for Systems with Dependent Components.” IIE Trans, 35, pp.1103-1110.
  13. Shahbaz, M. Q., Shahbaz, S., & Butt, N. S. (2012). The Kumaraswamy-Inverse Weibull Distribution. Pakistan journal of statistics and operation research, 8(3), 479-489.
  14. Silva, A.N.F.D. (2004). Evolutionary study of children exposed to HIV and notified by the HCFMRP-USP epidemiological surveillance center (Doctoral dissertation, University of São Paulo).