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A Journal of Theoretical and Applied Statistics
Volume 50, 2016 - Issue 2
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Original Articles

A new useful three-parameter extension of the exponential distribution

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Pages 312-337 | Received 26 Sep 2013, Accepted 02 Sep 2015, Published online: 03 Nov 2015

References

  • Alexander C, Cordeiro GM, Ortega EMM, Sarabia JM. Generalized beta-generated distributions. Comput Stat Data Anal. 2012;56:1880–1897. doi: 10.1016/j.csda.2011.11.015
  • Aly EAA, Benkherouf L. A new family of distributions based on probability generating functions. Sankhya B. 2011;73:70–80. doi: 10.1007/s13571-011-0017-9
  • Cordeiro GM, de Castro M. A new family of generalized distributions. J Statist Comput Simul. 2011;81:883–898. doi: 10.1080/00949650903530745
  • Eugene N, Lee C, Famoye F. Beta-normal distribution and its applications. Commun Stat – Theory Methods. 2002;31:497–512. doi: 10.1081/STA-120003130
  • Marshall AW, Olkin I. A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika. 1997;84:641–652. doi: 10.1093/biomet/84.3.641
  • Zografos K, Balakrishnan N. On families of beta-and generalized gamma-generated distribution and associate inference. Statist Methodol. 2009;6:344–362. doi: 10.1016/j.stamet.2008.12.003
  • Marshall AW, Olkin I. Life distributions: structure of nonparametric, semiparametric, and parametric families. New York: Springer Series in Statistics; 2007.
  • Ghitany ME, Al-Hussaini EK, AlJarallah RA. Marshall–Olkin extended Weibull distribution and its application to censored data. J Appl Stat. 2005;32:1025–1034. doi: 10.1080/02664760500165008
  • Zhang T, Xie M. Failure data analysis with extended Weibull distribution. Commun Stat – Simul Comput. 2007;36:579–592. doi: 10.1080/03610910701236081
  • Caroni C. Testing for the Marshall–Olkin extended form of the Weibull distribution. Statist Pap. 2010;51:325–336. doi: 10.1007/s00362-008-0172-x
  • Cordeiro GM, Lemonte AJ. On the Marshall–Olkin extended Weibull distribution. Statist Pap. 2013;54:333–353. doi: 10.1007/s00362-012-0431-8
  • Lam KF, Leung TL. Marginal likelihood estimation for proportional odds models with right censored data. Lifetime Data Anal. 2001;7:39–54. doi: 10.1023/A:1009673026121
  • Gupta RD, Peng C. Estimating reliability in proportional odds ratio models. Comput Stat Data Anal. 2009;53:1495–1510. doi: 10.1016/j.csda.2008.10.014
  • Economou P, Caroni C. Parametric proportional odds frailty models. Commun Stat – Simul Comput. 2007;36:579–592. doi: 10.1080/03610910701569143
  • Gupta RC, Lvin S, Peng C. Estimating turning points of the failure rate of the extended Weibull distribution. Comput Stat Data Anal. 2010;54:924–934. doi: 10.1016/j.csda.2009.10.004
  • Rubio FJ, Steel MFJ. On the Marshall–Olkin transformation as a skewing mechanism. Comput Stat Data Anal. 2012;56:2251–2257. doi: 10.1016/j.csda.2012.01.003
  • Nanda AK, Das S. Stochastic orders of the Marshall–Olkin extended distribution. Stat Probab Lett. 2012;82:295–302. doi: 10.1016/j.spl.2011.10.003
  • Ghitany ME. Marshall–Olkin extended Pareto distribution and its application. Int J Appl Math. 2005;18:17–32.
  • Ristić MM, Jose KK, Ancy J. A Marshall–Olkin gamma distribution and minification process. STARS: Stress Anxiety Res Soc. 2007;11:107–117.
  • Ghitany ME, Al-Awadhi FA, Alkhalfan LA. Marshall–Olkin extended Lomax distribution and its application to censored data. Commun Stat – Theory Methods. 2007;36:1855–1866. doi: 10.1080/03610920601126571
  • Ghitany ME, Kotz S. Reliability properties of extended linear failure-rate distributions. Probab Eng Inform Sci. 2007;21:441–450. doi: 10.1017/S0269964807000071
  • Gómez–Déniz E. Another generalization of the geometric distribution. Test. 2010;19:399–415. doi: 10.1007/s11749-009-0169-3
  • García VJ, Gómez–Déniz E, Vázquez–Polo FJ. A new skew generalization of the normal distribution: properties and applications. Comput Stat Data Anal. 2010;54:2021–2034. doi: 10.1016/j.csda.2010.03.003
  • Jose KK, Naik SR, Ristić MM. Marshall–Olkin q-Weibull distribution and max-min processes. Statist Pap. 2010;51:837–851. doi: 10.1007/s00362-008-0173-9
  • Gui W. Marshall-Olkin extended log-logistic distribution and its application in minification processes. Appl Math Sci. 2013;7:3947–3961.
  • Maiti SS, Dey M. Tilted normal distribution and its survival properties. J Data Sci. 2012;10:225–240.
  • Lemonte AJ. A new extension of the Birnbaum–Saunders distribution. Braz J Probab Stat. 2013;27:133–149. doi: 10.1214/11-BJPS160
  • Nadarajah S. Marshall and Olkin's distributions. Acta Appl Math. 2008;103:87–100. doi: 10.1007/s10440-008-9221-7
  • Nadarajah S, Haghighi F. An extension of the exponential distribution. Statistics. 2011;45:543–558. doi: 10.1080/02331881003678678
  • Mudholkar GS, Srivastava DK. Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Trans Reliab. 1993;42:299–302. doi: 10.1109/24.229504
  • Gilchrist WG. Statistical modelling with quantile functions. Boca Raton, LA: Chapman and Hall/CRC; 2001.
  • Shaked M, Shanthikumar JG. Stochastic orders. New York: Springer Series in Statistics; 2007.
  • Barlow RE, Proschan F. Statistical theory of reliability and life testing: probability models. New York: Holt, Rinehart and Winston; 1975.
  • Ross SM. Stochastic processes. 2nd ed. New York: Wiley; 1996.
  • Stoyan D. Comparison methods for queues and other stochastic models. New York: Wiley; 1983.
  • Nekoukhou V, Alamatsaz MH. A family of skew-symmetric-Laplace distributions. Statistical Papers. 2012;53:685–696. doi: 10.1007/s00362-011-0372-7
  • Lai C, Xie M. Stochastic ageing and dependence for reliability. New York: Springer; 2006.
  • Barreto–Souza W, Lemonte AJ, Cordeiro GM. General results for the Marshall and Olkin's family of distributions. Ann Braz Acad Sci. 2013;85:3–21. doi: 10.1590/S0001-37652013000100002
  • MacGillivray HL. Skewness and asymmetry: measures and orderings. Ann Stat. 1986;14:994–1011. doi: 10.1214/aos/1176350046
  • Gradshteyn IS, Ryzhik IM. Table of integrals ccc series, and products. New York: Academic Press; 2007.
  • Cox DR, Hinkley DV. Theoretical statistics. London: Chapman and Hall; 1974.
  • Kundu D, Gupta AK. On bivariate Weibull Geometric distribution. J Multivariate Anal. 2014;123:19–29. doi: 10.1016/j.jmva.2013.08.004
  • Lee ET, Wang JW. Statistical methods for survival data analysis. 3rd ed. New York: Wiley; 2003.
  • Aarset MV. How to identify bathtub hazard rate. IEEE Trans Reliab. 1987;36:106–108. doi: 10.1109/TR.1987.5222310
  • Chen G, Balakrishnan N. A general purpose approximate goodness-of-fit test. J Qual Technol. 1995;27:154–161.
  • Nadarajah S, Kotz S. The beta exponential distribution. Reliab Eng Syst Safety. 2006;91:689–697. doi: 10.1016/j.ress.2005.05.008
  • Cordeiro GM, Lemonte AJ. The β-Birnbaum–Saunders distribution: an improved distribution for fatigue life modeling. Comput Stat Data Anal. 2011;55:1445–1461. doi: 10.1016/j.csda.2010.10.007
  • Lemonte AJ. A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function. Comput Stat Data Anal. 2013;62:149–170. doi: 10.1016/j.csda.2013.01.011
  • Sarhan AM, Balakrishnan N. A new class of bivariate distributions and its mixture. J Multivariate Anal. 2007;98:1508–1527. doi: 10.1016/j.jmva.2006.07.007
  • Kundu D, Gupta RD. Bivariate generalized exponential distribution. J Multivariate Anal. 2009;100:581–593. doi: 10.1016/j.jmva.2008.06.012
  • Kundu D, Gupta RD. Modified Sarhan–Balakrishnan singular bivariate distribution. J Statist Plan Inference. 2010;140:526–538. doi: 10.1016/j.jspi.2009.07.026
  • Kundu D, Gupta RD. A class of bivariate models with proportional reversed hazard marginals. Sankhya B. 2010;72:236–253. doi: 10.1007/s13571-011-0012-1
  • Kundu D, Gupta RD. Absolute continuous bivariate generalized exponential distribution. Adv Statist Anal. 2011;95:169–185. doi: 10.1007/s10182-010-0151-0
  • Sarhan A, Hamilton DC, Smith B, Kundu D. The bivariate generalized linear failure rate distribution and its multivariate extension. Comput Stat Data Anal. 2011;55:644–654. doi: 10.1016/j.csda.2010.06.006
  • Barreto–Souza W, Lemonte AJ. Bivariate Kumaraswamy distribution: properties and a new method to generate bivariate classes. Statistics. 2013;47:1321–1342. doi: 10.1080/02331888.2012.694446
  • Jamalizadeh A, Kundu D. Weighted Marshall-Olkin bivariate exponential distribution. Statistics. 2013;47:917–928. doi: 10.1080/02331888.2012.670640

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