On the Harris extended family of distributions

References

• C Alexander, GM Cordeiro, EMM Ortega, JM Sarabia. Generalized beta-generated distributions. Comput Stat Data Anal. 2012;56:1880–1897. doi: 10.1016/j.csda.2011.11.015
   Web of Science ®Google Scholar
• EAA Aly, L Benkherouf. A new family of distributions based on probability generating functions. Sankhya B. 2011;73:70–80. doi: 10.1007/s13571-011-0017-9
   Google Scholar
• GM Cordeiro, M de Castro. A new family of generalized distributions. J Statist Comput Simul. 2011;81:883–898. doi: 10.1080/00949650903530745
   Web of Science ®Google Scholar
• N Eugene, C Lee, F Famoye. Beta-normal distribution and its applications. Commun Stat – Theory Methods. 2002;31:497–512. doi: 10.1081/STA-120003130
   Web of Science ®Google Scholar
• AW Marshall, I Olkin. 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
   Web of Science ®Google Scholar
• K Zografos, N Balakrishnan. 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
   Google Scholar
• TE Harris. Branching processes. Ann Math Stat. 1948;19:474–494. doi: 10.1214/aoms/1177730146
   Google Scholar
• W Barreto-Souza, AJ Lemonte, GM Cordeiro. General results for the Marshall and Olkin's family of distributions. Ann Braz Acad Sci. 2013;85:3–21. doi: 10.1590/S0001-37652013000100002
   Web of Science ®Google Scholar
• AK Nanda, S Das. Stochastic orders of the Marshall–Olkin extended distribution. Stat Probab Lett. 2012;82: 295–302. doi: 10.1016/j.spl.2011.10.003
   Web of Science ®Google Scholar
• M Shaked, JG Shanthikumar. Stochastic orders, Springer Series in Statistics. New York: Springer; 2007.
   Google Scholar
• RE Barlow, F Proschan. Statistical theory of reliability and life testing: probability models. New York: Holt, Rinehart and Winston; 1975.
   Google Scholar
• SM Ross, Stochastic processes. 2nd ed. New York:Wiley, 1996.
   Google Scholar
• D Stoyan. Comparison methods for queues and other stochastic models. New York: Wiley; 1983.
   Google Scholar
• V Nekoukhou, MH Alamatsaz. A family of skew-symmetric-Laplace distributions. Statist Pap. 2012;53:685–696. doi: 10.1007/s00362-011-0372-7
   Web of Science ®Google Scholar
• C Lai, M Xie. Stochastic ageing and dependence for reliability. New York: Springer; 2006.
   Google Scholar
• FJ Rubio, MFJ Steel. 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
   Web of Science ®Google Scholar
• JA Greenwood, JM Landwehr, NC Matalas, JR Wallis. Probability weighted moments: definition and relation to parameters of several distributions expressable in inverse form. Water Resour Res. 1979;15:1049–1054. doi: 10.1029/WR015i005p01049
   Web of Science ®Google Scholar
• HM Barakat, ME Ghitany, EK Al-Hussaini. Asymptotic distributions of order statistics and record values under the Marshall–Olkin parametrization operation. Commun Stat – Theory Methods. 2009;38:2267–2273. doi: 10.1080/03610920802361373
   Web of Science ®Google Scholar
• BC Arnold, N Balakrishnan, HN Nagaraja. A first course in order statistics. New York: Wiley; 1992.
   Google Scholar
• J Galambos. The asymptotic theory of extreme order statistics. New York: Wiley; 1978.
   Google Scholar
• E Castillo, AS Hadi, N Balakrishnan, JM Sarabia. Extreme value and related models with applications in engineering and science. Hoboken, NJ: Wiley; 2005.
   Google Scholar
• ME Ghitany, EK Al-Hussaini, RA Al-Jarallah. Marshall–Olkin extended Weibull distributions and its application to censored data. J Appl Stat. 2005;32:1025–1034. doi: 10.1080/02664760500165008
   Web of Science ®Google Scholar
• ME Ghitany, FA Al-Awadhi, LA Alkhalfan. Marshall–Olkin extended Lomax distribution and its application to censored data. Commun Stat – Theory Methods. 2007;36:1855–1866. doi: 10.1080/03610920601126571
   Web of Science ®Google Scholar
• ME Ghitany, S Kotz. Reliability properties of extended linear failure rate distributions. Probab Eng Inform Sci. 2007;21:441–450. doi: 10.1017/S0269964807000071
   Web of Science ®Google Scholar
• C Fox. The asymptotic expansion of generalized hypergeometric functions. Proc London Math Soc (Ser. 2). 1928;27:389–400. doi: 10.1112/plms/s2-27.1.389
   Google Scholar
• EM Wright. The asymptotic expansion of the generalized hypergeometric function. J London Math Soc. 1935;10:286–293.
   Google Scholar
• EM Wright. The asymptotic expansion of the generalized hypergeometric function. Proc London Math Soc (Ser. 2). 1940;46:389–408. doi: 10.1112/plms/s2-46.1.389
   Google Scholar
• ME Ghitany. Marshall-Olkin extended Pareto distribution and its application. Int J Appl Math. 2005;18:17–31.
   Google Scholar
• IS Gradshteyn, IM Ryzhik. Table of integrals, series, and products. New York: Academic Press; 2007.
   Google Scholar
• E Krishna, KK Jose, MM Ristic. Applications of Marshall–Olkin Fréchet distribution. Commun Stat – Simul Comput. 2013;42:76–89. doi: 10.1080/03610918.2011.633196
   Web of Science ®Google Scholar
• E Krishna, KK Jose, T Alice, MM Ristic. The Marshall–Olkin Fréchet distribution. Commun Stat Theory. 2013;22:4001–4107.
   Google Scholar
• AH El-Bassiouny, NF Abdo. Reliability properties of seven parameters Burr XII distribution. Comput Methods Sci Technol. 2010;16:127–133. doi: 10.12921/cmst.2010.16.02.127-133
   Google Scholar
• DR Cox, DV Hinkley. Theoretical statistics. London: Chapman and Hall; 1974.
   Google Scholar
• V Choulakian, MA Stephens. Goodness-of-fit for the generalized Pareto distribution. Technometrics. 2001;43: 478–484. doi: 10.1198/00401700152672573
   Web of Science ®Google Scholar
• GS Mudholkar, DK Srivastava. Exponentiated Weibull family for analyzing bathtub failure-rate data. IEEE Trans Reliab. 1993;42:299–302. doi: 10.1109/24.229504
   Web of Science ®Google Scholar
• RD Gupta, D Kundu. Exponentiated exponential family: an alternative to gamma and Weibull distributions. Biom J. 2001;33:117–130. doi: 10.1002/1521-4036(200102)43:1<117::AID-BIMJ117>3.0.CO;2-R
   Web of Science ®Google Scholar
• M Xie, Y Tang, TN Goh. A modified Weibull extension with bathtub-shaped failure rate function. Reliab Eng Syst Saf. 2002;76:279–285. doi: 10.1016/S0951-8320(02)00022-4
   Web of Science ®Google Scholar
• Z Chen. A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Stat Probab Lett. 2000;49:155–162. doi: 10.1016/S0167-7152(00)00044-4
   Web of Science ®Google Scholar
• S Nadarajah, S Kotz. The beta exponential distribution. Reliab Eng Syst Saf. 2006;91:689–697. doi: 10.1016/j.ress.2005.05.008
   Web of Science ®Google Scholar
• AJ Lemonte. 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
   Web of Science ®Google Scholar
• S Nadarajah, F Haghighi. An extension of the exponential distribution. Statistics. 2011;45:543–558. doi: 10.1080/02331881003678678
   Web of Science ®Google Scholar
• G Chen, N Balakrishnan. A general purpose approximate goodness-of-fit test. J Qual Technol. 1995;27:154–161.
   Web of Science ®Google Scholar