Stochastic Aging Classes for the Maximum Statistic from Friday and Patil Bivariate Exponential Distribution Family

References

• Baggs , G. E. , Nagaraja , H. N. ( 1996 ). Reliability properties of order statistics from bivariate exponential distributions . Commun. Statist. Stochastic Mod. 12 : 611 – 631 .
   Google Scholar
• Barlow , R. E. , Proschan , F. ( 1981 ). Statistical Theory of Reliability and Life Testing: Probability Models . Silver Springs , MD : McArdale Press .
   Google Scholar
• Block , H. W. , Basu , A. P. ( 1974 ). A continuous bivariate exponential extension . J. Amer. Statist. Assoc. 69 : 1031 – 1037 .
   Web of Science ®Google Scholar
• Corless , R. M. , Gonnet , G. H. , Hare , D. E. G. , Jeffrey , D. J. , Knuth , D. E. ( 1996 ). On the Lambert W function . Adv. Comput. Math. 5 : 329 – 359 .
   Web of Science ®Google Scholar
• Di Crescenzo , A. , Longobardi , M. ( 2006 ). On the NBU ageing notion within the competing risks model . J. Statist. Plann. Infer. 136 : 1638 – 1654 .
   Google Scholar
• Franco , M. , Vivo , J. M. ( 2002 ). Reliability properties of series and parallel systems from bivariate exponential models . Commun. Statist. Theor. Meth. 31 : 2349 – 2360 .
   Web of Science ®Google Scholar
• Franco , M. , Vivo , J. M. ( 2006 ). On log-concavity of the extremes from Gumbel bivariate exponential distributions . Statistics 40 : 415 – 433 .
   Web of Science ®Google Scholar
• Franco , M. , Vivo , J. M. ( 2007 ). Generalized mixtures of gamma and exponentials and reliability properties of the maximum from Friday and Patil bivariate exponential model . Commun. Statist. Theor. Meth. 36 : 2011 – 2025 .
   Web of Science ®Google Scholar
• Freund , J. E. ( 1961 ). A bivariate extension of the exponential distribution . J. Amer. Statist. Assoc. 56 : 971 – 977 .
   Web of Science ®Google Scholar
• Friday , D. S. , Patil , G. P. ( 1977 ). A bivariate exponential model with applications to reliability and computer generation of random variables . In: Tsokos , C. P. , Shimi , I. , eds. Theory and Applications of Reliability . Vol. 1 . New York : Academic Press , pp. 527 – 549 .
   Google Scholar
• Hutchison , T. P. , Lai , C. D. ( 1990 ). Continuous Bivariate Distributions, Emphasizing Applications . Adelaide , Australia : Rumsby Scientific Publishing .
   Google Scholar
• Kotz , S. , Balakrishnan , N. , Johnson , N. L. ( 2000 ). Continuous Multivariate Distributions . New York : Wiley .
   Google Scholar
• Lai , C. D. , Xie , M. ( 2006 ). Stochastic Ageing and Dependence for Reliability . New York : Springer .
   Google Scholar
• Marshall , A. W. , Olkin , I. ( 1967 ). A multivariate exponential distribution . J. Amer. Statist. Assoc. 62 : 30 – 44 .
   Web of Science ®Google Scholar
• Nadarajah , S. , Gupta , A. K. ( 2006 ). Friday and Patil's bivariate exponential distribution with application to drought data . Water Res. Manage. 20 : 749 – 759 .
   Google Scholar
• Nadarajah , S. , Kotz , S. ( 2007 ). Block and Basu's bivariate exponential distribution with application to drought data . Probab. Eng. Inform. Sci. 21 : 143 – 155 .
   Google Scholar
• Proschan , F. , Sullo , P. ( 1974 ). Estimating the parameters of a bivariate exponential distribution in several sampling situations . In: Proschan , F. , Serfling , R. , eds. Reliability and Biometry: Statistical Analysis of Lifelengths . Philadelphia : SIAM , pp. 423 – 440 .
   Google Scholar
• Shaked , M. , Shantikumar , J. G. ( 1994 ). Stochastic Orders and Their Applications . Boston : Academic Press .
   Google Scholar