Abstract
In this paper we introduce a new probability model known as type 2 Marshall–Olkin bivariate Weibull distribution as an extension of type 1 Marshall–Olkin bivariate Weibull distribution of Marshall–Olkin (J Am Stat Assoc 62:30–44, 1967). Various properties of the new distribution are considered. Bivariate minification processes with the two types of Weibull distributions as marginals are constructed and their properties are considered. It is shown that the processes are strictly stationary. The unknown parameters of the type 1 process are estimated and their properties are discussed. Some numerical results of the estimates are also given.
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References
Alice T, Jose KK (2002) Multivariate minification processes. STARS Int J 3: 1–9
Alice T, Jose KK (2005a) Marshall–Olkin semi-Weibull minification processes. Recent Adv Stat Theory Appl I: 6–17
Alice T, Jose KK (2005b) Marshall–Olkin logistic processes. STARS Int J 6: 1–11
Arnold BC, Robertson CA (1989) Autoregressive logistic processes. J Appl Probab 26: 524–531
Balakrishna N, Jacob TM (2003) Parameter estimation in minification processes. Commun Stat Theory Methods 32: 2139–2152
Balakrishna N, Jayakumar K (1997) Bivariate semi-Pareto distributions and processes. Stat Pap 38: 149–165
Hanagal DD (1996) A multivariate Weibull distribution. Econ Qual Control 11: 193–200
Jayakumar K, Thomas M (2007) On a generalization to Marshall–Olkin scheme and its application to Burr type XII distribution. Stat Pap. doi:10.1007/s00362-006-0024-5
Marshall AW, Olkin I (1967) A multivariate exponential distribution. J Am Stat Assoc 62: 30–44
Marshall AW, Olkin I (1997) A new method of adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika 84: 641–652
Mino T, Yoshikawa N, Suzuki K, Horikawa Y, Abe Y (2003) The mean of lifespan under dependent competing risks with application to mice data. J Health Sports Sci Juntendo Univ 7: 68–74
Pillai RN (1991) Semi-Pareto processes. J Appl Probab 28: 461–465
Rachev ST, Wu C, Yakovlev AY (1995) A bivariate limiting distribution of tumor latency time. Math Biosci 127: 127–147
Ristić MM (2006) Stationary bivariate minification processes. Stat Probab Lett 76: 439–445
Sim CH (1986) Simulation of Weibull and gamma autoregressive stationary processes. Commun Stat Simul Comput 15: 1141–1146
Tavares LV (1980) An exponential Markovian stationary process. J Appl Probab 17: 1117–1120
Thomas A, Jose KK (2004) Bivariate semi-Pareto minification processes. Metrika 59: 305–313
Yeh HC, Arnold BC, Robertson CA (1988) Pareto process. J Appl Probab 25: 291–301
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Jose, K.K., Ristić, M.M. & Joseph, A. Marshall–Olkin bivariate Weibull distributions and processes. Stat Papers 52, 789–798 (2011). https://doi.org/10.1007/s00362-009-0287-8
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DOI: https://doi.org/10.1007/s00362-009-0287-8
Keywords
- Type 1 and type 2 Marshall–Olkin bivariate Weibull distribution
- Marshall–Olkin bivariate exponential distribution
- Bivariate minification process
- Stationary process
- Estimation