Keywords:-
Keywords:
AR(1) models, Max-Min processes, Marshall-Olkin q-exponential distribution, q-exponential distribution.
Article Content:-
Abstract
In this paper we review the q-exponential distribution and its properties.
Distributions of extreme order statistics are obtained. The Marshall-Olkin q-exponential
distribution is developed and studied in detail. Estimation of parameters is also discussed.
AR(1) models and max-min AR(1) models are developed and sample path properties are
explored. These can be used for modeling time series data on river flow, dam levels, finance
and exchange rates.
References:-
References
Alice,T.,and Jose, K.K. (2004). Bivariate semi-Pareto minification processes,Metrika 59,
305-313.
Jayakumar,K., and Thomas, M. (2008). On a generalization of Marshall-Olkin scheme
and its application to Burr type XII distribution, Statistical Papers,49, 421-439.
Jose, K.K., Krishna, E., and Ristic,M.M. (2014). On Record Values and Reliability Properties
of Marshall-Olkin Extended Exponential Distribution, Journal of Applied Statistical
Science, 21(1), 83-100.
Jose, K.K., Naik, S.R., and Ristic, M.M. (2010). Marshall-Olkin q-Weibul distribution
and max-min processes,Statistical Papers, 51,4, 837-851.
Jose, K.K.,Ristic, M.M., and Ancy (2011). Marshall-Olkin BivariateWeibull distributions
and processes, Statistical Papers, 52, 789-798.
Jose, K.K., and Remya (2015). Negative binomial Marshall-Olkin Rayleigh distribution
and its applications, Econ.Quality Control,30,2,189-198.
Krishna, E., Jose,K.K., Alice,T. and Ristic,M.M. (2013 a). Marshall-Olkin Fréchet distribution,
Communications in Statistics-Theory and methods, 42, 4091-4107.
Krishna, E. Jose, K.K. and Ristic, M.M. (2013 b). Applications of Marshall-Olkin Fréchet
distribution,Communications in Statistics-Simulation and Computation, 42, 76-89.
Lewis, P. A. W. and McKenzie, E. (1991). Minification process and their transformations,
J. Appl. Prob., 28, 45-57.
Marshall, A.W., Olkin, I. (1997). A new method for adding a parameter to a family of
distributions with application to the exponential andWeibull families,Biometrika, 84,
641-652.
Picoli, S.,Mendes, R.S.,and Malacarne,L.C.(2003).q-exponential,Weibul,q-Weibul distributions:
an empirical analysis ,Physica A, 324,3-4,678-688.
14
Sankaran,P.G., and Jayakumar, K. (2008). On proportional odds model. Statistical Papers,
49, 779-789.
Seetha Lekshmi, V. and Catherine, T. (2012 b). On q- Exponential Count Models, Journal
of Applied Statistical Science,20,2.
Seethalekshmi, V. and Jose, K.K.(2004). An autoregressive process with geometric a-
Laplace marginals, Statistical Papers, 45,337-350.
Seethalekshmi, V., and Jose, K.K.(2006). Autoregressive processes with pakes andgeometric
Pakes generalized Linnik marginals, Statistics and Probability Letters,76,318-
326.
Travers, L.V.(1977). The exact distribution of extremes of a non Gaussian process. Stochastic
Process Appl 5,151-156.
Tavares, L.V.(1980). An exponential markovian stationary process, J Appl Prob 17,1117-
1120.
Tsallis, C. (1988). Possible generalisation of Boltzmann-Gibbs statisics,Journal of Statistical
Physics, 52,1-2,479-487.
305-313.
Jayakumar,K., and Thomas, M. (2008). On a generalization of Marshall-Olkin scheme
and its application to Burr type XII distribution, Statistical Papers,49, 421-439.
Jose, K.K., Krishna, E., and Ristic,M.M. (2014). On Record Values and Reliability Properties
of Marshall-Olkin Extended Exponential Distribution, Journal of Applied Statistical
Science, 21(1), 83-100.
Jose, K.K., Naik, S.R., and Ristic, M.M. (2010). Marshall-Olkin q-Weibul distribution
and max-min processes,Statistical Papers, 51,4, 837-851.
Jose, K.K.,Ristic, M.M., and Ancy (2011). Marshall-Olkin BivariateWeibull distributions
and processes, Statistical Papers, 52, 789-798.
Jose, K.K., and Remya (2015). Negative binomial Marshall-Olkin Rayleigh distribution
and its applications, Econ.Quality Control,30,2,189-198.
Krishna, E., Jose,K.K., Alice,T. and Ristic,M.M. (2013 a). Marshall-Olkin Fréchet distribution,
Communications in Statistics-Theory and methods, 42, 4091-4107.
Krishna, E. Jose, K.K. and Ristic, M.M. (2013 b). Applications of Marshall-Olkin Fréchet
distribution,Communications in Statistics-Simulation and Computation, 42, 76-89.
Lewis, P. A. W. and McKenzie, E. (1991). Minification process and their transformations,
J. Appl. Prob., 28, 45-57.
Marshall, A.W., Olkin, I. (1997). A new method for adding a parameter to a family of
distributions with application to the exponential andWeibull families,Biometrika, 84,
641-652.
Picoli, S.,Mendes, R.S.,and Malacarne,L.C.(2003).q-exponential,Weibul,q-Weibul distributions:
an empirical analysis ,Physica A, 324,3-4,678-688.
14
Sankaran,P.G., and Jayakumar, K. (2008). On proportional odds model. Statistical Papers,
49, 779-789.
Seetha Lekshmi, V. and Catherine, T. (2012 b). On q- Exponential Count Models, Journal
of Applied Statistical Science,20,2.
Seethalekshmi, V. and Jose, K.K.(2004). An autoregressive process with geometric a-
Laplace marginals, Statistical Papers, 45,337-350.
Seethalekshmi, V., and Jose, K.K.(2006). Autoregressive processes with pakes andgeometric
Pakes generalized Linnik marginals, Statistics and Probability Letters,76,318-
326.
Travers, L.V.(1977). The exact distribution of extremes of a non Gaussian process. Stochastic
Process Appl 5,151-156.
Tavares, L.V.(1980). An exponential markovian stationary process, J Appl Prob 17,1117-
1120.
Tsallis, C. (1988). Possible generalisation of Boltzmann-Gibbs statisics,Journal of Statistical
Physics, 52,1-2,479-487.
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Lekshmi V., S., & Thomas, C. (2019). MARSHALL-OLKIN Q-EXPONENTIAL PROCESSES. International Journal Of Mathematics And Computer Research, 7(08). Retrieved from https://ijmcr.in/index.php/ijmcr/article/view/258
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