A max-autoregressive process based on Marshall-Olkin new Pareto-type distribution
M. Shirozhanms.shirozhan@gmail.comWater and Wastewater CompanyMazandaran, IranView full profile → , A. Saadati Niksaadatiali1994@yahoo.comDepartment of Statistics University of MazandaranBabolsar, IranView full profile → , A. Asgharzadeha.asgharzadeh@umz.ac.irDepartment of Statistics University of MazandaranBabolsar, IranView full profile → , Hassan S. Bakouchh.bakouch@qu.edu.saDepartment of Mathematics College of Science Qassim UniversityBuraydah, 51452, Saudi ArabiaView full profile → , *M. MohammadpourCorresponding authorm.mohammadpour@umz.ac.irDepartment of Statistics University of MazandaranBabolsar, IranView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 18 Jan 2023
- Published Online:
- 18 Dec 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JSMS-1236
- Pages:
- 1657–1681
Abstract
Keywords
Subject Classifications
References
[1] M. V. Aarset, “How to identify a bathtub hazard rate,” IEEE Trans. Reliab., vol. 36, pp. 106-108 (1987).
[2] B. Abraham and N. Balakrishna, “Inverse Gaussian autoregressive models,” J. Time Ser. Anal., vol. 20, no. 6, pp. 605-618 (1999).
[3] T. Alice and K. K. Jose, “Marshall-Olkin logistic processes,” STARS Int. Journal., vol. 6, pp. 1-11 (2005).
[4] A. M. Alshangiti, M. Kayid, and B. Alarfaj, “A new family of Marshall-Olkin extended distributions,” J. Comput. Appl. Math., vol. 271, pp. 369-379 (2014).
[5] H. S. Bakouch and B. V. Popović, “Lindley first-order autoregressive model with applications,” Commun. Stat. Theory Methods, vol. 45, pp. 4988-5006 (2016).
[6] M. Bourguignon, H. Saulo, and R. N. Fernandez, “A new Pareto-type distribution with applications in reliability and income data,” Physica A, vol. 457, pp. 166-175 (2016).
[7] F. H. Fernandes, M. Bourguignon, and L. L. Ho, “Control charts to monitor integer-valued autoregressive process with inflation or deflation of zeros,” J. Stat. Manag. Syst., vol. 23, no. 8, pp. 1463-1484 (2020).
[8] D. P. Gaver and P. A. W. Lewis, “First order autoregressive gamma sequences and point processes,” Adv. Appl. Probab., vol. 12, no. 3, pp. 727-745 (1980).
[9] M. E. Ghitany, E. K. Al-Hussaini, and A. L. Jarallah, “Marshall-Olkin Extended Weibull distribution and its application to censored data,” J. Appl. Stat., vol. 32, no. 10, pp. 1025-1034 (2005).
[10] M. E. Ghitany, F. A. Al-Awadhi, and L. A. Alkhalfan, “Marshall-Olkin extended Lomax distribution and its applications to censored data,” Commun. Stat. Theory Methods, vol. 36, pp. 1855-1866 (2007).
[11] K. Jayakumar and T. Mathew, “On a generalization to Marshall-Olkin scheme and its application to Burr type XII distribution,” Stat. Pap., vol. 49, pp. 421-439 (2008).
[12] V. Jevremović, “Two examples of nonlinear processes with mixed exponential marginal distribution,” Stat. Probab. Lett., vol. 10, pp. 221-224 (1990).
[13] K. K. Jose, S. R. Naik, and M. M. Ristić, “Marshall-Olkin q-Weibull distribution and max-min processes,” Stat. Pap., vol. 51, no. 4, pp. 837-851 (2010).
[14] K. K. Jose and M. M. Thomas, “Generalized Laplacian distributions and autoregressive processes,” Commun. Stat. Theory Methods, vol. 40, pp. 4263-4277 (2011).
[15] K. K. Jose, L. Tomya, and J. Sreekumar, “Autoregressive processes with normal-Laplace marginals,” Stat. Probab. Lett., vol. 78, pp. 2456-2462 (2008).
[16] W. C. Khoo, S. H. Ong, and A. Biswas, “Modeling time series of counts with a new class of INAR(1) model,” Stat. Pap., vol. 58, pp. 393-416 (2017).
[17] E. Krishna and K. K. Jose, “Marshall-Olkin Asymmetric Laplace Distribution and Processes,” Statistica, vol. LXXI, no. 4, pp. 453-467 (2011).
[18] E. Krishna, K. K. Jose, T. Alice, and M. M. Ristić, “Marshall-Olkin Fréchet distribution,” Commun. Stat. Theory Methods, vol. 42, pp. 4091-4107 (2013).
[19] E. Krishna, K. K. Jose, and M. M. Ristić, “Applications of Marshall-Olkin Fréchet distribution,” Commun. Stat. Simul. Comput., vol. 42, pp. 76-89 (2013b).
[20] D. Kumar, “The Burr type XII distribution with some statistical properties,” Data Sci. J., vol. 16, pp. 509-534 (2017).
[21] A. Lawrence, “The mixed exponential solution to the first order autoregressive model,” J. Appl. Probab., vol. 17, pp. 546-552 (1980).
[22] A. Lawrence and P. Lewis, “A new autoregressive time series model in exponential variables (NEAR(1)),” Adv. Appl. Probab., vol. 13, pp. 826-845 (1980).
[23] S. V. Lekshmi and C. Thomas, “Marshall-Olkin new Pareto distribution and max-min processes,” IOSR-JBM, vol. 21, pp. 48-55 (2019).
[24] M. T. Madi and M. Z. Raqab, “Bayesian prediction of temperature records using the Pareto model,” Environmetrics, vol. 15, pp. 701-710 (2004).
[25] J. Mališić, “On exponential autoregressive time series models,” Math. Stat. Prob. Theory B., pp. 147-153 (1987).
[26] A. N. Marshall and I. Olkin, “A new method for adding a parameter to a family of distributions with applications to the exponential and Weibull families,” Biometrika, vol. 84, pp. 641-652 (1997).
[27] M. Nassar, D. Kumar, S. Dey, G. M. Cordeiro, and A. Z. Afify, “The Marshall-Olkin alpha power family of distributions with applications,” J. Comput. Appl. Math., vol. 351, pp. 41-53 (2019).
[28] W. B. Nelson, Statistical methods for accelerated life test data-the inverse power law model, General Electric Co. Tech. Rep. 71-C011, New York: Schenectady (1970).
[29] H. M. Okasha and M. Kayid, “A new family of Marshall-Olkin extended generalized linear exponential distribution,” J. Comput. Appl. Math., vol. 296, pp. 576-592 (2016).
[30] V. Pareto, Cours d’économie Politique, Rouge et Cie, Paris (1987).
[31] R. V. Parikh, D. K. Ghosh, and K. Muralidharan, “On Marshall-Olkin generalized exponential distribution,” IAPQR Trans., vol. 33, no. 1, pp. 71-81 (2008).
[32] G. G. S. Pegram, “An autoregressive model for multilag Markov chains,” J. Appl. Probab., vol. 17, no. 2, pp. 350-362 (1980).
[33] J. Picklands, “Statistical inference using extreme value statistics,” Ann. Stat., vol. 3, pp. 119-131 (1975).
[34] B. Č. Popović, “AR(1) time series with approximated Beta marginal,” Publ. de l’Institut Math., vol. 88, pp. 87-98 (2010).
[35] M. Z. Raqab, A. Asgharzadeh, and R. Valiollahi, “Prediction for Pareto distribution based on progressively type-II censored samples,” Comput. Stat. Data Anal., vol. 54, pp. 1732-1743 (2010).
[36] M. Ristić and B. Č. Popović, “The uniform autoregressive process of the second order (UAR(2)),” Stat. Probab. Lett., vol. 57, pp. 113-119 (2002).
[37] M. Shirozhan, M. Mohammadpour, and H. S. Bakouch, “A new geometric INAR(1) model with mixing Pegram and generalized binomial thinning operators,” Iran J. Sci. Technol. Trans. A. Sci., vol. 43, pp. 1011-1020 (2019).
[38] C. H. Sim, “Simulation of Weibull and Gamma autoregressive stationary process,” Commun. Stat. Simul. Comput., vol. 15, pp. 1141-1146 (1986).
[39] C. H. Sim, “First-order autoregressive models for gamma and exponential process,” J. Appl. Probab., vol. 27, pp. 325-332 (1990).
[40] M. L. Tiku and A. D. Akkaya, Robust Estimation and Hypothesis Testing, New Age International (P) Limited, New Delhi (2004).
