پیوندهای مفید
آمار
| تعداد نشریات | 7 |
| تعداد شماره‌ها | 399 |
| تعداد مقالات | 5,389 |
| تعداد مشاهده مقاله | 5,288,198 |
| تعداد دریافت فایل اصل مقاله | 4,882,940 |
A generalization of Marshall-Olkin bivariate Pareto model and its applications in shock and competing risk models | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 7، دوره 1، شماره 1، اردیبهشت 2020، صفحه 69-87 اصل مقاله (655.49 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2018.14869.1012 | ||
| نویسندگان | ||
| Shirin Shoaee* 1؛ Esmaeil Khorram2 | ||
| 1Department of Statistics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran | ||
| 2Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran | ||
| چکیده | ||
| Statistical inference for extremes has been a subject of intensive research during the last years. In this paper, we generalize the Marshall-Olkin bivariate Pareto distribution. In this case, a new bivariate distribution is introduced by compounding the Pareto Type $\rm{II}$ and geometric distributions. This new bivariate distribution has natural interpretations and can be applied in fatal shock models or in competing risks models. We call the new proposed model Marshall-Olkin bivariate Pareto-geometric (MOBPG) distribution, and then investigate various properties of the new distribution. This model has five unknown parameters and the maximum likelihood estimators cannot be afforded in explicit structure. We suggest to use the EM algorithm to calculate the maximum likelihood estimators of the unknown parameters, and this structure is quite flexible. Also, Monte Carlo simulations are performed to investigate the effectiveness of the proposed algorithm. Finally, we analyze a real data set to investigate our purposes. | ||
| کلیدواژه‌ها | ||
| Bivariate model؛ Competing risk model؛ Expectation-Maximization algorithm؛ Pareto Type $\rm{II}$ distribution؛ Shock model | ||
| مراجع | ||
|
[1] M.V. Aarset, How to identify a bathtub hazard rate, IEEE Transactions on Reliability, 36 (1987) 106-108.
[2] A. Al-Khedhairi, A. El-Gohary, A new class of bivariate Gompertz distributions and its mixture, International Journal of Mathematical Analysis, 2 (2008) 235-253.
[3] A.V. Asimit, E. Furman, R. Vernic, On a multivariate Pareto distribution, Insurance: Mathematics and Economics, 2 (2010) 308–316.
[4] A.V. Asimit, E. Furman, R. Vernic, Statistical inference for a new class of multivariate Pareto distributions, Communications in Statistics-Simulation and Computation, 2, (2016) 456-471.
[5] S.F. Bagheri, E. Bahrami Samani, M. Ganjali, The generalized modified Weibull power series distribution: Theory and applications, Computational Statistics and Data Analysis, 94 (2016) 136-160.
[6] N. Balakrishnan, C.D. Lai, Continuous bivariate distributions, New York, Springer, 2 2009.
[7] R.E. Barlow, F. Proschan, Statistical Theory of Reliability and Life Testing, Probability Models, Maryland, Silver Spring, 1981.
[8] W. Barreto-Souza, Bivariate gamma-geometric law and its induce Levy process, Journal of Multivariate Analysis, 109 (2012) 130-145.
[9] G. Dinse, Non-parametric estimation of partially incomplete time and types of failure data, Biometrics, 38 (1982) 417-431.
[10] M. Chahkandi, M. Ganjali, On some lifetime distributions with decreasing failure rate, Computational Statistics and Data Analysis, 53 (2009) 4433-4440.
[11] M. Ghitany, E. Al-Hussaini, R. Al-Jarallah, Marshall-Olkin extended Weibull distribution and its application to censored data, Journal of Applied Statistics, 32 (2005) 1025-1034.
[12] M. Ghitany, F. Al-Awadhi, L. Alkhalfan, Marshall-Olkin extended lomax distribution and its application to censored data, Communications in Statistics - Theory and Methods, 36 (2007) 1855-1866.
[13] N.L. Johnson, S. Kotz, A vector of multivariate hazard rate, Journal of Multivariate Analysis, 5 (1975) 53-66.
[14] R.A. Johnson, D.W. Wiechern, Applied Multivariate Statistical Analysis, New Jersey, Prentice Hall, 1992.
[15] S. Kotz, N. Balakrishnan, N.L. Johnson, Continuous multivariate distributions, New York, John Wiley and Sons, 2000.
[16] D. Kundu, Parameter estimation for partially complete time and type of failure data, Biometrical Journal, 46 (2004) 165–179.
[17] D. Kundu, A. Dey, Estimating the parameters of the Marshall-Olkin bivariate Weibull distribution by EM algorithm, Computational Statistics and Data Analysis, 35 (2009) 956–965.
[18] D. Kundu, R.D. Gupta, Estimation of R = P(Y < X) for Weibull distribution, IEEE Transactions on Reliability, 55 (2006) 270–280.
[19] D. Kundu, R.D. Gupta, Modified Sarhan-Balakrishnan singular bivariate distribution, Journal of Statistical Planning and Inference, 140 (2010) 526–538.
[20] E.L. Lehmann, Some concepts of dependence, Annals of Mathematical Statistics, 37 (1966) 1137–1153.
[21] T.A. Louis, Finding the observed information matrix when using the EM algorithm, Journal of the Royal Statistical Society, 44 (1982) 226–233.
[22] A.W. Marshall, I. Olkin, A multivariate exponential distribution, Journal of the American Statistical Association, 62 (1967) 30–44.
[23] A.W. Marshall, I. Olkin, Families of multivariate distributions, Journal of the American Statistical Association, 83 (1988) 834–841.
[24] A.W. Marshall, I. Olkin, A new method of adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika, 84 (1997) 641–652.
[25] S.G. Meintanis, Test of fit for Marshall-Olkin distributions with applications, Journal of Statistical Planning and inference, 137 (2007) 3954–3963.
[26] H. Pham, C.D. Lai, On recent generalizations of the Weibull distribution, IEEE Transactions on Reliability, 56 (2007) 454–458.
[27] A.M. Sarhan, N. Balakrishnan, A new class of bivariate distributions and its mixture, Journal of Multivariate Analysis, 98 (2007) 1508–1527.
[28] R.B. Silva, M. Bourguignon, C.R.B. Dias, G.M. Cordeiro, The compound class of extended Weibull power series distributions, Computational Statistics and Data Analysis, 58 (2013) 352–367.
[29] P. Veenus, KRM. Nair, Characterization of a bivariate Pareto distribution, Journal of Indian Statistical Association, 32 (1994) 15–20 | ||
|
آمار تعداد مشاهده مقاله: 19,974 تعداد دریافت فایل اصل مقاله: 854 |
||