[Home ] [Archive]   [ فارسی ]  
:: Main :: About :: Current Issue :: Archive :: Search :: Submit :: Contact ::
:: Volume 26, Issue 2 (3-2022) ::
Andishe 2022, 26(2): 33-41 Back to browse issues page
Joint marginal densities of order statistics: simple proof and some useful identities
Mahmood Mirjalili, Jaber Kazempoor *, Behshid Yasavoli
Mashhad, Iran
Abstract:   (1472 Views)
The cumulative distribution and density functions of a product of some random variables following the power distribution with different parameters have been provided.
The corresponding characteristic and moment-generating functions are also derived.
We extend the results to the exponential variables and furthermore, some useful identities have been investigated in detail.
Keywords: exponential distribution, joint distributions, marginal densities, order statistics, power distribution.
Full-Text [PDF 202 kb]   (1316 Downloads)    
Type of Study: Research | Subject: Special
Received: 2021/12/17 | Accepted: 2022/03/30 | Published: 2022/09/8
1. [1] Ahsanullah, Mohammad and Nevzorov, Valery and Shakil, Mohammad (2013). An intoduction to order statistics, Springer. [DOI:10.2991/978-94-91216-83-1]
2. [2] Barry, C. A., Balakrishnan, N. and Nagaraja, N. H. (2011). Records, John wiley & Sons.
3. [3] Barry, C. A., Balakrishnan, N. and Nagaraja, N. H. (2008). A first course in order statistics, SIAM.
4. [4] Bairamov, I. and Tavangar, M. (2015). Residual lifetomes of k-out-of-n systems with exchangeable components. Journal of the Iranian Statistical Society, 14(1), 63-87.
5. [5] Balakrishnan, N. Bendre, S. M., and Malik. H. J (1992). General relations and identities for order statostics from nonindependent non-identical variables. Annals of the Institute of Statistical Mathematics, 44(1), 177-183. [DOI:10.1007/BF00048680]
6. [6] Balakrishnan, N., Zhao, P. (2013). Ordering properties of order statistics from heterogeneus population: a review with an emphasis on some recent developments. Probability in the Engineering and Informational Sciences, 27(4), 403. [DOI:10.1017/S0269964813000156]
7. [7] Bayramoglu, I. (2018). A note on the ordering of distribution functions of inid random variables.Journal of Computational and Applied Mathematics, 343, 49-54. [DOI:10.1016/j.cam.2018.03.042]
8. [8] Cooper, G. F. and Herskovits, E. (1992). A Bayesian method for the induction of probabilistic networks from data.Machine learning, 9(4), 309-347. [DOI:10.1007/BF00994110]
9. [9] David, H. A., Nagaraja, N. H. (2004). Order statistics. Encyclopedia of statistical sciences. [DOI:10.1002/0471667196.ess6023]
10. [10] Heckerman, D. (1998). A tutorial on learning with Bayesian networks. Springer Netherlands. [DOI:10.1007/978-94-011-5014-9_11]
11. [11] Hogg, V. R., McKean, J., and Craig, T. A. (2005). Introduction to mathematical statistics, Pearson Education.
12. [12] Kazempoor, J., Habibrad. A., and Okhli, KH. (2020). Bounds for cdfs of order statistics arising from inid random variables. Journal of the Iranian Statistical Society, 19(1), 39-57. [DOI:10.29252/jirss.19.1.39]
13. [13] Kelkinnama, M., Tavangar, M., and Asadi, M. (2015). New developments on stachastic properties of coherent systems. IEEE Transactions on Reliability, 64(4), 1276-1286. [DOI:10.1109/TR.2015.2431682]
14. [14] Likes, J. (1967). Distributions of some statistics in samples from exponential and power-function populations. Journal of the American Statistical Association, 62(317), 259-271. [DOI:10.2307/2282928]
15. [15] Malmquist, S. (1950). On a property of order statistics from a rectangular distribution. Scandinavian Actuarial Journal, (3-4), 214-222. [DOI:10.1080/03461238.1950.10432043]
16. [16] Salehi, E., Tavangar, M. (2019). Stochastic comparisons on conditional residual lifetime and inactivity time of coherent systems with exchangeable components. Statistics & Probability Letters, 145, 327-337. [DOI:10.1016/j.spl.2018.10.007]
17. [17] Scheffe. H., Tukey, W. J., and et al. (1945). Non-parametric estimation. I. Validation of order statistics. The Annals of Mathematical Statistics, 16(2), 187-192. [DOI:10.1214/aoms/1177731119]
18. [18] Zhao, P., Li, X. (2009). Stochastic order of sample range from heterogeneous exponential random variables. Probability in the Engineering and Informational Sciences, 23(1), 17. [DOI:10.1017/S0269964809000023]
19. [19] Zhao, P., Zhang, Y. (2012). On sample ranges in multiple-outlier models. Journal of Multivariate Analysis, 111, 335- 349. [DOI:10.1016/j.jmva.2012.04.010]
Send email to the article author

Add your comments about this article
Your username or Email:


XML   Persian Abstract   Print

Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Mirjalili M, Kazempoor J, Yasavoli B. Joint marginal densities of order statistics: simple proof and some useful identities. Andishe 2022; 26 (2) :33-41
URL: http://andisheyeamari.irstat.ir/article-1-876-en.html

Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Volume 26, Issue 2 (3-2022) Back to browse issues page
مجله اندیشه آماری Andishe _ye Amari
Persian site map - English site map - Created in 0.05 seconds with 30 queries by YEKTAWEB 4540