In this article, we show that the well-known Helmert matrix has strong relationship with stochastic matrices in modern probability theory. In fact, we show that we can construct some stochastic matrices by the Helmert matrix. Hence, we introduce a new class of regular and doubly stochastic matrices by use of the Helmert matrix and a special diagonal matrix that is defined in this article. Afterwards, we obtain the stationary distribution for this new class of stochastic matrices.
| Published in | American Journal of Theoretical and Applied Statistics (Volume 6, Issue 3) |
| DOI | 10.11648/j.ajtas.20170603.14 |
| Page(s) | 156-160 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Helmert Matrix, Stochastic Matrix, Markov Chain, Transition Probability, Stationary Distribution, Regular Chain, Ergodic Chain
| [1] | B. R. Clarke. Linear Models: The Theory and Application of Analysis of variance. Wiley, 2008. |
| [2] | J. E. Gentie, Numerical Linear Algebra for Application in Statistics, springer, 1998. |
| [3] | A. Kehagias, Approximation of stochastic processes by hidden Markov models, U.M.I, 1992. |
| [4] | H. O. Lancaster. The Helmert Matrices. The American Mathematical Monthly, 72(1965), no. 1, 4-12. |
| [5] | E. Parzen, Stochastic Processes, San Francisco: Holden-Day, Inc., 1962. |
| [6] | P. Perkins, “A theorem on regular matrices”. Pacific J. Math. 11 (1961), no. 4, 1529-1533. |
| [7] | Ch. M. Grinstead, J. L. Snell, Introduction to Probability, American Mathematical Society, 1997. |
| [8] | G. A. F. seber, A Matrix Handbook for Statistician, Wiley, 2007. |
| [9] | S. M. Roos, A first cours in probability, 6th ed, Pearson Prentice Hall, 2002. |
| [10] | S. M. Ross, Introduction to Probability Models. 7thth ed. San Diego, colif: Academic Press, Inc., 2000. |
| [11] | S. M. Ross, Stochastic Processes. 2thndth ed. New York: john wiley & Sons, Inc., 1996. |
| [12] | X. Zhan, Matrix Theory, Graduate studies in mathematics, volume 147, American Mathematical Society, 2013. |
APA Style
Reza Farhadian, Nader Asadian. (2017). On a New Class of Regular Doubly Stochastic Processes. American Journal of Theoretical and Applied Statistics, 6(3), 156-160. https://doi.org/10.11648/j.ajtas.20170603.14
ACS Style
Reza Farhadian; Nader Asadian. On a New Class of Regular Doubly Stochastic Processes. Am. J. Theor. Appl. Stat. 2017, 6(3), 156-160. doi: 10.11648/j.ajtas.20170603.14
AMA Style
Reza Farhadian, Nader Asadian. On a New Class of Regular Doubly Stochastic Processes. Am J Theor Appl Stat. 2017;6(3):156-160. doi: 10.11648/j.ajtas.20170603.14
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.ajtas.20170603.14,
author = {Reza Farhadian and Nader Asadian},
title = {On a New Class of Regular Doubly Stochastic Processes},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {6},
number = {3},
pages = {156-160},
doi = {10.11648/j.ajtas.20170603.14},
url = {https://doi.org/10.11648/j.ajtas.20170603.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20170603.14},
abstract = {In this article, we show that the well-known Helmert matrix has strong relationship with stochastic matrices in modern probability theory. In fact, we show that we can construct some stochastic matrices by the Helmert matrix. Hence, we introduce a new class of regular and doubly stochastic matrices by use of the Helmert matrix and a special diagonal matrix that is defined in this article. Afterwards, we obtain the stationary distribution for this new class of stochastic matrices.},
year = {2017}
}
TY - JOUR T1 - On a New Class of Regular Doubly Stochastic Processes AU - Reza Farhadian AU - Nader Asadian Y1 - 2017/05/25 PY - 2017 N1 - https://doi.org/10.11648/j.ajtas.20170603.14 DO - 10.11648/j.ajtas.20170603.14 T2 - American Journal of Theoretical and Applied Statistics JF - American Journal of Theoretical and Applied Statistics JO - American Journal of Theoretical and Applied Statistics SP - 156 EP - 160 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.20170603.14 AB - In this article, we show that the well-known Helmert matrix has strong relationship with stochastic matrices in modern probability theory. In fact, we show that we can construct some stochastic matrices by the Helmert matrix. Hence, we introduce a new class of regular and doubly stochastic matrices by use of the Helmert matrix and a special diagonal matrix that is defined in this article. Afterwards, we obtain the stationary distribution for this new class of stochastic matrices. VL - 6 IS - 3 ER -
Information
Email: