We propose a method of obtaining the moment of some continuous bi-variate distributions with parameters α1 β1 andα2 β2 in finding the nth moment of the variable x^c y^d (c≥0, d≥0) where X and Y are continuous random variables having the joint pdf, f(x,y).Here we find the so called gn(c, d)defined gn(c, d)= E(X^cY^d+λ)^n, the nth moment of expected value of the t distribution of the cth power of X and dth power of Y about the constant λ.These moments are obtained by the use of bi-variate moment generating functions, when they exist. The proposed gn(c, d) is illustrated with some continuous bi-variate distributions and is shown to be easy to use even when the powers of the random variables being considered are non-negative real numbers that need not be integers. The results obtained using gn(c, d) are the same as results obtained using other methods such as moment generating functions when they exist.
| Published in | Science Journal of Applied Mathematics and Statistics (Volume 1, Issue 5) |
| DOI | 10.11648/j.sjams.20130105.15 |
| Page(s) | 62-69 |
| 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), 2013. Published by Science Publishing Group |
Moment Generating Functions, Bivariate Distributions, Continuous Random Variables, Joint Pdf
| [1] | Baisnab AP, Manoranjan J (1993). Elements of Probability and Statistics, Tata McGraw – Hill Publishing Company Limited, New Delhi. pp. 208-232. |
| [2] | Freund JE (1992). Mathematical Statistics (5th Edition), Prentice – Hall International Editions, USA. pp. 161-177. |
| [3] | Hay, William (1973).Statistics for the social sciences: Holt, Rinchart and Winston Inc New York, PP 778-780. |
| [4] | Spiegel M.R (1998): Theory and Problems of Statistics, McGraw-Hill Book Company, New York. Pp 261-264. |
| [5] | Uche PI (2003). Probability: Theory and Applications, Longman Nigeria PLC, Ikeja Lagos. pp. 149-155. |
APA Style
Oyeka ICA, Okeh UM. (2013). Moments of Continuous Bi-Variate Distributions: An Alternative Approach. Science Journal of Applied Mathematics and Statistics, 1(5), 62-69. https://doi.org/10.11648/j.sjams.20130105.15
ACS Style
Oyeka ICA; Okeh UM. Moments of Continuous Bi-Variate Distributions: An Alternative Approach. Sci. J. Appl. Math. Stat. 2013, 1(5), 62-69. doi: 10.11648/j.sjams.20130105.15
AMA Style
Oyeka ICA, Okeh UM. Moments of Continuous Bi-Variate Distributions: An Alternative Approach. Sci J Appl Math Stat. 2013;1(5):62-69. doi: 10.11648/j.sjams.20130105.15
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Download@article{10.11648/j.sjams.20130105.15,
author = {Oyeka ICA and Okeh UM},
title = {Moments of Continuous Bi-Variate Distributions: An Alternative Approach},
journal = {Science Journal of Applied Mathematics and Statistics},
volume = {1},
number = {5},
pages = {62-69},
doi = {10.11648/j.sjams.20130105.15},
url = {https://doi.org/10.11648/j.sjams.20130105.15},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20130105.15},
abstract = {We propose a method of obtaining the moment of some continuous bi-variate distributions with parameters α1 β1 andα2 β2 in finding the nth moment of the variable x^c y^d (c≥0, d≥0) where X and Y are continuous random variables having the joint pdf, f(x,y).Here we find the so called gn(c, d)defined gn(c, d)= E(X^cY^d+λ)^n, the nth moment of expected value of the t distribution of the cth power of X and dth power of Y about the constant λ.These moments are obtained by the use of bi-variate moment generating functions, when they exist. The proposed gn(c, d) is illustrated with some continuous bi-variate distributions and is shown to be easy to use even when the powers of the random variables being considered are non-negative real numbers that need not be integers. The results obtained using gn(c, d) are the same as results obtained using other methods such as moment generating functions when they exist.},
year = {2013}
}
TY - JOUR T1 - Moments of Continuous Bi-Variate Distributions: An Alternative Approach AU - Oyeka ICA AU - Okeh UM Y1 - 2013/11/20 PY - 2013 N1 - https://doi.org/10.11648/j.sjams.20130105.15 DO - 10.11648/j.sjams.20130105.15 T2 - Science Journal of Applied Mathematics and Statistics JF - Science Journal of Applied Mathematics and Statistics JO - Science Journal of Applied Mathematics and Statistics SP - 62 EP - 69 PB - Science Publishing Group SN - 2376-9513 UR - https://doi.org/10.11648/j.sjams.20130105.15 AB - We propose a method of obtaining the moment of some continuous bi-variate distributions with parameters α1 β1 andα2 β2 in finding the nth moment of the variable x^c y^d (c≥0, d≥0) where X and Y are continuous random variables having the joint pdf, f(x,y).Here we find the so called gn(c, d)defined gn(c, d)= E(X^cY^d+λ)^n, the nth moment of expected value of the t distribution of the cth power of X and dth power of Y about the constant λ.These moments are obtained by the use of bi-variate moment generating functions, when they exist. The proposed gn(c, d) is illustrated with some continuous bi-variate distributions and is shown to be easy to use even when the powers of the random variables being considered are non-negative real numbers that need not be integers. The results obtained using gn(c, d) are the same as results obtained using other methods such as moment generating functions when they exist. VL - 1 IS - 5 ER -
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