Abstract
We derive some characterizations of probability distributions based on the joint distributions of linear forms of Q-conditional independent random variables.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bairamov, I. (2011). Copula representations and order statistics for conditionally independent random variables. arXiv:11107.3200v1 [math.ST] 16.
Chow, Y.S. and Teicher, H. (1978) Probability Theory: Independence, Interchangeability, Martingales, Springer, New York.
Dawid, A.P. (1979). Conditional independence in statistical theory. J. Roy. Statist. Soc. Ser. B 41, 1–31.
Dawid, A.P. (1980). Conditional independence for statistical operations. Ann. Statist. 8, 598–617.
Kagan, A.M., Linnik, Yu.V. and Rao, C.R. (1973). Characterization Problems in Mathematical Statistics. Wiley, New York.
Kagan, A.M. and Székely, G.J. (2016). An analytic generalization of independence and identical distributiveness. Statistics and Probability Letters. doi:10.1016/j.spl.2015.10.005.
Kotlarski, I.I. (1967). On characterizing the gamma and the normal distribution. Pacific. J. Math. 20, 69–76.
Majerak, D., Nowak, W. and Zieba, W. (2005). Conditional strong law of large numbers, Internat. J. Pure and Appl. Math. 20, 143–157.
Prakasa Rao, B.L.S. (1992). Identifiability in Stochastic Models: Characterization of Probability Distributions. Academic Press, San Diego.
Prakasa Rao, B.L.S. (2009). Conditional independence, conditional mixing and conditional association. Ann. Inst. Statist. Math. 61, 441–460.
Prakasa Rao, B.L.S. (2013). Characterization of distributions based on functions of conditionally independent random variables. J. Indian Statist. Assoc. 51, 183–200.
Prakasa Rao, B.L.S (2016). Characterization of probability distributions through Q-independence, Research Report, CR Rao Advanced Institute of Mathematics, Statistics and Computer Science, Hyderabad, India.
Rao, C.R. (1966). Characterization of the distribution of random variables in linear structural relations. Sankhya 28, 251–260.
Rao, C.R. (1967). On some characterization of the normal law. Sankhya 29, 1–14.
Rao, C.R. (1971). Characterization of probability laws by linear functions. Sankhya Series A 33, 265–270.
Roussas, G.G. (2008). On conditional independence, mixing and association. Stoch. Anal. Appl. 26, 1274–1309.
Sasvári, Z. (1986). Characterizing the distribution of the random variables X 1,X 2,X 3 by the distribution of (X 1−X 3, X 2−X 3). Prob. Theory. and Relat. Fields 73, 43–49.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Prakasa Rao, B.L.S. Characterizations of Probability Distributions Through Linear Forms of Q-Conditional Independent Random Variables. Sankhya A 78, 221–230 (2016). https://doi.org/10.1007/s13171-016-0086-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13171-016-0086-y
Keywords and phrases.
- Q-conditional independence
- Q-conditional identically distributiveness
- Linear forms
- Characterization of probability distributions