Abstract
A solution of Dugue’s problem of finding characteristic functions φ1, φ2 such that \( \frac{{{\varphi _1}\left( t \right) + {\varphi _2}\left( t \right)}}{2} = {\varphi _1}\left( t \right){\varphi _2}\left( t \right) \) is presented. Some results in this direction are given.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Dugué D. (1957): Arithmétique des lois de probabilités. Mémorial des Sciencis Math., v. 137.
Kubik L. (1969): Sur un probleme de M.D. Dugué. Comment. Math., v. XIII, 1 – 2.
Puri P., Rubin H. (1970): A Characterization based on the Absolute Difference of two i.i.d. Random Variables. Ann. Math. Statist., v. 41, No 6, 2113 – 2122.
Rossberg H.-J. (1972): Characterization of the Exponential and Pareto Distributions by Means of some Properties of the Distributions which the Differences and Quotients of Order Statistics are subject to. Math. Operationsforsch. Statist. Ser. Statist. 3, No 3, 207 – 216.
Vallander S., Ibragimov I., Lindtrop N. (1969): On Limiting Distributions for Moduli of Sequential Differences of Independent Variables. Teorja Verojatn. i ee Primen., v. XIV, No 4, 693 – 707.
Wolińska A. (1982): On a Problem of Dugué. Lect. Notes Math., v. 982, 244 – 253.
Wolińska-Welcz A. (1985): On a Solution of the Dugué Problem. Bull. Acad. Polon. Sci. Ser. Sci. Math., v. 33, No 7 – 8, 421 – 423.
Wolińska-Welcz A. (1986): On a Solution of the Dugué Problem. Probab. Math. Statistics, v. 7, 169 – 185.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1988 Academia, Publishing House of the Czechoslovak Academy of Sciences, Prague
About this chapter
Cite this chapter
Wolińska-Welcz, A. (1988). Note on a Solution of the Degué’s Problem. In: Transactions of the Tenth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes. Transactions of the Tenth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, vol 10A-B. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9913-4_54
Download citation
DOI: https://doi.org/10.1007/978-94-010-9913-4_54
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-9915-8
Online ISBN: 978-94-010-9913-4
eBook Packages: Springer Book Archive