Summary
There are some probability distributions which remain invariant in their form under suitable transformations. In this paper, we show that the logarithmic series distribution and the geometric distribution enjoy the property of invariance of form as a characterizing property under a special type of transformation which we introduce below as a modulo sequence. Further, we provide a necessary and sufficient condition for the generalized power series distribution to have this characteristic property.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Patil, G. P. (1962). Ann. Inst. Statist. Math. Tokyo. 14, 179–182.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1975 D. Reidel Publishing Company, Dordrecht-Holland
About this paper
Cite this paper
Patil, G.P., Seshadri, V. (1975). A Characteristic Property of Certain Generalized Power Series Distributions. In: Patil, G.P., Kotz, S., Ord, J.K. (eds) A Modern Course on Statistical Distributions in Scientific Work. NATO Advanced Study Institutes Series, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1842-5_7
Download citation
DOI: https://doi.org/10.1007/978-94-010-1842-5_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-1844-9
Online ISBN: 978-94-010-1842-5
eBook Packages: Springer Book Archive