A note on derivation of the generating function for the right truncated Rayleigh distribution

Arni S.R.Srinivasa Rao

doi:10.1016/j.aml.2005.04.018

A note on derivation of the generating function for the right truncated Rayleigh distribution

Arni S.R.Srinivasa Rao

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

An expression is obtained for the probability that a Weibull random variable falls after the truncation and within a finite interval. However small, the truncation in the Weibull distribution (when the value of the shape parameter is two, it is called the Rayleigh distribution) has an impact. An attempt is made to obtain generating functions for two fixed shape parameters.

Original language	English (US)
Pages (from-to)	789-794
Number of pages	6
Journal	Applied Mathematics Letters
Volume	19
Issue number	8
DOIs	https://doi.org/10.1016/j.aml.2005.04.018
State	Published - Aug 2006
Externally published	Yes

Keywords

Incomplete gamma
Kummer's function
Weibull distribution

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aml.2005.04.018

Cite this

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title = "A note on derivation of the generating function for the right truncated Rayleigh distribution",

abstract = "An expression is obtained for the probability that a Weibull random variable falls after the truncation and within a finite interval. However small, the truncation in the Weibull distribution (when the value of the shape parameter is two, it is called the Rayleigh distribution) has an impact. An attempt is made to obtain generating functions for two fixed shape parameters.",

keywords = "Incomplete gamma, Kummer's function, Weibull distribution",

author = "Rao, \{Arni S.R.Srinivasa\}",

note = "Funding Information: Thanks go to Professor Masayuki Kakehashi for introducing me to the truncated Weibull distribution during our collaborations in Japan, which motivated me to study its properties further. A substantial part of this work was carried out when I was at the Mathematical Institute, Oxford. Thanks go to Professor Philip Maini for his encouragement and enthusiasm during this work. I am grateful to Sir David Cox for valuable discussions and questions about the application aspect of the content, which helped me to revise the manuscript. I wish to thank both the referees for their highly constructive comments (one of their suggestions resulted in the present title), which helped a lot in the revision. I was supported by DST, New Delhi, and had partial support from LMS, London. ",

year = "2006",

month = aug,

doi = "10.1016/j.aml.2005.04.018",

language = "English (US)",

volume = "19",

pages = "789--794",

journal = "Applied Mathematics Letters",

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AU - Rao, Arni S.R.Srinivasa

N1 - Funding Information: Thanks go to Professor Masayuki Kakehashi for introducing me to the truncated Weibull distribution during our collaborations in Japan, which motivated me to study its properties further. A substantial part of this work was carried out when I was at the Mathematical Institute, Oxford. Thanks go to Professor Philip Maini for his encouragement and enthusiasm during this work. I am grateful to Sir David Cox for valuable discussions and questions about the application aspect of the content, which helped me to revise the manuscript. I wish to thank both the referees for their highly constructive comments (one of their suggestions resulted in the present title), which helped a lot in the revision. I was supported by DST, New Delhi, and had partial support from LMS, London.

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N2 - An expression is obtained for the probability that a Weibull random variable falls after the truncation and within a finite interval. However small, the truncation in the Weibull distribution (when the value of the shape parameter is two, it is called the Rayleigh distribution) has an impact. An attempt is made to obtain generating functions for two fixed shape parameters.

AB - An expression is obtained for the probability that a Weibull random variable falls after the truncation and within a finite interval. However small, the truncation in the Weibull distribution (when the value of the shape parameter is two, it is called the Rayleigh distribution) has an impact. An attempt is made to obtain generating functions for two fixed shape parameters.

KW - Incomplete gamma

KW - Kummer's function

KW - Weibull distribution

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DO - 10.1016/j.aml.2005.04.018

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VL - 19

SP - 789

EP - 794

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 8

ER -

A note on derivation of the generating function for the right truncated Rayleigh distribution

Abstract

Keywords

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