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UBC Theses and Dissertations
A transformation to stabilize the variance of binomial distributions Green, Virginia Beryl (Berry)
Abstract
A transformation is sought for a binomially distributed random variable f, such that the transformed variate Y(f) exhibits a homogeneous variance, E{(Y(f )-E{Y(f)})² } = 1, and an unbiased mean, E{Y(f)} = Y(p), for the family of binomial distributions of given sample size generated by p . Y(f) is expanded in a Taylor series about p, conditions are set corresponding to the above requirements, and the resulting non-linear differential equations in Y(p) are solved numerically. The success of the transformation is comparable to published transformations.
Item Metadata
| Title |
A transformation to stabilize the variance of binomial distributions
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| Creator | |
| Publisher |
University of British Columbia
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| Date Issued |
1967
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| Description |
A transformation is sought for a binomially distributed random variable f, such that the transformed variate Y(f) exhibits a homogeneous variance, E{(Y(f )-E{Y(f)})² } = 1, and an unbiased mean, E{Y(f)} = Y(p), for the family of binomial distributions
of given sample size generated by p .
Y(f) is expanded in a Taylor series about p, conditions are set corresponding to the above requirements, and the resulting non-linear differential equations in Y(p) are solved numerically.
The success of the transformation is comparable to published transformations.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2011-08-16
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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| DOI |
10.14288/1.0080578
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Campus | |
| Scholarly Level |
Graduate
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| Aggregated Source Repository |
DSpace
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.