The Reflected Weibull Distribution

For combinations of parameter values ordinarily encountered in life testing and reliability data, the similarity of the Weibull with the Pearson Type III (gamma) distri-bution is well known. When the Weibull distribution is reflected about the vertical axis x = γ, we obtain a version with cumulative...

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Bibliographic Details
Published in:Technometrics 1973-11, Vol.15 (4), p.867-873
Main Author: Cohen, A. Clifford
Format: Article
Language:English
Subjects:
Asymptotic value
Decimals
Distribution functions
Estimators
Log Normal
Mathematical independent variables
Mathematical moments
Military logistics
Parallel lines
Pearson Curves
Pearson's Betas
Skewed distribution
Skewness
Weibull Distributions
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Summary:For combinations of parameter values ordinarily encountered in life testing and reliability data, the similarity of the Weibull with the Pearson Type III (gamma) distri-bution is well known. When the Weibull distribution is reflected about the vertical axis x = γ, we obtain a version with cumulative probability function When δ > δ 0 , where to 13 decimals δ 0 = 3.6023494257197, we have a distribution with positive skewness (i.e., α 3 > 0), which for certain combinations of parameter values, closely resembles the Pearson Type VI distribution. It is to be noted that when δ = δ 0 , then α 0 = 0. The fil, β 1 , β 2 curves (Pearson's Betas) for the case in which δ > δ 0 and for the case in which 0 < δ < δ 0 , are presented. An illustrative example is included to demonstrate use of the reflected Weibull in fitting sample data and to provide comparisons with results obtained from fitting the Type VI, Type III, Type V, and lognormal distributions.
ISSN:0040-1706
1537-2723
DOI:10.1080/00401706.1973.10489119