Inverse Box–Cox: The power-normal distribution

Freeman, Jade; Modarres, Reza

doi:10.1016/j.spl.2005.10.036

Cited by 71 publications

(27 citation statements)

References 16 publications

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“…Since χ χ χ ∼ PN(λ,μ, σ 2 ), for the power-normal random fuzzy variable χ χ χ, the probability distribution function by Freeman and Modarres (2001) …”

Section: Power-normal Fuzzy Distributionmentioning

confidence: 99%

Correlation Test by Reduced-Spread of Fuzzy Variance

Kang

2012

Communications for Statistical Applications and Methods

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We propose some properties for a fuzzy correlation test by reduced-spread fuzzy variance for sample fuzzy data. First, we define the condition of fuzzy data for repeatedly observed data or that which includes error term data. By using the average of spreads for fuzzy numbers, we reduce the spread of fuzzy variance and define the agreement index for the degree of acceptance and rejection. Given a non-normal random fuzzy sample, we have bivariate normal distribution by apply Box-Cox power fuzzy transformation and test the fuzzy correlation for independence between the variables provided by the agreement index.

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“…Since χ χ χ ∼ PN(λ,μ, σ 2 ), for the power-normal random fuzzy variable χ χ χ, the probability distribution function by Freeman and Modarres (2001) …”

Section: Power-normal Fuzzy Distributionmentioning

confidence: 99%

Correlation Test by Reduced-Spread of Fuzzy Variance

Kang

2012

Communications for Statistical Applications and Methods

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“…Transformation [2] is always possible, but Z can only be N(0,1) when λ=1 and in the log() case. However, Z is a truncated normal (Freeman and Modarres 2006).…”

Section: The Powernormal Distributionmentioning

confidence: 99%

“…Goto and Inoue (1980) provide some formulas for the skewness and kurtosis of the PN. Freeman and Modarres (2006) provide explicit formulas for some special cases, but these formulas are rather complicated. Herein, simulated skewness and kurtosis values are used as evidence of the capabilities of PN.…”

Section: /16mentioning

confidence: 99%

“…The Box-Cox procedure assumes that the data distribution can be transformed to the normal distribution (Hernandez and Johnson 1980). Thus the inverse Box-Cox transformation can give rise to a family of distributions (PN), shown by Goto and Inoue (1980) and Freeman and Modarres (2006). With respect to forestry applications, Garcia (1983) has described the application of Box-Cox transformation to forestry growth curves.…”

Section: Introductionmentioning

confidence: 99%

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The power-normal distribution: application to forest stands

Mønness¹

2011

Can. J. For. Res.

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The Power-Normal distribution (PN) originates from the inverse Box-Cox transformation and is used in this study to fit the frequency distributions of tree diameter and height. PN is flexible in describing different shapes of observed distributions as indicated by the certain areas in the skewness x kurtosis shape plane. The estimation of the parameters using maximum likelihood is straightforward and the resulting numerical properties are desirable. The shapes achieved by PN are very diverse, even though only three parameters are used. In forestry, Johnson's System Bounded distribution (S B ) has been widely used to fit tree diameter distributions, but it is often susceptible to numerical problems when fitted by maximum likelihood estimation. Our results indicate that the performance of PN is superior to Johnson's S B , as shown by the Kolmogorov-Smirnov statistic and visual inspection, particularly for fitting the tree height distributions.

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“…However, the moments of the Box-Cox normal distribution are not so straightforward to estimate, except for some specific transformations, such as ν = 2 or ν = .5. Freeman and Modarres (2006) studied the properties of the inverse Box-Cox transformation.…”

Section: Moments Of the Response-time Distributionsmentioning

confidence: 99%

Statistical models for responses and response times

Entink¹

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Inverse Box–Cox: The power-normal distribution

Cited by 71 publications

References 16 publications

Correlation Test by Reduced-Spread of Fuzzy Variance

Correlation Test by Reduced-Spread of Fuzzy Variance

The power-normal distribution: application to forest stands

Statistical models for responses and response times

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