Systems of Frequency Curves Generated by Methods of Translation

Johnson, Norman L.

doi:10.2307/2332539

Cited by 822 publications

(685 citation statements)

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“…For simplicity, we restrict all of the models to a maximum order of one. In addition, for each GARCH-type model, the innovation process Z t is allowed to follow one of eight distributions; these are the normal distribution, skew normal distribution (Azzalini (1985)), Student's t distribution (Gosset (1908)), skew Student's distribution (Fernandez and Steel (1998)), skew generalized error distribution (Theodossiou (1998)), generalized hyperbolic distribution Barndorff-Nielsen (1977; normal inverse Gaussian distribution Barndorff-Nielsen (1977) and Johnson's SU distribution (Johnson (1949)). The standard GARCH model (Bollerslev (1986)), denoted by SGARCH (1, 1), has:…”

Section: Garch Modelsmentioning

confidence: 99%

GARCH Modelling of Cryptocurrencies

Chu

Chan

Nadarajah

et al. 2017

JRFM

278

165

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With the exception of Bitcoin, there appears to be little or no literature on GARCH modelling of cryptocurrencies. This paper provides the first GARCH modelling of the seven most popular cryptocurrencies. Twelve GARCH models are fitted to each cryptocurrency, and their fits are assessed in terms of five criteria. Conclusions are drawn on the best fitting models, forecasts and acceptability of value at risk estimates.

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Section: Garch Modelsmentioning

confidence: 99%

GARCH Modelling of Cryptocurrencies

Chu

Chan

Nadarajah

et al. 2017

JRFM

278

165

View full text Add to dashboard Cite

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“…In the second study actual human exposure data from the literature were fit to the S B distribution. In addition to the methods listed above, a CML method was also explored in this second study by setting the minimum exposure to 0 a priori and using the percentile approach originally suggested by Johnson (1949) to estimate the maximum. This approach has been used previously (Flynn, 2004c) for exposure data when the a priori minimum is set to 0.…”

Section: Methodsmentioning

confidence: 99%

“…The distribution has also been applied to occupational exposures, and confidence intervals for the mean were estimated with a parametric bootstrap technique (Flynn, 2004c). This distribution was described in a classic paper (Johnson, 1949) that considered a variety of transformations on random variables that ultimately led to normal distributions. A more recent summary can be found in (Johnson et al, 1994).…”

Section: Introductionmentioning

confidence: 99%

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Fitting human exposure data with the Johnson SB distribution

Flynn

2005

J Expo Sci Environ Epidemiol

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Exposure evaluations for epidemiological investigations and risk assessments may require estimates of background concentrations and peak exposures, as well as the population mean and variance. The S B distribution is a theoretically appealing probability function for characterizing ratios, and random variables bound by extremes, such as human exposures and environmental concentrations. However, fitting the parameters of this distribution with maximum likelihood methods is often problematic, and some alternative methods are examined here. Two methods based on percentiles, a quantile estimator, and a method-of-moments fitting procedure are explored. The quantile and method-of-moments procedures are based on new explicit expressions for the first four moments of this distribution. The fitting procedures are compared by simulation, and with actual data sets consisting of measurements of human exposure to airborne contaminants.

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“…He applied the Mage (1980a) percentile solution procedure for estimating S B distribution parameters (Johnson, 1949) and compared it with four other methods for fitting the S B model. However, he concluded that Mage's percentile procedure did not always return values for the four S B parameters, and that ''the quantile and method-of-moments fitting procedures may provide performance superior to that of the percentile method.''…”

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confidence: 99%

The correct application of Mage's Johnson SB procedure for fitting exposure data

Mage

2007

J Expo Sci Environ Epidemiol

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Flynn (2006) made an excellent review of different methods of applying the Johnson S B distribution, also known as the four-parameter lognormal distribution, to exposure data. He applied the Mage (1980a) percentile solution procedure for estimating S B distribution parameters (Johnson, 1949) and compared it with four other methods for fitting the S B model. However, he concluded that Mage's percentile procedure did not always return values for the four S B parameters, and that ''the quantile and method-of-moments fitting procedures may provide performance superior to that of the percentile method.'' For y ¼ (x-X min )/(X max -x), where x is an exposure variable bounded between a minimum value (X min ) and a maximum value (X max ), the S B probability density function p(x) is written as Eq. (1), where m and s are the mean and SD of log(y), respectively: pðxÞ ¼ ffi p ð2p s 2 Þ À1 ½ðX max À xÞ À1 þ ðx À X min Þ À1 expð À 0:5½ðlogðyÞ À mÞ=s 2 Þ;

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Systems of Frequency Curves Generated by Methods of Translation

Cited by 822 publications

References 0 publications

GARCH Modelling of Cryptocurrencies

GARCH Modelling of Cryptocurrencies

Fitting human exposure data with the Johnson SB distribution

The correct application of Mage's Johnson SB procedure for fitting exposure data

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