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Package ‘JohnsonDistribution’ February 19, 2015 Version 0.24 Date 2012-04-16 Title Johnson Distribution Author A.I. McLeod and Leanna King Maintainer A.I. McLeod <[email protected]> Depends R (>= 2.1.0) Description Johnson curve distributions. Implementation of AS100 and AS99. LazyLoad yes License GPL (>= 2) URL http://www.stats.uwo.ca/faculty/aim Repository CRAN Date/Publication 2012-04-17 10:28:39 NeedsCompilation yes R topics documented: JohnsonDistribution-package FitJohnsonDistribution . . . yJohnsonDistribution . . . . zJohnsonDistribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3 4 6 8 1 2 JohnsonDistribution-package JohnsonDistribution-package Johnson Curve Distribution Description Fit and simulate from the family of Johnson Curve Distributions Details FitJohnsonDistribution 3 Package: Type: Version: Date: License: LazyLoad: JohnsonDistribution Package 0.24 2012-04-16 GPL (>= 2) yes Author(s) A. I. McLeod and Leanna King Maintainer: [email protected] References D. Hill, R. Hill, and R. L. Holder, Algorithm AS 99. Fitting Johnson curves by moments, Appl. Statist.,25, No. 2, 180-189 (1976). I. D. Hill, Algorithm AS 100. Normal-Johnson and Johnson-normal transformations, Appl. Statist.,25, No. 2, 190-192 (1976). See Also cor Examples FitJohnsonDistribution(1, 1, 2, -1) FitJohnsonDistribution Fit Johnson Curve by Moments Description This implements the Fortran algorithm AS 99 by Hill et al. Usage FitJohnsonDistribution(XBAR, SD, RB1, BB2) Arguments XBAR SD RB1 BB2 mean standard deviation coefficient of skewness coefficient of kurtosis or a negative value to indicate the lognormal family 4 yJohnsonDistribution Value Vector of length 6 with named elements: "ITYPE", "GAMMA", "DELTA", "XLAM", "XI", "IFAULT". ITYPE is 1, SL; 2 for SU, 3 for SB, 4 for Normal. GAMMA, DELTA, XLAM, XI are the parameters for the Johnson distribution, where for the SL family, XI=-1. IFAULT is an error indicator, 0 means no error, 1 if the input standard deviation is negative, 2 if the kurotis, BB2, is less than skewness coefficient plus 1 and 3 if SB-fitting failed to converge and an SL or ST was fit instead. Author(s) A. I. McLeod References D. Hill, R. Hill, and R. L. Holder, Algorithm AS 99. Fitting Johnson curves by moments, Appl. Statist.,25, No. 2, 180-189 (1976). I. D. Hill, Algorithm AS 100. Normal-Johnson and Johnson-normal transformations, Appl. Statist.,25, No. 2, 190-192 (1976). See Also yJohnsonDistribution, zJohnsonDistribution Examples #fit SL with mean 1, variance 1 and skewness 2. FitJohnsonDistribution(1, 1, 2, -1) yJohnsonDistribution Standard normal (Z) to Johnson variable (Y) transformation Description A normal variable with mean zero and variance one is transformed to a Johnson distribution variate specified by the Johnson distribution parameters. This is useful in simulating random variables from a specified Johnson distribution and in computing the quantiles for a Johnson distribution. Usage yJohnsonDistribution(z, ITYPE, GAMMA, DELTA, XLAM, XI) Arguments z ITYPE GAMMA DELTA XLAM XI vector of standard normal variables is 1, SL; 2 for SU, 3 for SB and 4 for Normal parameter in Johnson distribution parameter in Johnson distribution parameter in Johnson distribution parameter in Johnson distribution yJohnsonDistribution 5 Details Our function provides an interface to the Fortran algorithm AS 100 (Hill, 1976). Value Corresponding vector of Johnson distribution variables. Note The input parameters ITYPE, GAMMA, DELTA, XLAM, XI must all be scalars. An error is given if they are not. Author(s) A. I. McLeod and Leanna King References I. D. Hill, Algorithm AS 100. Normal-Johnson and Johnson-normal transformations, Appl. Statist.,25, No. 2, 190-192 (1976). See Also zJohnsonDistribution, FitJohnsonDistribution Examples #Example 1. #fit SL with mean 1, variance 1, skewness 2 then find corresponding variate to Z=2 ans <- FitJohnsonDistribution(1, 1, 2, -1) GAMMA <- ans["GAMMA"] DELTA <- ans["DELTA"] XLAM <- ans["XLAM"] XI <- ans["XI"] ITYPE <- 1 z <- 2 yJohnsonDistribution(z, ITYPE, GAMMA, DELTA, XLAM, XI) #Example 2: find quantiles of SL distribution #The 0.01, 0.05, 0.1, 0.25, 0.5, 0.75, 0.9, 0.95, 0.99 #quantiles for an SL distribution are found and a qq plot is produced. #SL distribution parameters is determined # with mean 1, standard deviation 1, skewness 3 ans <- FitJohnsonDistribution(1, 1, 3, -1) GAMMA <- ans["GAMMA"] DELTA <- ans["DELTA"] XLAM <- ans["XLAM"] XI <- ans["XI"] ITYPE <- 1 p<-c(0.01, 0.05, 0.1, 0.25, 0.5, 0.75, 0.9, 0.95, 0.99) z <- qnorm(p) y<-yJohnsonDistribution(z, ITYPE, GAMMA, DELTA, XLAM, XI) 6 zJohnsonDistribution plot(z,y,xlab="normal quantiles", ylab="SL quantiles") # #Example 3: simulate SL distribution #with mean 1, sd 1 and skewness 3 #plot estimated pdf ans <- FitJohnsonDistribution(1, 1, 3, -1) GAMMA <- ans["GAMMA"] DELTA <- ans["DELTA"] XLAM <- ans["XLAM"] XI <- ans["XI"] ITYPE <- 1 z <- rnorm(1000) y <- yJohnsonDistribution(z, ITYPE, GAMMA, DELTA, XLAM, XI) pdf <- density(y, bw = "sj") plot(pdf, main="Estimated pdf of SL with mean 1, sd 1, g1 3", xlab="x", ylab="est.pdf(x)" ) zJohnsonDistribution Johnson variable (Y) to standard normal (Z) transformation Description A Johnson distribution variable with specified parameters is transformed to a unit normal variable and can be used to compute percentiles. Usage zJohnsonDistribution(s, ITYPE, GAMMA, DELTA, XLAM, XI) Arguments s value of Johnson distribution variable. May be vector ITYPE is 1, SL; 2 for SU, 3 for SB and 4 for Normal GAMMA parameter in Johnson distribution DELTA parameter in Johnson distribution XLAM parameter in Johnson distribution XI parameter in Johnson distribution Details Our function provides an interface to the Fortran algorithm AS 100 (Hill, 1976). Value Corresponding vector of standard normal variables. zJohnsonDistribution 7 Note The input parameters ITYPE, GAMMA, DELTA, XLAM, XI must all be scalars. An error is given if they are not. Author(s) A. I. McLeod and Leanna King References I. D. Hill, Algorithm AS 100. Normal-Johnson and Johnson-normal transformations, Appl. Statist.,25, No. 2, 190-192 (1976). See Also yJohnsonDistribution, FitJohnsonDistribution Examples # #Example: find the percentage points for an SL distribution # with mean 1, standard deviation 1, skewness 3 # corresponding to observed values 1, 2, 3, 4, 5 ans <- FitJohnsonDistribution(1, 1, 3, -1) GAMMA <- ans["GAMMA"] DELTA <- ans["DELTA"] XLAM <- ans["XLAM"] XI <- ans["XI"] ITYPE <- 1 y <- 1:5 Z <- zJohnsonDistribution(y, ITYPE, GAMMA, DELTA, XLAM, XI) pnorm(Z) Index ∗Topic distribution FitJohnsonDistribution, 3 JohnsonDistribution-package, 2 yJohnsonDistribution, 4 zJohnsonDistribution, 6 ∗Topic package JohnsonDistribution-package, 2 cor, 3 FitJohnsonDistribution, 3, 5, 7 JohnsonDistribution-package, 2 yJohnsonDistribution, 4, 4, 7 zJohnsonDistribution, 4, 5, 6 8