R : Copyright 2005, The R Foundation for Statistical Computing
Version 2.1.1  (2005-06-20), ISBN 3-900051-07-0

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> ### * <HEADER>
> ###
> attach(NULL, name = "CheckExEnv")
> assign(".CheckExEnv", as.environment(2), pos = length(search())) # base
> ## add some hooks to label plot pages for base and grid graphics
> setHook("plot.new", ".newplot.hook")
> setHook("persp", ".newplot.hook")
> setHook("grid.newpage", ".gridplot.hook")
> 
> assign("cleanEx",
+        function(env = .GlobalEnv) {
+ 	   rm(list = ls(envir = env, all.names = TRUE), envir = env)
+            RNGkind("default", "default")
+ 	   set.seed(1)
+    	   options(warn = 1)
+ 	   delayedAssign("T", stop("T used instead of TRUE"),
+ 		  assign.env = .CheckExEnv)
+ 	   delayedAssign("F", stop("F used instead of FALSE"),
+ 		  assign.env = .CheckExEnv)
+ 	   sch <- search()
+ 	   newitems <- sch[! sch %in% .oldSearch]
+ 	   for(item in rev(newitems))
+                eval(substitute(detach(item), list(item=item)))
+ 	   missitems <- .oldSearch[! .oldSearch %in% sch]
+ 	   if(length(missitems))
+ 	       warning("items ", paste(missitems, collapse=", "),
+ 		       " have been removed from the search path")
+        },
+        env = .CheckExEnv)
> assign("..nameEx", "__{must remake R-ex/*.R}__", env = .CheckExEnv) # for now
> assign("ptime", proc.time(), env = .CheckExEnv)
> grDevices::postscript("sn-Examples.ps")
> assign("par.postscript", graphics::par(no.readonly = TRUE), env = .CheckExEnv)
> options(contrasts = c(unordered = "contr.treatment", ordered = "contr.poly"))
> options(warn = 1)    
> library('sn')
Loading required package: mvtnorm
> 
> assign(".oldSearch", search(), env = .CheckExEnv)
> assign(".oldNS", loadedNamespaces(), env = .CheckExEnv)
> cleanEx(); ..nameEx <- "T.Owen"
> 
> ### * T.Owen
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: T.Owen
> ### Title: Owen's function
> ### Aliases: T.Owen
> ### Keywords: math
> 
> ### ** Examples
> 
> owen <- T.Owen(1:10, 2)
> 
> 
> 
> cleanEx(); ..nameEx <- "ais"
> 
> ### * ais
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ais
> ### Title: Australian Institute of Sport data
> ### Aliases: ais
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(ais, package="sn")
> attach(ais)
> pairs(ais[,c(3:4,10:13)], main = "AIS data")
> plot(Wt~sport)
> 
> 
> 
> cleanEx(); ..nameEx <- "cp.to.dp"
> 
> ### * cp.to.dp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: cp.to.dp
> ### Title: Conversion between equivalent parametrizations
> ### Aliases: cp.to.dp dp.to.cp
> ### Keywords: distribution
> 
> ### ** Examples
> 
> cp <- dp.to.cp(c(30,30,2,4))
> dp <- cp.to.dp(cp)
> 
> 
> 
> cleanEx(); ..nameEx <- "dmsn"
> 
> ### * dmsn
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: dmsn
> ### Title: Multivariate skew-normal distribution
> ### Aliases: dmsn pmsn rmsn
> ### Keywords: distribution multivariate
> 
> ### ** Examples
> 
> x <- seq(-3,3,length=15)
> xi <- c(0.5, -1)
> Omega <- diag(2)
> Omega[2,1] <- Omega[1,2] <- 0.5
> alpha <- c(2,2)
> pdf <- dmsn(cbind(x,2*x-1), xi, Omega, alpha)
> rnd <- rmsn(10,  xi, Omega, alpha)
> library(mvtnorm)                        # only once in the session
> cdf <- pmsn(c(2,1), xi, Omega, alpha)
> 
> 
> 
> cleanEx(); ..nameEx <- "dmst"
> 
> ### * dmst
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: dmst
> ### Title: Multivariate skew-t distribution
> ### Aliases: dmst pmst rmst
> ### Keywords: distribution multivariate
> 
> ### ** Examples
> 
> x <- seq(-4,4,length=15)
> xi <- c(0.5, -1)
> Omega <- diag(2)
> Omega[2,1] <- Omega[1,2] <- 0.5
> alpha <- c(2,2)
> pdf <- dmst(cbind(x,2*x-1), xi, Omega, alpha, df=5)
> rnd <- rmst(10,  xi, Omega, alpha, 6)
> library(mvtnorm)                # only once in the session
> cdf <- pmst(c(2,1), xi, Omega, alpha, df=5)
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "dsn"
> 
> ### * dsn
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: dsn
> ### Title: Skew-Normal Distribution
> ### Aliases: dsn psn qsn rsn
> ### Keywords: distribution
> 
> ### ** Examples
> 
> pdf <- dsn(seq(-3,3,by=0.1), shape=3)
> cdf <- psn(seq(-3,3,by=0.1), shape=3)
> qu <- qsn(seq(0.1,0.9,by=0.1), shape=-2)
> rn <- rsn(100, 5, 2, 5)
> 
> 
> 
> cleanEx(); ..nameEx <- "dsn2.plot"
> 
> ### * dsn2.plot
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: dsn2.plot
> ### Title: Plot of Bivariate Skew-normal Density Function
> ### Aliases: dsn2.plot
> ### Keywords: distribution
> 
> ### ** Examples
> 
> x <- y <- seq(-5, 5, length=35)
> dsn2.plot(x, y, c(-1,2), diag(c(1,2.5)), c(2,-3))
> 
> 
> 
> cleanEx(); ..nameEx <- "dst"
> 
> ### * dst
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: dst
> ### Title: Skew-t Distribution
> ### Aliases: dst pst qst rst
> ### Keywords: distribution
> 
> ### ** Examples
> 
> pdf <- dst(seq(-4,4,by=0.1), shape=3, df=5)
> rnd <- rst(100, 5, 2, -5, 8)
> q <- qst(c(0.25,0.5,0.75), shape=3, df=5)
> pst(q, shape=3, df=5)  # must give back c(0.25,0.5,0.75)
[1] 0.25 0.50 0.75
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "dst2.plot"
> 
> ### * dst2.plot
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: dst2.plot
> ### Title: Plot of Bivariate Skew-t Density Function
> ### Aliases: dst2.plot
> ### Keywords: distribution
> 
> ### ** Examples
> 
> x <- y <- seq(-5, 5, length=35)
> dst2.plot(x, y, c(-1,2), diag(c(1,2.5)), c(2,-3), df=5)
> 
> 
> 
> cleanEx(); ..nameEx <- "frontier"
> 
> ### * frontier
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: frontier
> ### Title: Simulated sample from a skew-normal distribution
> ### Aliases: frontier
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(frontier, package="sn")
> a <- sn.2logL.profile(y=frontier)
Running until 15 : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
> a <- sn.2logL.profile(y=frontier, param.range=c(0.8,1.6,10,30),
+         use.cp=FALSE, npts=11)
Running until 11 : 1 2 3 4 5 6 7 8 9 10 11
> 
> 
> 
> cleanEx(); ..nameEx <- "gamma1.to.lambda"
> 
> ### * gamma1.to.lambda
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: gamma1.to.lambda
> ### Title: Converts skewness to shape parameter of skew-normal distribution
> ### Aliases: gamma1.to.lambda
> ### Keywords: distribution
> 
> ### ** Examples
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "msn.affine"
> 
> ### * msn.affine
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: msn.affine
> ### Title: Affine transformation a multivariate skew-normal or skew-t
> ###   variable
> ### Aliases: msn.affine mst.affine
> ### Keywords: multivariate distribution
> 
> ### ** Examples
> 
> dp<- list(xi=c(1,1,2), Omega=toeplitz(1/1:3), alpha=c(3,-1,2))
> A <- matrix(c(1,-1,1,3,0,-2), 2, 3, byrow=TRUE) 
> dp1 <- msn.affine(dp, A, 1:2)
> #
> dp$df <- 5
> dp2<-  mst.affine(dp,A[1,,drop=FALSE])
> dp3<-  mst.affine(dp,A[1,,drop=FALSE], drop=FALSE)
> if(zapsmall(dp2$scale^2 - dp3$Omega)) print("something wrong here!")
> 
> 
> 
> cleanEx(); ..nameEx <- "msn.cond.plot"
> 
> ### * msn.cond.plot
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: msn.cond.plot
> ### Title: Plot of the density of a conditional skew-normal variate
> ### Aliases: msn.cond.plot
> ### Keywords: multivariate distribution
> 
> ### ** Examples
> 
> Omega <- diag(3)+0.5*outer(rep(1,3),rep(1,3))
> a<- msn.cond.plot(rep(0,3), Omega, 1:3, 3, -0.75)
> 
> 
> 
> cleanEx(); ..nameEx <- "msn.conditional"
> 
> ### * msn.conditional
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: msn.conditional
> ### Title: Cumulants and distribution of a skew-normal variate after
> ###   conditioning
> ### Aliases: msn.conditional
> ### Keywords: multivariate distribution
> 
> ### ** Examples
> 
> Omega <- diag(3)+0.5*outer(rep(1,3),rep(1,3))
> a<- msn.conditional(rep(0,3), Omega, 1:3, 3, -0.75)
> 
> 
> 
> cleanEx(); ..nameEx <- "msn.fit"
> 
> ### * msn.fit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: msn.fit
> ### Title: Fitting multivariate skew-normal distributions
> ### Aliases: msn.fit
> ### Keywords: distribution regression
> 
> ### ** Examples
> 
> data(ais, package="sn")
> attach(ais)
> # a simple-sample case
> b <- msn.fit(y=cbind(Ht,Wt))
Press <Enter> to continue...#
Press <Enter> to continue...# a regression case:
> a <- msn.fit(X=cbind(1,Ht,Wt), y=bmi, control=list(x.tol=1e-6))
Press <Enter> to continue...#
Press <Enter> to continue...# refine the previous outcome
> a1 <- msn.fit(X=cbind(1,Ht,Wt), y=bmi, control=list(x.tol=1e-9), start=a$dp)
Press <Enter> to continue...
Press <Enter> to continue...
> 
> cleanEx(); ..nameEx <- "msn.marginal"
> 
> ### * msn.marginal
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: msn.marginal
> ### Title: Marginal components of a multivariate skew-normal distribution
> ### Aliases: msn.marginal
> ### Keywords: multivariate distribution
> 
> ### ** Examples
> 
> xi <- c(10,0,-30)
> Omega <- 5*diag(3)+outer(1:3,1:3)
> alpha <- c(1,-3,5)
> marg31 <- msn.marginal(xi,Omega,alpha,c(3,1))
> 
> 
> 
> cleanEx(); ..nameEx <- "msn.mle"
> 
> ### * msn.mle
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: msn.mle
> ### Title: Maximum likelihood estimation for a multivariate skew-normal
> ###   distribution
> ### Aliases: msn.mle
> ### Keywords: distribution regression
> 
> ### ** Examples
> 
> data(ais, package="sn")
> attach(ais)
> # a simple-sample case
> b <- msn.mle(y=cbind(Ht,Wt))
> #
> # a regression case:
> a <- msn.mle(X=cbind(1,Ht,Wt), y=bmi, control=list(x.tol=1e-6))
> #
> # refine the previous outcome
> a1 <- msn.mle(X=cbind(1,Ht,Wt), y=bmi, control=list(x.tol=1e-9), start=a$dp)
> 
> 
> 
> cleanEx(); ..nameEx <- "msn.quantities"
> 
> ### * msn.quantities
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: msn.quantities
> ### Title: Quantities related to the multivariate skew-normal distribution.
> ### Aliases: msn.quantities
> ### Keywords: multivariate distribution
> 
> ### ** Examples
> 
> Omega <- 5*diag(3)+outer(1:3,1:3)
> msn.quantities(c(0,0,1), Omega, c(-2,2,3))
$xi
[1] 0 0 1

$Omega
     [,1] [,2] [,3]
[1,]    6    2    3
[2,]    2    9    6
[3,]    3    6   14

$alpha
[1] -2  2  3

$omega
[1] 2.449490 3.000000 3.741657

$mean
[1] -0.2163595  1.7113615  3.3822360

$variance
         [,1]     [,2]     [,3]
[1,] 5.953189 2.370269 3.515419
[2,] 2.370269 6.071242 1.923133
[3,] 3.515419 1.923133 8.324952

$Omega.conc
            [,1]        [,2]        [,3]
[1,]  0.18947368 -0.02105263 -0.03157895
[2,] -0.02105263  0.15789474 -0.06315789
[3,] -0.03157895 -0.06315789  0.10526316

$Omega.cor
          [,1]      [,2]      [,3]
[1,] 1.0000000 0.2721655 0.3273268
[2,] 0.2721655 1.0000000 0.5345225
[3,] 0.3273268 0.5345225 1.0000000

$Omega.pcor
          [,1]      [,2]      [,3]
[1,] 1.0000000 0.1217161 0.2236068
[2,] 0.1217161 1.0000000 0.4898979
[3,] 0.2236068 0.4898979 1.0000000

$lambda
[1] -0.1113878  1.0225845  1.3239490

$Psi
          [,1]        [,2]        [,3]
[1,] 1.0000000  0.50558175  0.69392104
[2,] 0.5055818  1.00000000 -0.08539405
[3,] 0.6939210 -0.08539405  1.00000000

$delta
[1] -0.1107032  0.7149579  0.7979592

$skewness
[1] -0.0002992724  0.1438044833  0.2415712104

> 
> 
> 
> cleanEx(); ..nameEx <- "mst.fit"
> 
> ### * mst.fit
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: mst.fit
> ### Title: Fitting multivariate skew-t distributions
> ### Aliases: mst.fit
> ### Keywords: distribution regression
> 
> ### ** Examples
> 
> data(ais, package="sn")
> attach(ais)
> # a simple-sample case
> b <- mst.fit(y=cbind(Ht,Wt))
Press <Enter> to continue...#
Press <Enter> to continue...# a regression case:
> a <- mst.fit(X=cbind(1,Ht,Wt), y=bmi, control=list(x.tol=1e-6))
Press <Enter> to continue...#
Press <Enter> to continue...# refine the previous outcome
> a1 <- mst.fit(X=cbind(1,Ht,Wt), y=bmi, control=list(x.tol=1e-9), start=a$dp)
Press <Enter> to continue...
Press <Enter> to continue...
> 
> cleanEx(); ..nameEx <- "mst.mle"
> 
> ### * mst.mle
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: mst.mle
> ### Title: Maximum likelihood estimation for a (multivariate) skew-t
> ###   distribution
> ### Aliases: mst.mle st.mle
> ### Keywords: distribution regression
> 
> ### ** Examples
> 
> data(ais, package="sn")
> attach(ais)
> X.mat <- model.matrix(~lbm+sex)
> b <- sn.mle(X.mat, bmi)
> # 
> b <- mst.mle(y=cbind(Ht,Wt))
> #
> # a multivariate regression case:
> a <- mst.mle(X=cbind(1,Ht,Wt), y=bmi, control=list(x.tol=1e-6))
> #
> # refine the previous outcome
> a1 <- mst.mle(X=cbind(1,Ht,Wt), y=bmi, control=list(x.tol=1e-9), start=a$dp)
> 
> 
> 
> cleanEx(); ..nameEx <- "pnorm2"
> 
> ### * pnorm2
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: pnorm2
> ### Title: Bivariate normal integral
> ### Aliases: pnorm2
> ### Keywords: distribution multivariate
> 
> ### ** Examples
> 
> p <- pnorm2(1.2, 0.5, 0.67)
> 
> 
> 
> cleanEx(); ..nameEx <- "sn.2logL.profile"
> 
> ### * sn.2logL.profile
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: sn.2logL.profile
> ### Title: Profile twice loglikelihood for skew-normal models
> ### Aliases: sn.2logL.profile
> ### Keywords: distribution
> 
> ### ** Examples
> 
> data(ais, package="sn")
> attach(ais)
> a <- sn.2logL.profile(y=bmi)
Running until 15 : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
> a <- sn.2logL.profile(y=bmi, use.cp=FALSE, param.range=c(3,6,1,5))
Running until 15 : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
> a <- sn.2logL.profile(X=cbind(1,lbm), y=bmi, param.range=c(0,0.9),
+         npts=50)
Running until 50 : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
> #
> data(frontier, package="sn")
> a <- sn.2logL.profile(y=frontier, param.range=c(0.8,1.6,10,30),
+         use.cp=FALSE, npts=11)
Running until 11 : 1 2 3 4 5 6 7 8 9 10 11
> 
> 
> 
> cleanEx(); ..nameEx <- "sn.Einfo"
> 
> ### * sn.Einfo
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: sn.Einfo
> ### Title: Expected Fisher information for SN distribution parameters
> ### Aliases: sn.Einfo
> ### Keywords: distribution
> 
> ### ** Examples
> 
> info <- sn.Einfo(dp=c(0,1,5), n=3)
> #
> data(ais, package="sn")
> M <- model.matrix(~ais$"Ht")
> mle <- sn.mle(X=M, y=ais$"Wt", plot.it=FALSE)
> info <- sn.Einfo(cp=mle$cp, x=M)
> 
> 
> 
> cleanEx(); ..nameEx <- "sn.cumulants"
> 
> ### * sn.cumulants
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: sn.cumulants
> ### Title: Cumulants of the skew-normal distribution
> ### Aliases: sn.cumulants
> ### Keywords: distribution
> 
> ### ** Examples
> 
> cum <- sn.cumulants(c(0,1,2,5,10),4)
> 
> 
> 
> cleanEx(); ..nameEx <- "sn.em"
> 
> ### * sn.em
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: sn.em
> ### Title: Fitting Skew-normal variables using the EM algorithm
> ### Aliases: sn.em
> ### Keywords: regression distribution
> 
> ### ** Examples
> 
> data(ais, package="sn")
> attach(ais)
> #
> a<-sn.em(y=bmi)
> #
> a<-sn.em(X=cbind(1,lbm,lbm^2),y=bmi)
> #
> M<-model.matrix(~lbm+I(ais$sex))
> b<-sn.em(M,bmi)
> #
> fit <- sn.em(y=bmi, fixed=c(NA, 2, 3), l.eps=0.001)
> 
> 
> 
> cleanEx(); ..nameEx <- "sn.mle"
> 
> ### * sn.mle
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: sn.mle
> ### Title: Maximum likelihood estimation for skew-normal models
> ### Aliases: sn.mle
> ### Keywords: regression distribution
> 
> ### ** Examples
> 
> data(ais, package="sn")
> attach(ais)
> a<-sn.mle(y=bmi)
> #
> a<-sn.mle(X=cbind(1,lbm),y=bmi)
> #
> b<-sn.mle(X=model.matrix(~lbm+sex), y=bmi)
> 
> 
> 
> cleanEx(); ..nameEx <- "sn.mle.grouped"
> 
> ### * sn.mle.grouped
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: sn.mle.grouped
> ### Title: Maximum likelihood estimation of SN and ST distribution for
> ###   grouped data
> ### Aliases: sn.mle.grouped st.mle.grouped
> ### Keywords: distribution
> 
> ### ** Examples
> 
> data(ais, package="sn")
> attach(ais)
> breaks<- c(130,160, seq(170, 190, by=2.5), 200, 230)
> f <- cut(Ht[sex=="female"], breaks = breaks)
> freq <- tabulate(f, length(levels(f)))
> b1 <- sn.mle.grouped(breaks, freq)
Warning in log(x) : NaNs produced
Warning in log(x) : NaNs produced
> b2 <- st.mle.grouped(breaks, freq, start=c(b1$end,log(5)))
> print(b2$dp)
[1]  1.820848e+02  1.103457e+01 -1.802708e+00  4.044000e+08
> #
> us.income <- c(0,seq(from=0.2, to=1.8, by=0.1), 2.0, 2.5, 5.0, Inf)
> mid <- (us.income[-1]+us.income[-length(us.income)])/2
> mid[length(mid)] <- 6.5
> cum.freq<- c(1.78, 3.25, 5.56, 8.16, 11.12, 14.21, 17.54, 20.78, 24.00,
+              27.52, 30.77, 34.21, 37.56, 40.70, 44.41, 47.85, 51.22, 
+              57.60, 72.12, 96.40, 100) / 100
> freq<- round(diff(c(0,cum.freq*34660)))
> a <- st.mle.grouped(breaks=log(us.income), freq, trace=TRUE,
+         start=c(1.2, log(0.9), -2.1, log(20)))
[1]  1.200000e+00 -1.053605e-01 -2.100000e+00  2.995732e+00 -1.052365e+05
[1]  1.499573e+00 -1.053605e-01 -2.100000e+00  2.995732e+00 -1.090037e+05
[1]  1.200000e+00  1.942127e-01 -2.100000e+00  2.995732e+00 -1.068531e+05
[1]  1.200000e+00 -1.053605e-01 -1.800427e+00  2.995732e+00 -1.052218e+05
[1]  1.200000e+00 -1.053605e-01 -2.100000e+00  3.295306e+00 -1.052633e+05
[1]  9.004268e-01  4.442610e-02 -1.950213e+00  3.145519e+00 -1.091734e+05
[1]  1.349787e+00 -6.791386e-02 -2.062553e+00  3.033179e+00 -1.060077e+05
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[1]  1.328050e+00  1.457478e-01 -2.929629e+00  7.339139e+00 -9.382433e+04
[1]  1.324531e+00  1.449518e-01 -2.901150e+00  7.007445e+00 -9.382385e+04
[1]  1.324210e+00  1.449238e-01 -2.912223e+00  7.103739e+00 -9.382344e+04
[1]  1.319250e+00  1.438391e-01 -2.883478e+00  6.741725e+00 -9.382326e+04
[1]  1.316915e+00  1.394672e-01 -2.870662e+00  6.722580e+00 -9.382397e+04
[1]      1.321194      0.142012     -2.895165      6.971900 -93823.666140
[1]  1.322145e+00  1.471625e-01 -2.902564e+00  6.839092e+00 -9.382305e+04
[1]  1.320084e+00  1.497581e-01 -2.892394e+00  6.562206e+00 -9.382379e+04
[1]  1.311712e+00  1.415178e-01 -2.820036e+00  6.037238e+00 -9.382529e+04
[1]  1.326814e+00  1.459781e-01 -2.933366e+00  7.316441e+00 -9.382364e+04
[1]  1.320171e+00  1.445440e-01 -2.906137e+00  6.927134e+00 -9.382286e+04
[1]  1.317991e+00  1.443402e-01 -2.908630e+00  6.886979e+00 -9.382289e+04
[1]  1.322995e+00  1.487498e-01 -2.917607e+00  6.940297e+00 -9.382287e+04
[1]  1.322545e+00  1.470654e-01 -2.911997e+00  6.948198e+00 -9.382287e+04
[1]  1.315242e+00  1.453274e-01 -2.868722e+00  6.411633e+00 -9.382388e+04
[1]  1.323921e+00  1.458154e-01 -2.917205e+00  7.090239e+00 -9.382309e+04
[1]  1.325141e+00  1.484546e-01 -2.935473e+00  7.160606e+00 -9.382278e+04
[1]  1.328087e+00  1.507624e-01 -2.961470e+00  7.370047e+00 -9.382289e+04
[1]  1.321080e+00  1.477978e-01 -2.910880e+00  6.847276e+00 -9.382285e+04
[1]  1.321791e+00  1.473022e-01 -2.912461e+00  6.908017e+00 -9.382280e+04
[1]  1.322679e+00  1.465206e-01 -2.930470e+00  7.132886e+00 -9.382263e+04
[1]  1.322946e+00  1.461997e-01 -2.944423e+00  7.279782e+00 -9.382265e+04
[1]  1.322346e+00  1.463454e-01 -2.930274e+00  7.116124e+00 -9.382262e+04
[1]  1.322246e+00  1.459854e-01 -2.939412e+00  7.200087e+00 -9.382263e+04
[1]  1.325807e+00  1.497674e-01 -2.948202e+00  7.231682e+00 -9.382268e+04
[1]  1.324398e+00  1.484615e-01 -2.937686e+00  7.155545e+00 -9.382264e+04
[1]  1.325492e+00  1.475888e-01 -2.954490e+00  7.374564e+00 -9.382273e+04
[1]  1.324566e+00  1.475172e-01 -2.943983e+00  7.257927e+00 -9.382265e+04
[1]  1.321854e+00  1.459678e-01 -2.935734e+00  7.170634e+00 -9.382262e+04
[1]  1.320210e+00  1.447244e-01 -2.935864e+00  7.175648e+00 -9.382278e+04
[1]  1.321072e+00  1.461305e-01 -2.923099e+00  7.029668e+00 -9.382263e+04
[1]  1.321946e+00  1.464772e-01 -2.928320e+00  7.086732e+00 -9.382261e+04
[1]  1.320014e+00  1.441939e-01 -2.924713e+00  7.097643e+00 -9.382280e+04
[1]  1.323302e+00  1.473946e-01 -2.934443e+00  7.141070e+00 -9.382260e+04
[1]  1.322044e+00  1.465718e-01 -2.933915e+00  7.124395e+00 -9.382258e+04
[1]  1.321727e+00  1.465974e-01 -2.935637e+00  7.120149e+00 -9.382257e+04
[1]  1.322068e+00  1.468731e-01 -2.936793e+00  7.143169e+00 -9.382255e+04
[1]      1.321929      0.147137     -2.940052      7.156691 -93822.544953
[1]  1.322599e+00  1.478353e-01 -2.933492e+00  7.081687e+00 -9.382256e+04
[1]  1.322412e+00  1.473685e-01 -2.934053e+00  7.103924e+00 -9.382255e+04
[1]  1.322740e+00  1.477716e-01 -2.943772e+00  7.174184e+00 -9.382252e+04
[1]  1.323137e+00  1.484189e-01 -2.951499e+00  7.217910e+00 -9.382251e+04
[1]  1.321301e+00  1.473662e-01 -2.946178e+00  7.158268e+00 -9.382260e+04
[1]  1.322802e+00  1.473875e-01 -2.937376e+00  7.145369e+00 -9.382255e+04
[1]  1.323413e+00  1.485585e-01 -2.945853e+00  7.191798e+00 -9.382252e+04
[1]  1.322992e+00  1.480682e-01 -2.943299e+00  7.173886e+00 -9.382252e+04
[1]  1.323229e+00  1.483825e-01 -2.953337e+00  7.251961e+00 -9.382252e+04
[1]  1.323025e+00  1.481290e-01 -2.948516e+00  7.214951e+00 -9.382251e+04
[1]  1.322950e+00  1.487341e-01 -2.955584e+00  7.245306e+00 -9.382254e+04
[1]  1.322913e+00  1.483975e-01 -2.951032e+00  7.220322e+00 -9.382252e+04
[1]  1.324315e+00  1.496149e-01 -2.958398e+00  7.265800e+00 -9.382253e+04
[1]  1.323718e+00  1.489954e-01 -2.953811e+00  7.238523e+00 -9.382251e+04
[1]  1.323733e+00  1.486534e-01 -2.948808e+00  7.211269e+00 -9.382251e+04
[1]  1.323528e+00  1.485894e-01 -2.949364e+00  7.213532e+00 -9.382251e+04
[1]  1.323291e+00  1.485078e-01 -2.955742e+00  7.250660e+00 -9.382252e+04
[1]  1.323383e+00  1.485458e-01 -2.948325e+00  7.206514e+00 -9.382251e+04
[1]  1.323690e+00  1.487110e-01 -2.948509e+00  7.218850e+00 -9.382251e+04
[1]  1.323552e+00  1.486379e-01 -2.949257e+00  7.218615e+00 -9.382251e+04
[1]  1.324066e+00  1.492553e-01 -2.951862e+00  7.223640e+00 -9.382252e+04
[1]  1.323285e+00  1.484106e-01 -2.949353e+00  7.217124e+00 -9.382251e+04
[1]  1.323155e+00  1.480965e-01 -2.944338e+00  7.189370e+00 -9.382252e+04
[1]  1.323578e+00  1.487707e-01 -2.951443e+00  7.226234e+00 -9.382251e+04
> print(a$dp)
[1]    1.323285    1.159989   -2.949353 1362.564092
> 
> 
> 
> cleanEx(); ..nameEx <- "sn.mmle"
> 
> ### * sn.mmle
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: sn.mmle
> ### Title: Modified maximum likelihood estimation for skew-normal models
> ### Aliases: sn.mmle
> ### Keywords: regression distribution
> 
> ### ** Examples
> 
> data(ais, package="sn")
> attach(ais)
> a <-  sn.mmle(y=bmi)
> #
> M <- model.matrix(~lbm+sex)
> b <- sn.mmle(M,bmi)
> 
> 
> 
> cleanEx(); ..nameEx <- "st.2logL.profile"
> 
> ### * st.2logL.profile
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: st.2logL.profile
> ### Title: Profile twice loglikelihood for skew-t models
> ### Aliases: st.2logL.profile
> ### Keywords: distribution
> 
> ### ** Examples
> 
> data(ais, package="sn")
> attach(ais)
> a <- st.2logL.profile(y=bmi, xlab="alpha", ylab="log(df)")
Running up to 15 :  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15
> a <- st.2logL.profile(y=bmi, fixed.comp=4, fixed.values=log(c(1,25)))
Running up to 30 :  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30
> a <- st.2logL.profile(X=cbind(1,lbm), y=bmi, fixed.comp=5,  
+          fixed.values=log(c(5,25)), xlab="log(df)", npts=50)
Running up to 50 :  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50
> a <- st.2logL.profile(X=cbind(1,Ht), y=Wt, fixed.comp=c(4,5),
+          fixed.values=cbind(c(-1,5), log(c(2,25))),
+          xlab="alpha", ylab="log(df)")
Running up to 15 :  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15
> 
> 
> 
> cleanEx(); ..nameEx <- "st.cumulants"
> 
> ### * st.cumulants
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: st.cumulants
> ### Title: Cumulants of the skew-t distribution
> ### Aliases: st.cumulants
> ### Keywords: distribution
> 
> ### ** Examples
> 
> cum <- st.cumulants(shape=3, df=5)
> 
> 
> 
> cleanEx(); ..nameEx <- "zeta"
> 
> ### * zeta
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: zeta
> ### Title: Function `log(2*pnorm(x))' and its derivatives
> ### Aliases: zeta
> ### Keywords: math
> 
> ### ** Examples
> 
> y <- zeta(2,seq(-20,20,by=0.5))
> #
> for(k in 0:4) curve(zeta(k,x), from=-1, to=5, col = k+2, add = k > 0)
> legend(3, -0.5, legend=as.character(0:4), col=2:6, lty=1)
> 
> 
> 
> ### * <FOOTER>
> ###
> cat("Time elapsed: ", proc.time() - get("ptime", env = .CheckExEnv),"\n")
Time elapsed:  128.43 0.45 129.61 0 0 
> grDevices::dev.off()
null device 
          1 
> ###
> ### Local variables: ***
> ### mode: outline-minor ***
> ### outline-regexp: "\\(> \\)?### [*]+" ***
> ### End: ***
> quit('no')