sn (version 0.33)

sn.mle.grouped: Maximum likelihood estimation of SN and ST distribution for grouped data

Description

Fits a skew-normal (SN) and skew-t (ST) distribution to grouped data using exact maximum likelihood estimation

Usage

sn.mle.grouped(breaks, freq, trace=FALSE, start=NA)
st.mle.grouped(breaks, freq, trace=FALSE, start=NA)

Arguments

breaks

a vector contaning the cut points of the groups, given in ascending order. The last value can be Inf, the first one can be -Inf

freq

a vector containing the observed frequencies corresponding to the intervals defined by breaks; it is required that length(freq)=length(breaks)-1

trace

logical value which controls printing of the algorithm convergence. If trace=TRUE, details are printed. Default value is FALSE

start

vector of length with initial values for the woking parameters: location, log(scale), shape and (for the ST case) log(df).

Value

• a list containing the following components:
• call
  a string containing the calling statement
• dp
  for the SN case, a vector of length 3 containing the location, scale and shape parameter; for the ST case, there is an extra parameter, the degress of freedom
• end
  a vector of length 3 or 4 containing the working parameters; this vector can be used as a start for a new call to the function
• opt
  the list returned by the optimizer optim; see the documentation of this function for explanation of its components.

Background

Background information on the SN distribution is given by Azzalini (1985); see also Azzalini and Capitanio (1999). For the ST distribution, see Azzalini and Capitanio (2003).

Details

The optimizer optim is used, supplying the log-likelihood function for grouped data, namely the multinomial expression whose probabilities are assigned by the SN or ST distribution to the given intervals.

References

Azzalini, A. (1985). A class of distributions which includes the normal ones. Scand. J. Statist. 12, 171-178.

Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew-normal distribution. J.Roy.Statist.Soc. B 61, 579--602.

Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew-t distribution. J.Roy. Statist. Soc. B 65, 367--389.

See Also

dsn, dst, optim, sn.mle

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)
b2 <- st.mle.grouped(breaks, freq, start=c(b1$end,log(5)))
print(b2$dp)
#
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)))
print(a$dp)