extra.parameter function

Tool that supports the estimation of the extra parameter.

extra.parameter is used to plot a graph of the behaviour of the overall goodness-of-fit statistic and $-2\textsf{L}(\hat{\theta})$

versus the extra parameter $\zeta$ in the interval/region defined by the arguments lower and upper. These graphs may be used to choosing the extra parameter value.

extra.parameter(object, lower, upper, grid)

Arguments

• object: an object of the class ssym. This object is returned by the call to ssym.l(), ssym.nl() or ssym.l2()
• lower: lower limit(s) of the interest interval/region for the extra parameter.
• upper: upper limit(s) of the interest interval/region for the extra parameter.
• grid: Number of values of the extra parameter where the overall goodness-of-fit statistic and $-2\textsf{L}(\hat{\theta})$ are evaluated.

References

Vanegas, L.H. and Paula, G.A. (2015b) Log-symmetric distributions: statistical properties and parameter estimation. Brazilian Journal of Probability and Statistics (to appear)

Author(s)

Luis Hernando Vanegas hvanegasp@gmail.com and Gilberto A. Paula

Examples

###################################################################################
############### Textures of snacks Data - a log-Student-t model  #################
###################################################################################
#data("Snacks", package="ssym")
#fit <- extra.parameter(log(texture) ~ type + ncs(week) | type, data=Snacks,
#        family='Student', xi=10)
#summary(fit)
#
############################ Extra parameter ###########################
#extra.parameter(fit,5,50)

###################################################################################
################## Biaxial Fatigue Data - a Birnbaum-Saunders model   #############
###################################################################################
#data("Biaxial", package="ssym")
#fit <- ssym.nl(log(Life) ~ b1*Work^b2, start=c(b1=16, b2=-0.25),
#                data=Biaxial, family='Sinh-normal', xi=1.54)
#summary(fit)
#
########################### Extra parameter ###########################
#extra.parameter(fit,1.3,1.8)