Ultrasonic {nlsmsn}

Ultrasonic Calibration

Description

The data is a result of a ultrasonic calibration study perfomed by National Institute of Standard and Technology.

Usage

data(Ultrasonic)

Format

A data frame with 214 observations with y as the ultrasonic measuraments and x the metal distance

Author(s)

Aldo Garay [e-mail], Marcos Prates [e-mail] and Victor Lachos [e-mail]

Source

Victor H. Lachos, Dipankar Bandyopadhyay and Aldo M. Garay (2011). "Heteroscedastic nonlinear regression models based on scale mixture of skew-normal distributions". Statistics -and Probability Letters, 81, 1208-1217.

Examples

## Not run: 
##Load the data
data(Ultrasonic)

##Define non linear function
nlf<-function(x,betas){
resp<- exp(-betas[1]*x)/(betas[2] + betas[3]*x)
return(resp)
}

##Set the response y and covariate x
y <- Ultrasonic$y
x <- Ultrasonic$x

##Set initial values
z <- x
betas <- c(0.1913, 0.0061, 0.0110)
rho <- -0.1
sigma2 <- 3.2726
shape <- 0.1698
nu <- 4

## Skew.normal regression
analysis.sn <- smsn.nl(y = y, x = x, z = z, betas = betas, sigma2 = sigma2, shape = shape, 
                       rho = rho, nlf = nlf, rho.func = 2, reg.type = "Heteroscedastic", 
                       criteria = TRUE, family = "Skew.normal", iter.max = 200)

## Skew.t regression
analysis.st <- smsn.nl(y = y, x = x, z = z, betas = betas, sigma2 = sigma2, shape = shape, nu = nu, 
                       rho = rho, nlf = nlf, rho.func = 1, reg.type = "He", 
                       criteria = TRUE, family = "Skew.t", iter.max = 200)

## End(Not run)