EMbssn {bssn}

EM Algorithm Birnbaum-Saunders model based on Skew-Normal distribution

Description

Performs the EM algorithm for Birnbaum-Saunders model based on Skew-Normal distribution.

Usage

EMbssn(ti,alpha,beta,delta,initial.values=FALSE, loglik=F,accuracy=1e-8,
show.envelope="FALSE",iter.max=500)

Arguments

ti

Vector of observations.

alpha, beta, delta

Initial values.

initial.values

Logical; if TRUE, get the initial values for the parameters.

loglik

Logical; if TRUE, showvalue of the log-likelihood.

accuracy

The convergence maximum error.

show.envelope

Logical; if TRUE, show the simulated envelope for the fitted model.

iter.max

The maximum number of iterations of the EM algorithm

Value

The function returns a list with 11 elements detailed as

iter

Number of iterations.

alpha

Returns the value of the MLE of the shape parameter.

beta

Returns the value of the MLE of the scale parameter.

lambda

Returns the value of the MLE of the skewness parameter.

SE

Standard Errors of the ML estimates.

table

Table containing the ML estimates with the corresponding standard errors.

loglik

Log-likelihood.

AIC

Akaike information criterion.

BIC

Bayesian information criterion.

HQC

Hannan-Quinn information criterion.

time

processing time.

Author(s)

Rocio Maehara [e-mail] and Luis Benites [e-mail]

References

Vilca, Filidor; Santana, L. R.; Leiva, Victor; Balakrishnan, N. (2011). Estimation of extreme percentiles in Birnbaum Saunders distributions. Computational Statistics & Data Analysis (Print), 55, 1665-1678.

Santana, Lucia; Vilca, Filidor; Leiva, Victor (2011). Influence analysis in skew-Birnbaum Saunders regression models and applications. Journal of Applied Statistics, 38, 1633-1649.

See Also

bssn, EMbssn, momentsbssn, ozone, reliabilitybssn

Examples

## Not run: 
#Using the ozone data

data(ozone)
attach(ozone)

#################################
#The model
 ti        <- dailyozonelevel

#Initial values for the parameters
 initial   <- mmmeth(ti)
 alpha0    <- initial$alpha0ini
 beta0     <- initial$beta0init
 lambda0   <- 0
 delta0    <- lambda0/sqrt(1+lambda0^2)

#Estimated parameters of the model (by default)
 est_param <- EMbssn(ti,alpha0,beta0,delta0,loglik=T,
 accuracy = 1e-8,show.envelope = "TRUE", iter.max=500)

#ML estimates
 alpha     <- est_param$res$alpha
 beta      <- est_param$res$beta
 lambda    <- est_param$res$lambda


#########################################
#A simple output example

---------------------------------------------------------
Birnbaum-Saunders model based on Skew-Normal distribution
---------------------------------------------------------

Observations = 116
-----------
Estimates
-----------

       Estimate Std. Error z value Pr(>|z|)
alpha   1.26014    0.23673 5.32311  0.00000
beta   14.65730    4.01984 3.64624  0.00027
lambda  1.06277    0.54305 1.95706  0.05034
------------------------
Model selection criteria
------------------------

        Loglik   AIC   BIC   HQC
Value -542.768 4.705 4.741 4.719
-------
Details
-------

Iterations = 415
Processing time = 0.4283214 secs
Convergence = TRUE

## End(Not run)