EMbssn: EM Algorithm Birnbaum-Saunders model based on Skew-Normal...

In bssn: Birnbaum-Saunders Model

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)

bssn documentation built on Feb. 13, 2020, 5:08 p.m.