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

Description Usage Arguments Value Author(s) References See Also Examples

View source: R/EMbssn.R

Description

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

Usage

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

Arguments

ti

the response vector of dimension n where n is the total of observations.

alpha,beta,delta

an numeric of initial estimates.

loglik

showvalue of the log-likelihood (V) or not (F).

accuracy

the convergence maximum error.

show.envelope

TRUE or FALSE. Indicates if envelope graph should be built for the fitted model. Default is FALSE.

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

estimated shape parameter.

beta

estimated scale parameter.

lambda

estimate skewness parameter.

SE

Standard Error estimates.

table

Table containing the inference for the estimated parameters.

loglik

Log-likelihood value.

AIC

Akaike information criterion.

BIC

Bayesian information criterion.

HQC

Hannan-Quinn information criterion.

time

processing time.

Author(s)

Rocio Maehara [email protected] and Luis Benites [email protected]

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

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## 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 May 29, 2017, 2:16 p.m.