reliaR (version 0.2)

abic.loglog: Akaike information criterion (AIC) and Bayesian/ Schwartz information criterion (BIC)/ (SIC) for a sample from Loglog distribution

Description

The function abic.loglog( ) gives the loglikelihood, AIC and BIC values assuming Loglog distribution with parameters alpha and lambda. The function is based on the invariance property of the MLE.

Usage

abic.loglog(x, alpha.est, lambda.est)

Value

The function abic.loglog( ) gives the loglikelihood, AIC and BIC values.

Arguments

x

vector of observations

alpha.est

estimate of the parameter alpha

lambda.est

estimate of the parameter lambda

References

Akaike, H. (1978). A new look at the Bayes procedure, Biometrika, 65, 53-59.

Claeskens, G. and Hjort, N. L. (2008). Model Selection and Model Averaging, Cambridge University Press, London.

Konishi., S. and Kitagawa, G.(2008). Information Criteria and Statistical Modeling, Springer Science+Business Media, LLC.

Schwarz, S. (1978). Estimating the dimension of the model, Annals of Statistics, 6, 461-464.

Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and van der Linde, A. (2002). Bayesian measures of complexity and fit, Journal of the Royal Statistical Society Series B 64, 1-34.

See Also

qq.loglog for QQ plot and ks.loglog function

Examples

## Load data set
data(sys2)
## Maximum Likelihood(ML) Estimates of alpha & lambda for the data(sys2)
## alpha.est = 0.9058689 lambda.est = 1.0028228

## Values of AIC, BIC and LogLik for the data(sys2) 
abic.loglog(sys2, 0.9058689, 1.0028228)