Asian Science Citation Index is committed to provide an authoritative, trusted and significant information by the
coverage of the most important and influential journals
to meet the needs of the global scientific community.
We consider the Weibull distribution which has been extensively
used in life testing and reliability studies of the strength of materials. The
maximum likelihood method is the usual frequentist approach in the parameter
estimate for parametric survival data. In this study, we divert from this platform
and use the Bayesian paradigm instead. The Jeffreys and extension of Jeffreys
prior with the squared loss function are considered in the estimation. The Bayes
estimates of the survival function and hazard rate of the Weibull distribution
with censored data obtained using Lindley’s approximation are then compared
to its maximum likelihood counterparts. The comparison criteria is the Mean
Square Error (MSE) and the performance of these three estimates are assessed
using simulations considering various sample sizes, several specific values
of Weibull parameters and several values of extension of Jeffreys prior. The
maximum likelihood estimates of survival function and hazard rate are more efficient
than their Bayesian counterparts, however, the extension of Jeffreys is better
than the maximum likelihood for certain conditions.
Mean direction is a good measure to estimate circular location parameter in univariate circular data.
However, it is bias and cause misleading when the circular data has some outliers, especially with increasing
ratio of outliers. Trimmed mean is one of robust method to estimate location parameter. Therefore in this study,
it is focused to find a robust formula for trimming the circular data. This proposed method is compared with
mean direction, median direction and M estimator for clean and contaminated data. Results of simulation study
and real data prove that trimmed mean direction is very successful and the best among them.
