Bootstrap method for central and intermediate order statistics under power normalization

summary:It has been known for a long time that for bootstrapping the distribution of the extremes under the traditional linear normalization of a sample consistently, the bootstrap sample size needs to be of smaller order than the original sample size. In this paper, we show that the same is true if we use the bootstrap for estimating a central, or an intermediate quantile under power normalization. A simulation study illustrates and corroborates theoretical results

Estimation of the Parameters of the Reversed Generalized Logistic Distribution with Progressive Censoring Data

The reversed generalized logistic RGL distributions are very useful classes of densities as they posses a wide range of indices of skewness and kurtosis. This paper considers the estimation problem for the parameters of the RGL distribution based on progressive Type II censoring. The maximum likelihood method for RGL distribution yields equations that have to be solved numerically, even when the complete sample is available. By approximating the likelihood equations, we obtain explicit estimators which are in approximation to the MLEs. Using these approximate estimators as starting values, we obtain the MLEs using iterative method. We examine numerically MLEs estimators and the approximate estimators and show that the approximation provides estimators that are almost as efficient as MLEs. Also we show that the value of the MLEs decreases as the value of the shape parameter increases. An exact confidence interval and an exact joint confidence region for the parameters are constructed. Numerical example is presented in the methods proposed in this paper

On the continuation of the limit distribution of intermediate order statistics under power normalization

The property of the continuation of the convergence of the distribution function of intermediate order statistics under power normalizations is studied on an arbitrary nondegenerate interval to the whole real line

Estimation of the Parameters of the Reversed Generalized Logistic Distribution with Progressive Censoring Data

The reversed generalized logistic (RGL) distributions are very useful classes of densities as they posses a wide range of indices of skewness and kurtosis. This paper considers the estimation problem for the parameters of the RGL distribution based on progressive Type II censoring. The maximum likelihood method for RGL distribution yields equations that have to be solved numerically, even when the complete sample is available. By approximating the likelihood equations, we obtain explicit estimators which are in approximation to the MLEs. Using these approximate estimators as starting values, we obtain the MLEs using iterative method. We examine numerically MLEs estimators and the approximate estimators and show that the approximation provides estimators that are almost as efficient as MLEs. Also we show that the value of the MLEs decreases as the value of the shape parameter increases. An exact confidence interval and an exact joint confidence region for the parameters are constructed. Numerical example is presented in the methods proposed in this paper

On the continuation of the limit distribution of intermediate order statistics under power normalization

The property of the continuation of the convergence of the distribution function of intermediate order statistics under power normalizations is studied on an arbitrary nondegenerate interval to the whole real line

Estimation of the Parameters of the Reversed Generalized Logistic Distribution with Progressive Censoring Data

The reversed generalized logistic RGL distributions are very useful classes of densities as they posses a wide range of indices of skewness and kurtosis. This paper considers the estimation problem for the parameters of the RGL distribution based on progressive Type II censoring. The maximum likelihood method for RGL distribution yields equations that have to be solved numerically, even when the complete sample is available. By approximating the likelihood equations, we obtain explicit estimators which are in approximation to the MLEs. Using these approximate estimators as starting values, we obtain the MLEs using iterative method. We examine numerically MLEs estimators and the approximate estimators and show that the approximation provides estimators that are almost as efficient as MLEs. Also we show that the value of the MLEs decreases as the value of the shape parameter increases. An exact confidence interval and an exact joint confidence region for the parameters are constructed. Numerical example is presented in the methods proposed in this paper