This paper presents approximate confidence intervals for each function of parameters in a Banach space based on a bootstrap algorithm. We apply kernel density approach to estimate the persistence landscape. In addition, we evaluate the quality distribution function estimator of random variables using integrated mean square error (IMSE). The results of simulation studies show a significant impro...

In this paper, we consider the problem of estimating stress-strength reliability for inverse Weibull lifetime models having the same shape parameters but different scale parameters. We obtain the maximum likelihood estimator and its asymptotic distribution. Since the classical estimator doesn’t hold explicit forms, we propose an approximate maximum likelihood estimator. The asymptotic confidenc...

This paper combines the least squaress estimate, least absolute deviation estimate, least median estimate with Bootstrap method. When the overall error distribution is unknown or it is not the normal distribution, we estimate the regression coefficient and confidence interval of coefficient, and through data simulation, obtain Bootstrap method, which can improve stability of regression coeffici...

In this paper we investigate the (in)-consistency of different bootstrap methods for constructing confidence intervals in the class of estimators that converge at rate n 1 3 . The Grenander estimator, the nonparametric maximum likelihood estimator of an unknown nonincreasing density function f on [0,∞), is a prototypical example. We focus on this example and explore different approaches to cons...

We study asymptotic properties of the nonparametric maximum likelihood estimator (NPMLE) of a distribution function based on partly interval-censored data in which the exact values of some failure times are observed in addition to interval-censored observations. It is shown that the NPMLE converges weakly to a mean zero Gaussian process whose covariance function is determined by a Fredholm inte...

This paper introduces the confidence interval estimate for measuring the bullwhip effect, which has been observed across most industries. Calculating a confidence interval usually needs the assumption about the underlying distribution. Bootstrapping is a non-parametric, but computer intensive, estimation method. In this paper, a simulation study on the behavior of the 95% bootstrap confidence i...

In this paper, maximum likelihood estimation have been obtained for two Weibull populations under joint type II censored scheme, which generalize results of Balakrishnan and Rasouli (2008). Moreover, approximate confidence region are also discussed and compared with two Bootstrap confidence regions. A numerical illustration for these new results is given.

For a GARCH(1,1) sequence or an AR(1) model with ARCH(1) errors, it is known that the observations have a heavy tail and the tail index is determined by an estimating equation. Therefore, one can estimate the tail index by solving the estimating equation with unknown parameters replaced by quasi maximum likelihood estimation (QMLE), and profile empirical likelihood method can be employed to eff...

Multicomponent stress–strength reliability (MSR) is explored for the system with Burr XII distributed components under Type-II censoring. When distributions of strength and stress variables have common or unequal inner shape parameters, existence uniqueness maximum likelihood estimators are investigated established. The associated approximate confidence intervals obtained by using asymptotic no...

In this paper, we study generalized stress-strength model for logistic distribution. The maximum likelihood estimator of quantity is obtained and then a confidence interval presented it. Bayesian bootstrap methods are also applied the recommended model. A Markov Chain Monte Carlo (MCMC) simulation assessing estimation performed via Metropolis-Hastings algorithm in each step Gibbs algorithm. An ...