Applications of asymptotic confidence intervals with continuity corrections for asymmetric comparisons in noninferiority trials

2013 ◽  
Vol 12 (3) ◽  
pp. 147-155 ◽  
Author(s):  
Julia N. Soulakova ◽  
Brianna C. Bright
Keyword(s):  
Confidence Intervals ◽  
Noninferiority Trials ◽  
Asymptotic Confidence Intervals ◽  
Continuity Corrections

scholarly journals Inference on reliability of stress-strength model with Peng-Yan extended Weibull distributions

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 1927-1948
Author(s):  
Milan Jovanovic ◽  
Bojana Milosevic ◽  
Marko Obradovic ◽  
Zoran Vidovic
Keyword(s):  
Asymptotic Distribution ◽  
Confidence Intervals ◽  
Real Data ◽  
Independent Random Variables ◽  
Likelihood Estimator ◽  
Conjugate Priors ◽  
Asymptotic Confidence Intervals ◽  
Exact Confidence Intervals ◽  
Extended Weibull Distribution ◽  
Interval Estimator

In this paper we estimate R = PfX < Yg when X and Y are independent random variables following the Peng-Yan extended Weibull distribution. We find maximum likelihood estimator of R and its asymptotic distribution. This asymptotic distribution is used to construct asymptotic confidence intervals. In the case of equal shape parameters, we derive the exact confidence intervals, too. A procedure for deriving bootstrap-p confidence intervals is presented. The UMVUE of R and the UMVUE of its variance are derived and also the Bayes point and interval estimator of R for conjugate priors are obtained. Finally, we perform a simulation study in order to compare these estimators and provide a real data example.

scholarly journals A note on confidence intervals for deblurred images

2020 ◽  
Vol 40 (3) ◽  
pp. 361-373
Author(s):  
Michał Biel ◽  
Zbigniew Szkutnik
Keyword(s):  
Inverse Problem ◽  
Confidence Intervals ◽  
Convolution Operator ◽  
Regression Models ◽  
Inverse Regression ◽  
Finite Sample ◽  
Bootstrap Confidence Intervals ◽  
Additive White Noise ◽  
Asymptotic Confidence Intervals ◽  
Simulation Results

We consider pointwise asymptotic confidence intervals for images that are blurred and observed in additive white noise. This amounts to solving a stochastic inverse problem with a convolution operator. Under suitably modified assumptions, we fill some apparent gaps in the proofs published in [N. Bissantz, M. Birke, Asymptotic normality and confidence intervals for inverse regression models with convolution-type operators, J. Multivariate Anal. 100 (2009), 2364-2375]. In particular, this leads to modified bootstrap confidence intervals with much better finite-sample behaviour than the original ones, the validity of which is, in our opinion, questionable. Some simulation results that support our claims and illustrate the behaviour of the confidence intervals are also presented.

scholarly journals Inference for the Geometric Extreme Exponential Distribution under Progressive Type II Censoring

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Reza Pakyari
Keyword(s):  
Confidence Intervals ◽  
Skewed Distribution ◽  
Type Ii ◽  
Monte Carlo Simulation Study ◽  
Censored Samples ◽  
Percentage Points ◽  
Progressive Type ◽  
Coverage Probabilities ◽  
Wide Range ◽  
Asymptotic Confidence Intervals

Geometric extreme exponential (GE-exponential) is one of the nonnegative right-skewed distribution that is suitable for analyzing lifetime data. It is well known that the maximum likelihood estimators (MLEs) of the parameters lead to likelihood equations that have to be solved numerically. In this paper, we provide explicit estimators through an approximation of the likelihood equations based on progressively Type-II-censored samples. The approximate estimators are then used as starting values to find the MLEs numerically. The bias and variances of the MLEs are calculated for a wide range of sample sizes and different progressive censoring schemes through a Monte Carlo simulation study. Moreover, formulas for the observed Fisher information are given which could be used to construct asymptotic confidence intervals. The coverage probabilities of the confidence intervals and the percentage points of pivotal quantities associated with the MLEs are also calculated. A real dataset has been studied for illustrative purposes.

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