scholarly journals Preliminary Test Estimators and Confidence Intervals for the Parametric Functions of the Moore and Bilikam Family of Lifetime Distributions Based on Records

2019 ◽  
Vol 48 (4) ◽  
pp. 58-89
Author(s):  
Ajit Chaturvedi ◽  
Suk-Bok Kang ◽  
Ananya Malhotra
Keyword(s):  
Confidence Intervals ◽  
Empirical Bayes ◽  
Preliminary Test ◽  
Minimum Variance ◽  
Lifetime Distributions ◽  
Expected Length ◽  
Two Measures ◽  
Parametric Functions ◽  
Empirical Bayes Estimator ◽  
Better Than

We consider two measures of reliability functions namely R(t)=P(X>t) and P=P(X>Y) for the Moore and Bilikam (1978) family of lifetime distributions which covers fourteen distributions as specific cases. For record data from this family of distributions, preliminary test estimators (PTEs) and preliminary test confidence interval (PTCI) based on uniformly minimum variance unbiased estimator (UMVUE), maximum likelihood estimator (MLE), empirical Bayes estimator (EBE) are obtained for the parameter. The bias and mean square error (MSE) (exact and asymptotic) of the proposed estimators are derived to study their relative efficiency and through simulation studies we establish that PTEs perform better than ordinary UMVUE, MLE and EBE. We also obtain the coverage probability (CP) and the expected length of the PTCI of the parameter and establish that the confidence intervals based on MLE are more precise. An application of the ordinary preliminary test estimator is also considered. To the best of the knowledge of the authors, no PTEs have been derived for R(t) and P based on records and thus we define improved PTEs based on MLE and UMVUE of R(t) and P. A comparative study of different methods of estimation done through simulations establishes that PTEs perform better than ordinary UMVUE and MLE.

scholarly journals Multiple Comparisons for Exponential Median Lifetimes with the Control Based on Doubly Censored Samples

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 76
Author(s):  
Shu-Fei Wu
Keyword(s):  
Confidence Intervals ◽  
Minimum Variance ◽  
Control Population ◽  
Censored Samples ◽  
Doubly Censored ◽  
Pharmaceutical Industries ◽  
The Difference ◽  
The One ◽  
Multiple Comparison Procedures ◽  
Better Than

Under doubly censoring, the one-stage multiple comparison procedures with the control in terms of exponential median lifetimes are presented. The uniformly minimum variance unbiased estimator for median lifetime is found. The upper bounds, lower bounds and two-sided confidence intervals for the difference between each median lifetimes and the median lifetime of the control population are developed. Statistical tables of critical values are constructed for the practical use of our proposed procedures. Users can use these simultaneous confidence intervals to determine whether the performance of treatment populations is better than or worse than the control population in agriculture and pharmaceutical industries. At last, one practical example is provided to illustrate the proposed procedures.

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

scholarly journals Gait Stability Measurement by Using Average Entropy

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 412
Author(s):  
Han-Ping Huang ◽  
Chang Francis Hsu ◽  
Yi-Chih Mao ◽  
Long Hsu ◽  
Sien Chi
Keyword(s):  
Postural Stability ◽  
Multiscale Entropy ◽  
Gait Stability ◽  
Eyes Closed ◽  
Stride Interval ◽  
Step Interval ◽  
Stability Measurement ◽  
Eyes Open ◽  
Two Measures ◽  
Better Than

Gait stability has been measured by using many entropy-based methods. However, the relation between the entropy values and gait stability is worth further investigation. A research reported that average entropy (AE), a measure of disorder, could measure the static standing postural stability better than multiscale entropy and entropy of entropy (EoE), two measures of complexity. This study tested the validity of AE in gait stability measurement from the viewpoint of the disorder. For comparison, another five disorders, the EoE, and two traditional metrics methods were, respectively, used to measure the degrees of disorder and complexity of 10 step interval (SPI) and 79 stride interval (SI) time series, individually. As a result, every one of the 10 participants exhibited a relatively high AE value of the SPI when walking with eyes closed and a relatively low AE value when walking with eyes open. Most of the AE values of the SI of the 53 diseased subjects were greater than those of the 26 healthy subjects. A maximal overall accuracy of AE in differentiating the healthy from the diseased was 91.1%. Similar features also exists on those 5 disorder measurements but do not exist on the EoE values. Nevertheless, the EoE versus AE plot of the SI also exhibits an inverted U relation, consistent with the hypothesis for physiologic signals.

Combining two soil property rasters using an adaptive gating approach

Soil Research ◽  
2015 ◽  
Vol 53 (8) ◽  
pp. 907 ◽  
Author(s):  
David Clifford ◽  
Yi Guo
Keyword(s):  
Confidence Intervals ◽  
Soil Property ◽  
Mean Squared Error ◽  
Geographic Space ◽  
Covariate Information ◽  
Squared Error ◽  
Inverse Variance ◽  
Machine Learning Approach ◽  
Further Development ◽  
Better Than

Given the wide variety of ways one can measure and record soil properties, it is not uncommon to have multiple overlapping predictive maps for a particular soil property. One is then faced with the challenge of choosing the best prediction at a particular point, either by selecting one of the maps, or by combining them together in some optimal manner. This question was recently examined in detail when Malone et al. (2014) compared four different methods for combining a digital soil mapping product with a disaggregation product based on legacy data. These authors also examined the issue of how to compute confidence intervals for the resulting map based on confidence intervals associated with the original input products. In this paper, we propose a new method to combine models called adaptive gating, which is inspired by the use of gating functions in mixture of experts, a machine learning approach to forming hierarchical classifiers. We compare it here with two standard approaches – inverse-variance weights and a regression based approach. One of the benefits of the adaptive gating approach is that it allows weights to vary based on covariate information or across geographic space. As such, this presents a method that explicitly takes full advantage of the spatial nature of the maps we are trying to blend. We also suggest a conservative method for combining confidence intervals. We show that the root mean-squared error of predictions from the adaptive gating approach is similar to that of other standard approaches under cross-validation. However under independent validation the adaptive gating approach works better than the alternatives and as such it warrants further study in other areas of application and further development to reduce its computational complexity.

Robustness to Parametric Assumptions in Missing Data Models

2011 ◽  
Vol 101 (3) ◽  
pp. 538-543 ◽  
Author(s):  
Bryan S Graham ◽  
Keisuke Hirano
Keyword(s):  
Empirical Bayes ◽  
Missing At Random ◽  
Data Driven ◽  
Robust Estimator ◽  
Sampling Variance ◽  
Bayes Estimators ◽  
Cell Means ◽  
Double Robust ◽  
Empirical Bayes Estimators ◽  
Empirical Bayes Estimator

We consider estimation of population averages when data are missing at random. If some cells contain few observations, there can be substantial gains from imposing parametric restrictions on the cell means, but there is also a danger of misspecification. We develop a simple empirical Bayes estimator, which combines parametric and unadjusted estimates of cell means in a data-driven way. We also consider ways to use knowledge of the form of the propensity score to increase robustness. We develop an empirical Bayes extension of a double robust estimator. In a small simulation study, the empirical Bayes estimators perform well. They are similar to fully nonparametric methods and robust to misspecification when cells are moderate to large in size, and when cells are small they maintain the benefits of parametric methods and can have lower sampling variance.

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