scholarly journals Inference on Reliability of Stress-Strength Models for Poisson Data

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Alessandro Barbiero
Keyword(s):  
Sample Size ◽  
Asymptotic Theory ◽  
Average Length ◽  
Minimum Variance ◽  
Delta Method ◽  
Reliability Engineering ◽  
Likelihood Estimator ◽  
Poisson Data ◽  
Point Estimators ◽  
Strength Models

Researchers in reliability engineering regularly encounter variables that are discrete in nature, such as the number of events (e.g., failures) occurring in a certain spatial or temporal interval. The methods for analyzing and interpreting such data are often based on asymptotic theory, so that when the sample size is not large, their accuracy is suspect. This paper discusses statistical inference for the reliability of stress-strength models when stress and strength are independent Poisson random variables. The maximum likelihood estimator and the uniformly minimum variance unbiased estimator are here presented and empirically compared in terms of their mean square error; recalling the delta method, confidence intervals based on these point estimators are proposed, and their reliance is investigated through a simulation study, which assesses their performance in terms of coverage rate and average length under several scenarios and for various sample sizes. The study indicates that the two estimators possess similar properties, and the accuracy of these estimators is still satisfactory even when the sample size is small. An application to an engineering experiment is also provided to elucidate the use of the proposed methods.

scholarly journals Reliability Estimation for the Remained Stress-Strength Model under the Generalized Exponential Lifetime Distribution

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Mohammad Mehdi Saber ◽  
Marwa M. Mohie El-Din ◽  
Haitham M. Yousof
Keyword(s):  
Real Data ◽  
Lifetime Distribution ◽  
Reliability Estimation ◽  
Reliability Model ◽  
Strength Model ◽  
Generalized Exponential Distribution ◽  
Reliability Engineering ◽  
Likelihood Estimator ◽  
Strength Models ◽  
Psychology And Medicine

A stress-strength reliability model compares the strength and stresses on a certain system; it is used not only primarily in reliability engineering and quality control but also in economics, psychology, and medicine. In this paper, a novel extension of stress-strength models is presented. The mew model is applied under the generalized exponential distribution. The maximum likelihood estimator, asymptotic distribution, and Bayesian estimation are obtained. A comprehensive simulation study along with real data analysis is performed for illustrating the importance of the new stress-strength model.

Large-sample confidence intervals of information-theoretic measures in linguistics

2020 ◽  
Vol 6 (1) ◽  
pp. 19-54
Author(s):  
Ryan Ka Yau Lai ◽  
Youngah Do
Keyword(s):  
Maximum Likelihood ◽  
Corpus Linguistics ◽  
Delta Method ◽  
Confidence Bounds ◽  
Likelihood Estimator ◽  
Information Theoretic ◽  
Leibler Divergence ◽  
Information Theoretic Measures ◽  
Data Points ◽  
Measure Of Uncertainty

This article explores a method of creating confidence bounds for information-theoretic measures in linguistics, such as entropy, Kullback-Leibler Divergence (KLD), and mutual information. We show that a useful measure of uncertainty can be derived from simple statistical principles, namely the asymptotic distribution of the maximum likelihood estimator (MLE) and the delta method. Three case studies from phonology and corpus linguistics are used to demonstrate how to apply it and examine its robustness against common violations of its assumptions in linguistics, such as insufficient sample size and non-independence of data points.

scholarly journals Adaptive randomised controlled non-inferiority multicentre trial (the Ketodex Trial) on intranasal dexmedetomidine plus ketamine for procedural sedation in children: study protocol

BMJ Open ◽  
2020 ◽  
Vol 10 (12) ◽  
pp. e041319
Author(s):  
Naveen Poonai ◽  
Kamary Coriolano ◽  
Terry Klassen ◽  
Anna Heath ◽  
Maryna Yaskina ◽  
...  
Keyword(s):  
Sample Size ◽  
Error Rate ◽  
Closed Reduction ◽  
Primary Outcome ◽  
Average Length ◽  
Procedural Sedation ◽  
Type I ◽  
Size Estimation ◽  
To Receive ◽  
Intravenous Ketamine

IntroductionUp to 40% of orthopaedic injuries in children require a closed reduction, almost always necessitating procedural sedation. Intravenous ketamine is the most commonly used sedative agent. However, intravenous insertion is painful and can be technically difficult in children. We hypothesise that a combination of intranasal dexmedetomidine plus intranasal ketamine (Ketodex) will be non-inferior to intravenous ketamine for effective sedation in children undergoing a closed reduction.Methods and analysisThis is a six-centre, four-arm, adaptive, randomised, blinded, controlled, non-inferiority trial. We will include children 4–17 years with a simple upper limb fracture or dislocation that requires sedation for a closed reduction. Participants will be randomised to receive either intranasal Ketodex (one of three dexmedetomidine and ketamine combinations) or intravenous ketamine. The primary outcome is adequate sedation as measured using the Paediatric Sedation State Scale. Secondary outcomes include length of stay, time to wakening and adverse effects. The results of both per protocol and intention-to-treat analyses will be reported for the primary outcome. All inferential analyses will be undertaken using a response-adaptive Bayesian design. Logistic regression will be used to model the dose–response relationship for the combinations of intranasal Ketodex. Using the Average Length Criterion for Bayesian sample size estimation, a survey-informed non-inferiority margin of 17.8% and priors from historical data, a sample size of 410 participants will be required. Simulations estimate a type II error rate of 0.08 and a type I error rate of 0.047.Ethics and disseminationEthics approval was obtained from Clinical Trials Ontario for London Health Sciences Centre and McMaster Research Ethics Board. Other sites have yet to receive approval from their institutions. Informed consent will be obtained from guardians of all participants in addition to assent from participants. Study data will be submitted for publication regardless of results.Trial registration numberNCT0419525.

Standard Error of Linear Equating for the Counterbalanced Design

1995 ◽  
Vol 20 (4) ◽  
pp. 337-348 ◽  
Author(s):  
Lingjia Zeng ◽  
Ronald T. Cope
Keyword(s):  
Sample Size ◽  
Computer Simulations ◽  
Standard Error ◽  
Delta Method ◽  
Standard Errors ◽  
Large Sample Size ◽  
Symmetric Distributions ◽  
Large Sample ◽  
Normality Assumption ◽  
Linear Equating

Large-sample standard errors of linear equating for the counterbalanced design are derived using the general delta method. Computer simulations were conducted to compare the standard errors derived by Lord under the normality assumption with those derived in this article without such an assumption. The standard errors derived without the normality assumption were found to be more accurate than those derived with the normality assumption in an example using large sample size and moderately skewed score distributions. In an example using nearly symmetric distributions, the standard errors computed with the normality assumption were found to be at least as accurate as those derived without the normality assumption.

OPTIMAL INVARIANT INFERENCE WHEN THE NUMBER OF INSTRUMENTS IS LARGE

2009 ◽  
Vol 25 (3) ◽  
pp. 793-805 ◽  
Author(s):  
Laura Chioda ◽  
Michael Jansson
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Likelihood ◽  
Sample Size ◽  
Maximum Likelihood Estimator ◽  
Instrumental Variables ◽  
Asymptotic Efficiency ◽  
Rotation Invariance ◽  
Limited Information ◽  
Likelihood Estimator ◽  
Rotation Invariant

This paper studies the asymptotic behavior of a Gaussian linear instrumental variables model in which the number of instruments diverges with the sample size. Asymptotic efficiency bounds are obtained for rotation invariant inference procedures and are shown to be attainable by procedures based on the limited information maximum likelihood estimator. The bounds are obtained by characterizing the limiting experiment associated with the model induced by the rotation invariance restriction.

ESTIMATION OF THE CHANGE POINT OF THE PROCESS FRACTION NONCONFORMING IN SPC APPLICATIONS

2005 ◽  
Vol 12 (02) ◽  
pp. 95-110 ◽  
Author(s):  
MARCUS B. PERRY ◽  
JOSEPH J. PIGNATIELLO
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Control Chart ◽  
Change Point ◽  
Control Charts ◽  
Process Change ◽  
Likelihood Estimator ◽  
Ewma Control Chart ◽  
Point Estimator ◽  
Point Estimators

Knowing when a process has changed would simplify the search for and identification of the special cause. In this paper, we compare the maximum likelihood estimator (MLE) of the process change point (that is, when the process changed) to built-in change point estimators from binomial CUSUM and EWMA control charts. We conclude that it is better to use the maximum likelihood change point estimator when a CUSUM or EWMA control chart signals a change in the process fraction nonconforming. The results show that the MLE provides process engineers with an accurate and useful estimate of the last subgroup from the unchanged process.

scholarly journals Estimation of sensitivity and specificity and calculation of sample size for a validation study with stratified sampling

2020 ◽  
Author(s):  
Kiyoshi Kubota ◽  
Masao Iwagami ◽  
Takuhiro Yamaguchi
Keyword(s):  
Sample Size ◽  
Sensitivity And Specificity ◽  
Validation Study ◽  
Predictive Value ◽  
Validation Studies ◽  
Bootstrap Method ◽  
Stratified Sampling ◽  
Delta Method ◽  
Estimate Sample Size ◽  
The Bootstrap Method

Abstract Background:We propose and evaluate the approximation formulae for the 95% confidence intervals (CIs) of the sensitivity and specificity and a formula to estimate sample size in a validation study with stratified sampling where positive samples satisfying the outcome definition and negative samples that do not are selected with different extraction fractions. Methods:We used the delta method to derive the approximation formulae for estimating the sensitivity and specificity and their CIs. From those formulae, we derived the formula to estimate the size of negative samples required to achieve the intended precision and the formula to estimate the precision for a negative sample size arbitrarily selected by the investigator. We conducted simulation studies in a population where 4% were outcome definition positive, the positive predictive value (PPV)=0.8, and the negative predictive value (NPV)=0.96, 0.98 and 0.99. The size of negative samples, n0, was either selected to make the 95% CI fall within ± 0.1, 0.15 and 0.2 or set arbitrarily as 150, 300 and 600. We assumed a binomial distribution for the positive and negative samples. The coverage of the 95% CIs of the sensitivity and specificity was calculated as the proportion of CIs including the sensitivity and specificity in the population, respectively. For selected studies, the coverage was also estimated by the bootstrap method. The sample size was evaluated by examining whether the observed precision was within the pre-specified value.Results:For the sensitivity, the coverage of the approximated 95% CIs was larger than 0.95 in most studies but in 9 of 18 selected studies derived by the bootstrap method. For the specificity, the coverage of the approximated 95% CIs was approximately 0.93 in most studies, but the coverage was more than 0.95 in all 18 studies derived by the bootstrap method. The calculated size of negative samples yielded precisions within the pre-specified values in most of the studies.Conclusion:The approximation formulae for the 95% CIs of the sensitivity and specificity for stratified validation studies are presented. These formulae will help in conducting and analysing validation studies with stratified sampling.

scholarly journals Estimation a Stress-Strength Model for P (Yr:n1 < Xk:n2 ) Using the Lindley Distribution

2017 ◽  
Vol 40 (1) ◽  
pp. 105-121 ◽  
Author(s):  
Marwa Khalil
Keyword(s):  
Maximum Likelihood ◽  
Simulation Study ◽  
Real Data ◽  
Minimum Variance ◽  
Strength Model ◽  
Practical Application ◽  
Likelihood Estimator ◽  
Lindley Distribution ◽  
Minimum Variance Unbiased Estimator ◽  
Proposed Model

The problem of estimation reliability in a multicomponent stress-strength model, when the system consists of k components have strength each compo- nent experiencing a random stress, is considered in this paper. The reliability of such a system is obtained when strength and stress variables are given by Lindley distribution. The system is regarded as alive only if at least r out of k (r < k) strength exceeds the stress. The multicomponent reliability of the system is given by Rr,k . The maximum likelihood estimator (M LE), uniformly minimum variance unbiased estimator (UMVUE) and Bayes esti- mator of Rr,k are obtained. A simulation study is performed to compare the different estimators of Rr,k . Real data is used as a practical application of the proposed model.

scholarly journals The Validity of the Coalescent Approximation for Large Samples

2017 ◽  
Author(s):  
Andrew Melfi ◽  
Divakar Viswanath
Keyword(s):  
Sample Size ◽  
Population Size ◽  
Exponential Growth ◽  
Asymptotic Theory ◽  
Triple Collision ◽  
Demographic Models ◽  
Large Samples ◽  
Population Sizes ◽  
Sample Frequency ◽  
Haploid Population

AbstractThe Kingman coalescent, widely used in genetics, is known to be a good approximation when the sample size is small relative to the population size. In this article, we investigate how large the sample size can get without violating the coalescent approximation. If the haploid population size is 2N, we prove that for samples of size N1/3−ϵ, ϵ > 0, coalescence under the Wright-Fisher (WF) model converges in probability to the Kingman coalescent in the limit of large N. For samples of size N2/5−ϵ or smaller, the WF coalescent converges to a mixture of the Kingman coalescent and what we call the mod-2 coalescent. For samples of size N1/2 or larger, triple collisions in the WF genealogy of the sample become important. The sample size for which the probability of conformance with the Kingman coalescent is 95% is found to be 1.47 × N0.31 for N ∈ [103, 105], showing the pertinence of the asymptotic theory. The probability of no triple collisions is found to be 95% for sample sizes equal to 0.92 × N0.49, which too is in accord with the asymptotic theory.Varying population sizes are handled using algorithms that calculate the probability of WF coalescence agreeing with the Kingman model or taking place without triple collisions. For a sample of size 100, the probabilities of coalescence according to the Kingman model are 2%, 0%, 1%, and 0% in four models of human population with constant N, constant N except for two bottlenecks, recent exponential growth, and increasing recent exponential growth, respectively. For the same four demographic models and the same sample size, the probabilities of coalescence with no triple collision are 92%, 73%, 88%, and 87%, respectively. Visualizations of the algorithm show that even distant bottlenecks can impede agreement between the coalescent and the WF model.Finally, we prove that the WF sample frequency spectrum for samples of size N1/3−ϵ or smaller converges to the classical answer for the coalescent.

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