On Fixed width Confidence Interval Estimation of the Common Mean in Symmetric Multivariate Normal Distribution

2019 ◽  
Vol 71 (2) ◽  
pp. 113-120
Author(s):  
Uttam Bandyopadhyay ◽  
Pritam Sarkar
Keyword(s):  
Confidence Interval ◽  
Sequential Sampling ◽  
Interval Estimation ◽  
Multivariate Normal ◽  
Common Mean ◽  
Multivariate Normal Mean ◽  
Normal Mean ◽  
The Common ◽  
Sampling Procedures ◽  
Width Confidence Interval

This article deals with purely and accelerated sequential sampling procedures to find fixed-width confidence interval of completely symmetric multivariate normal mean. Procedures are studied asymptotically and are evaluated numerically. AMS 2000 subject classification: 62F25 62H12

Standardized likelihood ratio test for comparing several log-normal means and confidence interval for the common mean

2015 ◽  
Vol 26 (6) ◽  
pp. 2919-2937 ◽  
Author(s):  
K Krishnamoorthy ◽  
Evrim Oral
Keyword(s):  
Confidence Interval ◽  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
Ratio Test ◽  
Normal Distributions ◽  
Generalized Confidence Interval ◽  
Common Mean ◽  
Coverage Probabilities ◽  
The Common ◽  
Log Normal

Standardized likelihood ratio test (SLRT) for testing the equality of means of several log-normal distributions is proposed. The properties of the SLRT and an available modified likelihood ratio test (MLRT) and a generalized variable (GV) test are evaluated by Monte Carlo simulation and compared. Evaluation studies indicate that the SLRT is accurate even for small samples, whereas the MLRT could be quite liberal for some parameter values, and the GV test is in general conservative and less powerful than the SLRT. Furthermore, a closed-form approximate confidence interval for the common mean of several log-normal distributions is developed using the method of variance estimate recovery, and compared with the generalized confidence interval with respect to coverage probabilities and precision. Simulation studies indicate that the proposed confidence interval is accurate and better than the generalized confidence interval in terms of coverage probabilities. The methods are illustrated using two examples.

3 Power and sample size for ABE in the 2× 2 design Here we give formulae for the calculation of the power of the TOST procedure assuming that there are in total n subjects in the 2× 2 trial. Suppose that the null hypotheses given below are to be tested using a 100(1 − α)% two-sided confidence interval and a power of (1 − β) is required to reject these hypotheses when they are false. H :µ ≤− ln 1.25 H :µ ≥ ln 1.25. Let us define x to be a random variable that has a noncentral t-distribution with df degrees of freedom and noncentrality parameter nc, i.e., x ∼ t(df,nc). The cumulative distribution function of x is defined as CDF(t,df,nc) = Pr(x≤ t). Assume that the power is to be calculated using log(AUC). If σ is the common within-subject variance for T and R for log(AUC), and n/2 subjects are allocated to each of the sequences RT and TR, then 1−β = CDF(t , df,nc )−CDF(t , df,nc ) (7.1) where √ n(log(µ )− log(0.8)) nc = 2σ √ n(log(µ )− log(1.25)) nc = 2σ √ (n− 2)(nc −nc = ) df 2t and t is the 100(1 − α)% point of the central t-distribution on n− 2 degrees of freedom. Some SAS code to calculate the power for an ABE 2 × 2 trial is given below, where the required input variables are α, σ value of the ratio µ and n, the total number of subjects in the trial.

2003 ◽  
pp. 361-361
Keyword(s):  
Distribution Function ◽  
Confidence Interval ◽  
Degrees Of Freedom ◽  
Random Variable ◽  
Noncentrality Parameter ◽  
Cumulative Distribution ◽  
Total N ◽  
The Common ◽  
Input Variables ◽  
T Distribution

Systematic Review and Meta-Analysis on Using Acupressure to Promote the Health of Older Adults

2019 ◽  
Vol 39 (10) ◽  
pp. 1144-1152 ◽  
Author(s):  
Meng-Chin Chen ◽  
Li-Yen Yang ◽  
Kuei-Min Chen ◽  
Hui-Fen Hsu
Keyword(s):  
Quality Of Life ◽  
Systematic Review ◽  
Older Adults ◽  
Health Promotion ◽  
Confidence Interval ◽  
Meta Analysis ◽  
Common Elements ◽  
The Common ◽  
Moderate Effect

Acupressure is noninvasive, safe, and appropriate for use among older adults. However, there remains little evidence of the common elements that contribute to the effectiveness of acupressure in promoting the health of older adults. A systematic review using meta-analysis was designed to examine the effects of acupressure on the health promotion in older adults. Studies published between 2012 and 2017 were searched for in 11 electronic databases. Acupressure was highly effective for improving sleep quality and cognitive functioning (0.85, 95% confidence interval [CI] = [0.49, 1.22]; 1.23, 95% CI = [0.88, 1.59]). A slight to moderate effect was found in alleviating constipation (0.37, 95% CI = [0.03, 0.71]), and a moderate effect was found for alleviating pain and improving quality of life (0.71, 95% CI = [0.09, 1.32]; 0.59 95% CI = [0.36, 0.82]).

Estimation of the Common Mean of Two Normal Populations Using Two Stage Sampling

1998 ◽  
Vol 48 (1-2) ◽  
pp. 73-82
Author(s):  
Moloy De ◽  
Jyotirmoy Sarkar
Keyword(s):  
Sampling Scheme ◽  
Two Stage ◽  
Unequal Variances ◽  
Common Mean ◽  
Normal Populations ◽  
The Common

We exhibit the superiority of the Graybill- Deal estimator for estimating the common mean of two univariate normal populations with unequal variances, under a two stage sampling scheme. Some properties of the two-stage Graybill-Deal estimator are discussed.

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