scholarly journals Bayesian Inference for the Parameters of Kumaraswamy Distribution via Ranked Set Sampling

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1170
Author(s):  
Huanmin Jiang ◽  
Wenhao Gui
Keyword(s):  
Real Life ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Interval Length ◽  
Kumaraswamy Distribution ◽  
Credible Intervals ◽  
Average Confidence ◽  
Estimated Risk ◽  
Interval Estimators ◽  
Point Estimators

In this paper, we address the estimation of the parameters for a two-parameter Kumaraswamy distribution by using the maximum likelihood and Bayesian methods based on simple random sampling, ranked set sampling, and maximum ranked set sampling with unequal samples. The Bayes loss functions used are symmetric and asymmetric. The Metropolis-Hastings-within-Gibbs algorithm was employed to calculate the Bayes point estimates and credible intervals. We illustrate a simulation experiment to compare the implications of the proposed point estimators in sense of bias, estimated risk, and relative efficiency as well as evaluate the interval estimators in terms of average confidence interval length and coverage percentage. Finally, a real-life example and remarks are presented.

scholarly journals Permutation Tests for Two-sample Location Problem Under Extreme Ranked Set Sampling

2020 ◽  
pp. 387-408
Author(s):  
Monjed H. Samuh ◽  
Ridwan A. Sanusi
Keyword(s):  
Statistical Power ◽  
Permutation Test ◽  
Real Life ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Test Statistics ◽  
Empirical Coverage ◽  
Expected Length ◽  
Permutation Problem ◽  
Extreme Ranked Set Sampling

In this paper, permutation test of comparing two-independent samples is investigated in the context of extreme ranked set sampling (ERSS). Three test statistics are proposed. The statistical power of these new test statistics are evaluated numerically. The results are compared with the statistical power of the classical independent two-sample $t$-test, Mann-Whitney $U$ test, and the usual two-sample permutation test under simple random sampling (SRS). In addition, the method of computing a confidence interval for the two-sample permutation problem under ERSS is explained. The performance of this method is compared with the intervals obtained by SRS and Mann-Whitney procedures in terms of empirical coverage probability and expected length. The comparison shows that the proposed statistics outperform their counterparts. Finally, the application of the proposed statistics is illustrated using a real life example.

scholarly journals The Efficiency Comparison and Application of Proposed Rhombus Ranked Set Sampling

2021 ◽  
pp. 65-78
Author(s):  
Mishal Choudri ◽  
Nadia Saeed ◽  
Kanwal Saleem
Keyword(s):  
Probability Distributions ◽  
Real Life ◽  
Secondary Data ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Population Means ◽  
Zn Concentration ◽  
The Family ◽  
Efficiency Comparison ◽  
Extreme Ranked Set Sampling

A new scheme ‘Rhombus Ranked Set Sampling’ (RRSS) is developed in this research together with its properties for estimating the population means. Mathematical validation along with the simulation evaluation is presented. The proposed method is an addition to the family of different sampling methods and generalization of ‘Folded Ranked Set Sampling’ (FRSS). For the simulation process, nine probability distributions are considered for the efficiency comparison of proposed scheme from which four are symmetric and rest are asymmetric among which Weibull and beta distributions which are used twice, unlike parametric values. (Al-Naseer, 2007 and Bani-Mustafa, 2011). Through simulation processes, it is observed that RRSS is competent and more reliable relative to simple random sampling (SRS), ranked set sampling (RSS) and folded ranked set sampling (FRSS). It is noted that for all the underlying distributions, an increase in the efficiency of Rhombus Ranked Set Sampling (RRSS) is achieved via increasing the size of the sample ‘p’. Besides the efficiency comparison, consistency of the proposed method is also valued by using Co-efficient of Variation (CV).  Secondary data on zinc (Zn) concentration and lead (Pb) contamination in different parts and tissues of freshwater fish was collected to illustrate the evaluation of RRSS against SRS, RSS, FRSS and ERSS (extreme ranked set sampling). The results obtained through real life illustration defend the simulation study and hence indicates that the RRSS estimator is efficient substitute for existing methods (Al-Omari, 2011).

scholarly journals Comparison of Variance Estimators for Systematic Environmental Sample Surveys: Considerations for Post-Stratified Estimation

Forests ◽  
2021 ◽  
Vol 12 (6) ◽  
pp. 772
Author(s):  
Bryce Frank ◽  
Vicente J. Monleon
Keyword(s):  
Random Sampling ◽  
Simple Random Sampling ◽  
National Forest Inventory ◽  
Point Estimation ◽  
Systematic Sampling ◽  
Sampling Variance ◽  
Variance Estimators ◽  
The Past ◽  
Point Estimators ◽  
Species Specific

The estimation of the sampling variance of point estimators under two-dimensional systematic sampling designs remains a challenge, and several alternative variance estimators have been proposed in the past few decades. In this work, we compared six alternative variance estimators under Horvitz-Thompson (HT) and post-stratification (PS) point estimation regimes. We subsampled a multitude of species-specific forest attributes from a large, spatially balanced national forest inventory to compare the variance estimators. A variance estimator that assumes a simple random sampling design exhibited positive relative bias under both HT and PS point estimation regimes ranging between 1.23 to 1.88 and 1.11 to 1.78 for HT and PS, respectively. Alternative estimators reduced this positive bias with relative biases ranging between 1.01 to 1.66 and 0.90 to 1.64 for HT and PS, respectively. The alternative estimators generally obtained improved efficiencies under both HT and PS, with relative efficiency values ranging between 0.68 to 1.28 and 0.68 to 1.39, respectively. We identified two estimators as promising alternatives that provide clear improvements over the simple random sampling estimator for a wide variety of attributes and under HT and PS estimation regimes.

scholarly journals Interval estimation of the overall treatment effect in random-effects meta-analyses: Recommendations from a simulation study comparing frequentist, Bayesian, and bootstrap methods

2020 ◽  
Author(s):  
Frank Weber ◽  
Guido Knapp ◽  
Anne Glass ◽  
Günther Kundt ◽  
Katja Ickstadt
Keyword(s):  
Literature Review ◽  
Random Effects ◽  
Simulation Study ◽  
Treatment Effect ◽  
Profile Likelihood ◽  
Meta Analysis ◽  
Artery Bypass ◽  
Interval Length ◽  
Interval Estimators ◽  
Meta Analyses

There exists a variety of interval estimators for the overall treatment effect in a random-effects meta-analysis. A recent literature review summarizing existing methods suggested that in most situations, the Hartung-Knapp/Sidik-Jonkman (HKSJ) method was preferable. However, a quantitative comparison of those methods in a common simulation study is still lacking. Thus, we conduct such a simulation study for continuous and binary outcomes, focusing on the medical field for application.Based on the literature review and some new theoretical considerations, a practicable number of interval estimators is selected for this comparison: the classical normal-approximation interval using the DerSimonian-Laird heterogeneity estimator, the HKSJ interval using either the Paule-Mandel or the Sidik-Jonkman heterogeneity estimator, the Skovgaard higher-order profile likelihood interval, a parametric bootstrap interval, and a Bayesian interval using different priors. We evaluate the performance measures (coverage and interval length) at specific points in the parameter space, i.e. not averaging over a prior distribution. In this sense, our study is conducted from a frequentist point of view.We confirm the main finding of the literature review, the general recommendation of the HKSJ method (here with the Sidik-Jonkman heterogeneity estimator). For meta-analyses including only 2 studies, the high length of the HKSJ interval limits its practical usage. In this case, the Bayesian interval using a weakly informative prior for the heterogeneity may help. Our recommendations are illustrated using a real-world meta-analysis dealing with the efficacy of an intramyocardial bone marrow stem cell transplantation during coronary artery bypass grafting.

Stratified Ranked Set Sampling With Missing Observations for Estimating the Difference

2022 ◽  
pp. 209-232
Author(s):  
Carlos N. Bouza-Herrera
Keyword(s):  
Random Sampling ◽  
Real Data ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Missing Observations ◽  
Seminal Paper ◽  
Sample Error ◽  
The Difference ◽  
Stratified Ranked Set Sampling ◽  
Stratified Model

The authors develop the estimation of the difference of means of a pair of variables X and Y when we deal with missing observations. A seminal paper in this line is due to Bouza and Prabhu-Ajgaonkar when the sample and the subsamples are selected using simple random sampling. In this this chapter, the authors consider the use of ranked set-sampling for estimating the difference when we deal with a stratified population. The sample error is deduced. Numerical comparisons with the classic stratified model are developed using simulated and real data.

Ratio-Type Estimation Using Scrabled Auxiliary Variables in Stratification Under Simple Random Sampling and Ranked Set Sampling

2022 ◽  
pp. 62-85
Author(s):  
Carlos N. Bouza-Herrera ◽  
Jose M. Sautto ◽  
Khalid Ul Islam Rather
Keyword(s):  
Random Sampling ◽  
Mean Squared Error ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Auxiliary Variables ◽  
Mild Conditions ◽  
Squared Error ◽  
The Mean ◽  
Better Than

This chapter introduced basic elements on stratified simple random sampling (SSRS) on ranked set sampling (RSS). The chapter extends Singh et al. results to sampling a stratified population. The mean squared error (MSE) is derived. SRS is used independently for selecting the samples from the strata. The chapter extends Singh et al. results under the RSS design. They are used for developing the estimation in a stratified population. RSS is used for drawing the samples independently from the strata. The bias and mean squared error (MSE) of the developed estimators are derived. A comparison between the biases and MSEs obtained for the sampling designs SRS and RSS is made. Under mild conditions the comparisons sustained that each RSS model is better than its SRS alternative.

scholarly journals Estimation in meta-analyses of response ratios

2020 ◽  
Vol 20 (1) ◽  
Author(s):  
Ilyas Bakbergenuly ◽  
David C. Hoaglin ◽  
Elena Kulinskaya
Keyword(s):  
Meta Analysis ◽  
Weighted Average ◽  
Effective Sample Size ◽  
Logarithmic Scale ◽  
Response Ratio ◽  
Effect Measure ◽  
Interval Estimators ◽  
Point Estimators ◽  
Meta Analyses ◽  
And Control

Abstract Background For outcomes that studies report as the means in the treatment and control groups, some medical applications and nearly half of meta-analyses in ecology express the effect as the ratio of means (RoM), also called the response ratio (RR), analyzed in the logarithmic scale as the log-response-ratio, LRR. Methods In random-effects meta-analysis of LRR, with normal and lognormal data, we studied the performance of estimators of the between-study variance, τ2, (measured by bias and coverage) in assessing heterogeneity of study-level effects, and also the performance of related estimators of the overall effect in the log scale, λ. We obtained additional empirical evidence from two examples. Results The results of our extensive simulations showed several challenges in using LRR as an effect measure. Point estimators of τ2 had considerable bias or were unreliable, and interval estimators of τ2 seldom had the intended 95% coverage for small to moderate-sized samples (n<40). Results for estimating λ differed between lognormal and normal data. Conclusions For lognormal data, we can recommend only SSW, a weighted average in which a study’s weight is proportional to its effective sample size, (when n≥40) and its companion interval (when n≥10). Normal data posed greater challenges. When the means were far enough from 0 (more than one standard deviation, 4 in our simulations), SSW was practically unbiased, and its companion interval was the only option.

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