scholarly journals An Estimation of Sensitive Attribute Applying Geometric Distribution under Probability Proportional to Size Sampling

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1102
Author(s):  
Gi-Sung Lee ◽  
Ki-Hak Hong ◽  
Chang-Kyoon Son
Keyword(s):  
Sampling Methods ◽  
Geometric Distribution ◽  
Equal Probability ◽  
Two Stage ◽  
Generalized Model ◽  
Sampling Schemes ◽  
Variance Estimators ◽  
Numerical Studies ◽  
Sensitive Attribute ◽  
S Model

In this paper, we extended Yennum et al.’s model, in which geometric distribution is used as a randomization device for a population that consists of different-sized clusters, and clusters are obtained by probability proportional to size (PPS) sampling. Estimators of a sensitive parameter, their variances, and their variance estimators are derived under PPS sampling and equal probability two-stage sampling, respectively. We also applied these sampling schemes to Yennum et al.’s generalized model. Numerical studies were carried out to compare the efficiencies of the proposed sampling methods for each case of Yennum et al.’s model and Yennum et al.’s generalized model.

Dealing with Inaccurate Measures of Size in Two-Stage Probability Proportional to Size Sample Designs: Applications in African Household Surveys

2020 ◽  
Author(s):  
Graham Kalton ◽  
Ismael Flores Cervantes ◽  
Carlos Arieira ◽  
Mike Kwanisai ◽  
Elizabeth Radin ◽  
...  
Keyword(s):  
Final Stage ◽  
Population Based ◽  
Equal Probability ◽  
Household Surveys ◽  
Sample Design ◽  
African Countries ◽  
Two Stage ◽  
Fixed Sample ◽  
Multi Stage ◽  
Weighting Adjustments

Abstract The units at the early stages of multi-stage area samples are generally sampled with probabilities proportional to their estimated sizes (PPES). With such a design, an overall equal probability (EP) sample design would yield a constant number of final stage units from each final stage cluster if the measures of size used in the PPES selection at each sampling stage were directly proportional to the number of final stage units. However, there are often sizable relative differences between the measures of size used in the PPES selections and the number of final stage units. Two common approaches for dealing with these differences are: (1) to retain a self-weighting sample design, allowing the sample sizes to vary across the sampled primary sampling units (PSUs) and (2) to retain the fixed sample size in each PSU and to compensate for the unequal selection probabilities by weighting adjustments in the analyses. This article examines these alternative designs in the context of two-stage sampling in which PSUs are sampled with PPES at the first stage, and an equal probability sample of final stage units is selected from each sampled PSU at the second stage. Two-stage sample designs of this type are used for household surveys in many countries. The discussion is illustrated with data from the Population-based HIV Impact Assessment surveys that were conducted using this design in several African countries.

Forest inventory: further results for optimal sampling schemes based on the anticipated variance

2001 ◽  
Vol 31 (10) ◽  
pp. 1845-1853 ◽  
Author(s):  
Daniel Mandallaz ◽  
Adrian Lanz
Keyword(s):  
Forest Inventory ◽  
Optimal Allocation ◽  
Optimality Criterion ◽  
Second Phase ◽  
Optimal Sampling ◽  
Two Stage ◽  
Two Phase ◽  
Sampling Density ◽  
Sampling Schemes ◽  
Inclusion Probabilities

This work presents optimal allocation rules for two-phase, two-stage sampling schemes in which the sampling density and the costs of the second phase can vary over domains. The optimality criterion is based on the anticipated variance. It also gives an improved version of discrete approximation for the resulting inclusion probabilities. An example illustrates the theory.

scholarly journals Experimental and Numerical Studies of Two-Stage Ethane-Air Flames

1999 ◽  
Author(s):  
M. M. Y. Waly ◽  
S. C. Li ◽  
F. A. Williams
Keyword(s):  
Chemical Kinetic ◽  
Two Stage ◽  
Nox Formation ◽  
Pollutant Formation ◽  
Numerical Studies ◽  
Numerical Predictions ◽  
Air Stream ◽  
Stage Combustion ◽  
Reduce Emissions ◽  
Flame Chemistry

This paper reports results of experimental and numerical investigations on ethane-air two-stage combustion in a counterflow burner where the fuel stream, which is partially premixed with air for equivalence ratios from 1.6 to 3.0, flows against a pure air stream. Similar to methane, the two-stage ethane combustion exhibits a green fuel-rich premixed flame and a blue diffusion flame. Flame structures, including concentration profiles of stable intermediate species such as C2H4, C2H2 and CH4, are measured by a gas chromatography and are calculated by numerical integrations of the conservation equations employing an updated elementary chemical-kinetic data base. The implications of the results from these experimental measurements and numerical predictions are summarized, the flame chemistry of ethane two-stage combustion at different degrees of premixing (or equivalence ratio) is discussed, and the relationship between NOx formation and the degree of premixing is established. The present work helps to increase understanding of flame chemistry of hydrocarbon fuels, identify important reactions for pollutant formation and suggest means to reduce emissions.

scholarly journals A flexible ranked set sampling schemes: Statistical analysis on scale parameter

2020 ◽  
Vol 9 (1) ◽  
pp. 189-203
Author(s):  
Abbas Eftekharian ◽  
Mostafa Razmkhah ◽  
Jafar Ahmadi
Keyword(s):  
Maximum Likelihood ◽  
Existence And Uniqueness ◽  
Sampling Methods ◽  
Scale Parameter ◽  
Likelihood Estimation ◽  
Ranked Set Sampling ◽  
Likelihood Estimator ◽  
Normal Distributions ◽  
Sampling Schemes ◽  
The Cost

A flexible ranked set sampling scheme including some various existing sampling methods  is proposed. This scheme may be used to minimize the  error of ranking and the cost of sampling. Based on the data obtained from this scheme, the maximum likelihood estimation as well as the Fisher information are studied for the  scale family of distributions. The existence and uniqueness of  the  maximum likelihood estimator  of the scale parameter of the exponential  and  normal distributions are  investigated. Moreover, the optimal scheme is derived via simulation and numerical computations.

scholarly journals Efficiency of Variance Estimators for Two-stage PPS Systematic Sampling

2013 ◽  
Vol 26 (6) ◽  
pp. 1033-1041
Author(s):  
Young-Won Kim ◽  
Yeny Kim ◽  
Hye-Eun Han ◽  
Eun-Sun Kwak
Keyword(s):  
Systematic Sampling ◽  
Two Stage ◽  
Variance Estimators

scholarly journals Two-stage sector sampling for estimating small woodlot attributes

2011 ◽  
Vol 41 (9) ◽  
pp. 1819-1826 ◽  
Author(s):  
Piermaria Corona ◽  
Lorenzo Fattorini ◽  
Sara Franceschi
Keyword(s):  
Large Scale ◽  
Sampling Strategy ◽  
Sampling Variance ◽  
Sampling Strategies ◽  
Fixed Size ◽  
Two Stage ◽  
Sampling Schemes ◽  
Second Stage ◽  
Forest Inventories ◽  
Plot Sampling

A two-stage sampling strategy is proposed to assess small woodlots outside the forests scattered on extensive territories. The first stage is performed to select a sample of small woodlots using fixed-size sampling schemes, and the second stage is performed to sample trees within woodlots selected at first stage. Usually, fixed- or variable-area plots are adopted to sample trees. However, the use of plot sampling in small patches such as woodlots is likely to induce a relevant amount of bias owing to edge effects. In this framework, sector sampling proves to be particularly effective. The present paper investigates the statistical properties of two-stage sampling strategies for estimating forest attributes of woodlot populations when sector sampling is adopted at the second stage. A two-stage estimator of population totals is derived together with a conservative estimator of its sampling variance. By means of a simulation study, the performance of the proposed estimator is checked and compared with that achieved using traditional plot sampling with edge corrections. Simulation results prove the adequacy of sector sampling and provide some guidelines for the effective planning of the strategy. In some countries, the proposed strategy can be performed with few modifications within the framework of large-scale forest inventories.

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