Optimum Exponential Ratio Type Estimators for Estimating the Population Mean

2021 ◽  
Vol 8 (2) ◽  
pp. 73-82
Keyword(s):  
Population Mean

Reversion Toward the Mean Independently of Regression Toward the Mean

Methodology ◽  
2009 ◽  
Vol 5 (1) ◽  
pp. 3-6 ◽  
Author(s):  
Merton S. Krause
Keyword(s):  
Random Error ◽  
Evaluation Studies ◽  
Internal Validity ◽  
Intervention Evaluation ◽  
Population Mean ◽  
Experimental Intervention ◽  
Sample Data ◽  
The Mean ◽  
Regression Toward The Mean

There is another important artifactual contributor to the apparent improvement of persons subjected to an experimental intervention which may be mistaken for regression toward the mean. This is the phenomenon of random error and extreme selection, which does not at all involve the population regression of posttest on pretest scores but involves a quite different and independent reversion of subjects’ scores toward the population mean. These two independent threats to the internal validity of intervention evaluation studies, however, can be detected and differentiated on the sample data of such studies.

Has the Time Come to Employ Population and Individual Bioequivalence for the Evaluation of Generics?

2020 ◽  
Vol 21 (2) ◽  
pp. 112-125
Author(s):  
Francis Micheal ◽  
Mohanlal Sayana ◽  
Rajendra Prasad ◽  
Balamurali Musuvathi Motilal
Keyword(s):  
Therapeutic Index ◽  
Bioequivalence Study ◽  
Open Label ◽  
Statistical Parameters ◽  
Population Mean ◽  
Average Bioequivalence ◽  
Individual Bioequivalence ◽  
Population Bioequivalence ◽  
Enteric Coated ◽  
Bioequivalence Assessment

Background: Bioequivalence studies are a vital part of drug development. The average bioequivalence approach is the standard method of assessment to conclude whether the generic product is bioequivalent to the innovator product. Of late, debates are on whether the average bioequivalence approach adequately addresses drug interchangeability as it considers only population mean for the evaluation especially when highly variable drug products and narrow therapeutic index drugs are dealt with. Hence, the alternative approaches like population bioequivalence and individual bioequivalence assessment approaches emerge as they consider inter/intra-subject variance and subject- by-formulation variance along with population mean. Objectives: The objective of the study was to apply different bioequivalence assessment approaches in a replicate bioequivalence study to evaluate the drug interchangeability. Methods: This was an open-label, single-dose, randomized, balanced, two-treatment, three-period, three-sequence, partial replicate crossover bioequivalence study of omeprazole enteric-coated tablet 20 mg conducted on 48 normal healthy subjects under fed conditions. The plasma concentration of omeprazole was analyzed by a validated bioanalytical method to determine the pharmacokinetic and statistical parameters to assess average bioequivalence, population bioequivalence, and individual bioequivalence. Results: In this study, test formulation was shown to be bio-inequivalent to the reference formulation by average bioequivalence, population bioequivalence, and individual bioequivalence approaches. Conclusion: The outcome of the evaluation clearly states that the bioequivalence outcome of all these approaches are the same. Obviously, it does not mean that these three approaches provide the same outcome though the consideration of variances varies. Certainly, population bioequivalence and individual bioequivalence approach will be more accurate for the assessment of drug interchangeability.

scholarly journals Understanding variability in greenhouse gas emission estimates of smallholder dairy farms in Indonesia

2021 ◽  
Author(s):  
Titis Apdini ◽  
Windi Al Zahra ◽  
Simon J. Oosting ◽  
Imke J. M. de Boer ◽  
Marion de Vries ◽  
...  
Keyword(s):  
Greenhouse Gas ◽  
Rainy Season ◽  
Greenhouse Gas Emission ◽  
Dairy Farms ◽  
Dry Season ◽  
Enteric Fermentation ◽  
Tropical Regions ◽  
Population Mean ◽  
Smallholder Dairy ◽  
Smallholder Dairy Farms

Abstract Purpose Life cycle assessment studies on smallholder farms in tropical regions generally use data that is collected at one moment in time, which could hamper assessment of the exact situation. We assessed seasonal differences in greenhouse gas emissions (GHGEs) from Indonesian dairy farms by means of longitudinal observations and evaluated the implications of number of farm visits on the variance of the estimated GHGE per kg milk (GHGEI) for a single farm, and the population mean. Methods An LCA study was done on 32 smallholder dairy farms in the Lembang district area, West Java, Indonesia. Farm visits (FVs) were performed every 2 months throughout 1 year: FV1–FV3 (rainy season) and FV4–FV6 (dry season). GHGEs were assessed for all processes up to the farm-gate, including upstream processes (production and transportation of feed, fertiliser, fuel and electricity) and on-farm processes (keeping animals, manure management and forage cultivation). We compared means of GHGE per unit of fat-and-protein-corrected milk (FPCM) produced in the rainy and the dry season. We evaluated the implication of number of farm visits on the variance of the estimated GHGEI, and on the variance of GHGE from different processes. Results and discussion GHGEI was higher in the rainy (1.32 kg CO2-eq kg−1 FPCM) than in the dry (0.91 kg CO2-eq kg−1 FPCM) season (P < 0.05). The between farm variance was 0.025 kg CO2-eq kg−1 FPCM in both seasons. The within farm variance in the estimate for the single farm mean decreased from 0.69 (1 visit) to 0.027 (26 visits) kg CO2-eq kg−1 FPCM (rainy season), and from 0.32 to 0.012 kg CO2-eq kg−1 FPCM (dry season). The within farm variance in the estimate for the population mean was 0.02 (rainy) and 0.01 (dry) kg CO2-eq kg−1 FPCM (1 visit), and decreased with an increase in farm visits. Forage cultivation was the main source of between farm variance, enteric fermentation the main source of within farm variance. Conclusions The estimated GHGEI was significantly higher in the rainy than in the dry season. The main contribution to variability in GHGEI is due to variation between observations from visits to the same farm. This source of variability can be reduced by increasing the number of visits per farm. Estimates for variation within and between farms enable a more informed decision about the data collection procedure.

scholarly journals Neutrosophic ratio-type estimators for estimating the population mean

2021 ◽  
Author(s):  
Zaigham Tahir ◽  
Hina Khan ◽  
Muhammad Aslam ◽  
Javid Shabbir ◽  
Yasar Mahmood ◽  
...  
Keyword(s):  
Minimum Mean Square Error ◽  
Auxiliary Information ◽  
Population Parameter ◽  
Uncertain Information ◽  
Population Mean ◽  
Classical Statistics ◽  
Neutrosophic Statistics ◽  
The Mean ◽  
Type Data ◽  
First Time

AbstractAll researches, under classical statistics, are based on determinate, crisp data to estimate the mean of the population when auxiliary information is available. Such estimates often are biased. The goal is to find the best estimates for the unknown value of the population mean with minimum mean square error (MSE). The neutrosophic statistics, generalization of classical statistics tackles vague, indeterminate, uncertain information. Thus, for the first time under neutrosophic statistics, to overcome the issues of estimation of the population mean of neutrosophic data, we have developed the neutrosophic ratio-type estimators for estimating the mean of the finite population utilizing auxiliary information. The neutrosophic observation is of the form $${Z}_{N}={Z}_{L}+{Z}_{U}{I}_{N}\, {\rm where}\, {I}_{N}\in \left[{I}_{L}, {I}_{U}\right], {Z}_{N}\in [{Z}_{l}, {Z}_{u}]$$ Z N = Z L + Z U I N where I N ∈ I L , I U , Z N ∈ [ Z l , Z u ] . The proposed estimators are very helpful to compute results when dealing with ambiguous, vague, and neutrosophic-type data. The results of these estimators are not single-valued but provide an interval form in which our population parameter may have more chance to lie. It increases the efficiency of the estimators, since we have an estimated interval that contains the unknown value of the population mean provided a minimum MSE. The efficiency of the proposed neutrosophic ratio-type estimators is also discussed using neutrosophic data of temperature and also by using simulation. A comparison is also conducted to illustrate the usefulness of Neutrosophic Ratio-type estimators over the classical estimators.

scholarly journals Estimation of Population Mean by Using a Generalized Family of Estimators Under Classical Ranked Set Sampling

2021 ◽  
Vol 8 (1) ◽  
pp. 1948184
Author(s):  
Asad Ali ◽  
Muhammad Moeen Butt ◽  
Kanwal Iqbal ◽  
Muhammad Hanif ◽  
Muhammad Zubair
Keyword(s):  
Ranked Set Sampling ◽  
Population Mean
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