Investigation of Accuracy of a Calibrated Estimator of a Ratio by Modelling

Estimator of finite population parameter – ratio of totals of two variables – is investigated by modelling in the case of simple random sampling. Traditional estimator of the ratio is compared with the calibrated estimator of the ratio introduced by Plikusas [1]. The Taylor series expansion of the estimators are used for the expressions of approximate biases and approximate variances [2]. Some estimator of bias is introduced in this paper. Using data of artificial population the accuracy of two estimators of the ratio is compared by modelling. Dependence of the estimates of mean square error of the estimators of the ratio on the correlation coefficient of variables which are used in the numerator and denominator, is also shown in the modelling.

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Poisson Regression-Based Mean Estimator

Mathematical Problems in Engineering ◽

10.1155/2021/9769029 ◽

2021 ◽

Vol 2021 ◽

pp. 1-6

Author(s):

Usman Shahzad ◽

Shabnam Shahzadi ◽

Noureen Afshan ◽

Nadia H. Al-Noor ◽

David Anekeya Alilah ◽

...

Keyword(s):

Regression Model ◽

Mean Square Error ◽

Random Sampling ◽

Poisson Regression ◽

Simple Random Sampling ◽

Mean Square ◽

Poisson Regression Model ◽

The Mean ◽

Ratio Estimators

The most frequent method for modeling count responses in numerous investigations is the Poisson regression model. Under simple random sampling, this paper offers utilizing Poisson regression-based mean estimator and discovers its associated formula of the mean square error (MSE). The MSE of the proposed estimator is compared to the MSE of traditional ratio estimators in theory. As a result of these evaluations, the proposed estimator has been proven to be more efficient than traditional estimators. Furthermore, the practical results corroborated the theoretical findings.

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On the Estimation of Population Mean Under Systematic Sampling Using Auxiliary Attributes

Oriental Journal of Physical Sciences ◽

10.13005/ojps01.0102.05 ◽

2016 ◽

Vol 1 (1-2) ◽

pp. 21-25 ◽

Cited By ~ 3

Author(s):

Usman Shahzad

Keyword(s):

Mean Square Error ◽

Random Sampling ◽

Simple Random Sampling ◽

Sampling Scheme ◽

Systematic Sampling ◽

Mean Square ◽

Numerical Illustration ◽

Systematic Random Sampling ◽

Population Mean ◽

New Family

Naik and Gupta (1996), Singh et al. (2007) and Abd-Elfattah et al. (2010) introduced some estimators for estimating population mean using available auxiliary attributes under simple random sampling scheme. We adapt these estimators under systematic random sampling scheme using available auxiliary attributes. Further, a new family of estimators is proposed for the estimation of population mean under systematic random sampling scheme. The properties such as bias and mean square error of the proposed estimators are derived. From numerical illustration it is shown that proposed estimators are more efficient than the reviewed ones.

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MODEL EVALUASI PEMBELAJARAN AKIDAH DAN AKHLAK DI MADRASAH TSANAWIYAH (MTs)

Jurnal Penelitian dan Evaluasi Pendidikan ◽

10.21831/pep.v20i1.7517 ◽

2016 ◽

Vol 20 (1) ◽

pp. 11-26

Author(s):

Darodjat Darodjat ◽

Darmiyati Zuchdi

Keyword(s):

Root Mean Square Error ◽

Mean Square Error ◽

Content Validity ◽

Random Sampling ◽

Goodness Of Fit ◽

Evaluation Model ◽

Simple Random Sampling ◽

Face Validity ◽

Mean Square ◽

Learning Evaluation

Penelitian ini bertujuan: (1) menghasilkan model evaluasi pembelajaran Akidah dan Akhlak di MTs, (2) menghasilkan instrumen evaluasi yang memiliki reliabilitas dan validitas, (3) mengetahui kelayakan Model Logik Evaluasi Pembelajaran Akidah dan Akhlak (MLEPAA). Penelitian ini menggunakan model Borg dan Gall. Teknik penentuan subjek penelitian untuk unit analisis siswa dengan simple random sampling sejumlah 330 siswa dari tiga MTsN di Kabupaten Banyumas, 3 orang Guru Akidah dan Akhlak, dan 3 orang Kepala MTsN. Teknik pengumpulan data yang digunakan adalah: kuesioner, tes, dan penilaian antarteman. Validitas instrumen meliputi face validity dan content validity, dianalisis dengan expert judgment, validasi konstruk dianalisis dengan konfirmatori faktor analisis (CFA), sedangkan instrumen tes dianalisis dengan bantuan program ITEMAN. Estimasi reliabilitas instrumen menggunakan formula Alpha Cronbach dan reliabilitas interrater menggunakan Cohens’ Kappa dengan program SPSS for Window 16.0. Simpulan penelitian: pertama, model evaluasi yang dihasilkan (MLEPAA) mencakup empat komponen utama, yaitu: input, activities, output, dan outcomes. Kedua, hasil analisis dengan CFA diperoleh indeks: (1) ρ-value > 0,05; (2) Root Mean Square Error of Approximation (RMSEA) < 0,8; dan (3) Goodness of Fit Index (GFI) < 0,90. Ketiga, instrumen yang dikembangkan memenuhi validitas dan reliabilitas yang baik. Keempat, berdasarkan penilaian user, MLEPAA layak digunakan.Kata kunci: model logik, evaluasi pembelajaran Akidah dan Akhlak, MTs AKIDAH AND AKHLAK LEARNING EVALUATION MODEL IN THE MADRASAH TSANAWIYAHAbstractThis study aimed to: (1) develop an evaluation model on Akidah Akhlak subject of Madrasah Tsanawiyah (MTs), (2) generate some instruments of evaluation which have validity and reliability, (3) know a worthiness model evaluation of Akidah Akhlak subject in implementation. This study was a research and development of Borg and Gall model. The subjects were determined by simple random sampling which consisted of 330 students, 3 teachers, and 3 principles in three public Madrasah Tsanawiyah in Banyumas regencies. The data gathering techniques used were questionnaires, tests, and peer assessment. The instrument validation process was carried out in terms of the face validity and content validity through expert judgment, the construct validity through the confirmatory factor analysis (CFA), and test by using ITEMAN program. The instrument reliability was analyzed using the Cronbach's Alpha technique, and inter-rater reliability was assessed using SPSS for Window 16.0. with Cohens' Kappa technique. The results of the research were as follows: firstly, the components of MLEPAA evaluation model consisted of input, activities, output, and outcomes. Secondly, the results of CFA analysis were as follows: (a) Chi-Square, p > 0.05, the acquired value is= 553.72, (b) Goodness of Fit Indices (GFI) must be 0 to 1, the acquired value is = 0.892, and (c) Root Mean Square Error of Approximation (RMSEA) < 0.05, the acquired value is = 0.000. Thirdly, instrument utilized in research had fulfilled reliability and validity. Fourth, based on assessment from user, the MLEPAA was suitable for using in MTs.Keywords: logic model, Akidah Akhlak learning evaluation, MTs

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AN EFFICIENT CLASS OF PRODUCT ESTIMATORS USING MEASURES OF DISPERSIONS

Journal of Science and Arts ◽

10.46939/j.sci.arts-21.2-a03 ◽

2021 ◽

Vol 21 (2) ◽

pp. 347-354

Author(s):

MUHAMMAD IJAZ ◽

TOLGA ZAMAN ◽

BUSHRA HAIDER ◽

SYED MUHAMMAD ASIM

Keyword(s):

Standard Deviation ◽

Mean Square Error ◽

Random Sampling ◽

Simple Random Sampling ◽

Mean Deviation ◽

Mean Square ◽

Sampling Without Replacement ◽

Population Mean ◽

Class Of Estimators ◽

Secondary Information

The study suggests a class of product estimators for estimating the population mean of variable under investigation in simple random sampling without replacement (SRSWOR) scheme when secondary information on standard deviation, mean deviation, and quartile deviation is available. The expression for Bias and Mean Square Error (MSE) has been derived. A comparison is made both theoretically and numerically with other existing product estimators. It is concluded that compared to other product type estimators, suggested class of estimators estimate the population mean more efficiently.

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Dual Use of Auxiliary Information for Estimating the Finite Population Mean under the Stratified Random Sampling Scheme

Journal of Mathematics ◽

10.1155/2021/3860122 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12

Author(s):

Sohaib Ahmad ◽

Sardar Hussain ◽

Muhammad Aamir ◽

Uzma Yasmeen ◽

Javid Shabbir ◽

...

Keyword(s):

Mean Square Error ◽

Simulation Study ◽

Random Sampling ◽

Finite Population ◽

Stratified Random Sampling ◽

Data Sets ◽

Mean Square ◽

Sample Mean ◽

Population Mean ◽

Mean Square Errors

In this paper, we proposed an improved family of estimators for finite population mean under stratified random sampling, which needed a helping variable on the sample mean and rank of the auxiliary variable. The expression of the bias and mean square error of the proposed and existing estimators are computed up to the first-order approximation. The estimators proposed in different situations were investigated and provided a minimum mean square error relative to all other estimators considered. Four actual data sets and simulation studies are carried out to observe the performance of the estimators. For simulation study, R software is used. The mean square errors of all four data sets are minimum and percent relative efficiencies are more than a hundred percent higher than the other existing estimators, which indicated the importance of the newly proposed family of estimators. From the simulation study, it is concluded that the suggested family of estimators achieved better results. We demonstrate theoretically and numerically that the proposed estimator produces efficient results compared to all other contend estimators in entire situations. Overall, we conclude that the performance of the family of suggested estimators is better than all existing estimators.

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A MODIFIED RATIO TYPE ESTIMATOR OF FINITE POPULATION MEAN UNDER STRATIFIED RANDOM SAMPLING SCHEME

10.36106/4917049 ◽

2021 ◽

pp. 58-60

Author(s):

Naziru Fadisanku Haruna ◽

Ran Vijay Kumar Singh ◽

Samsudeen Dahiru

Keyword(s):

Mean Square Error ◽

Random Sampling ◽

Minimum Mean Square Error ◽

Real Life ◽

Population Data ◽

Auxiliary Variable ◽

Mean Square ◽

Data Set ◽

Population Mean ◽

The Mean

In This paper a modied ratio-type estimator for nite population mean under stratied random sampling using single auxiliary variable has been proposed. The expression for mean square error and bias of the proposed estimator are derived up to the rst order of approximation. The expression for minimum mean square error of proposed estimator is also obtained. The mean square error the proposed estimator is compared with other existing estimators theoretically and condition are obtained under which proposed estimator performed better. A real life population data set has been considered to compare the efciency of the proposed estimator numerically.

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Moments without tears in simple random sampling from a finite population

Biometrika ◽

10.1093/biomet/61.1.151 ◽

1974 ◽

Vol 61 (1) ◽

pp. 151-154 ◽

Cited By ~ 4

Author(s):

H. M. FINUCAN ◽

R. F. GALBRAITH ◽

M. STONE

Keyword(s):

Random Sampling ◽

Finite Population ◽

Simple Random Sampling

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Overlap coefficients based on Kullback-Leibler divergence: Exponential populations case

International Journal of Applied Mathematical Research ◽

10.14419/ijamr.v6i4.8493 ◽

2017 ◽

Vol 6 (4) ◽

pp. 135

Author(s):

Hamza Dhaker ◽

Papa Ngom ◽

Malick Mbodj

Keyword(s):

Statistical Inference ◽

Mean Square Error ◽

Confidence Intervals ◽

Taylor Series ◽

Simulation Study ◽

Invariance Property ◽

Mean Square ◽

Taylor Series Approximation ◽

Leibler Divergence ◽

Exponential Populations

This article is devoted to the study of overlap measures of densities of two exponential populations. Various Overlapping Coefficients, namely: Matusita’s measure ρ, Morisita’s measure λ and Weitzman’s measure ∆. A new overlap measure Λ based on Kullback-Leibler measure is proposed. The invariance property and a method of statistical inference of these coefficients also are presented. Taylor series approximation are used to construct confidence intervals for the overlap measures. The bias and mean square error properties of the estimators are studied through a simulation study.

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