Статті в журналах: "Ratio type estimator"

1

Shaheen, Nazia, Muhammad Nouman Qureshi, Osama Abdulaziz Alamri, and Muhammad Hanif. "Optimized inferences of finite population mean using robust parameters in systematic sampling." PLOS ONE 18, no. 1 (January 23, 2023): e0278619. http://dx.doi.org/10.1371/journal.pone.0278619.

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In this article, we have proposed a generalized estimator for mean estimation by combining the ratio and regression methods of estimation in the presence of auxiliary information using systematic sampling. We incorporated some robust parameters of the auxiliary variable to obtain precise estimates of the proposed estimator. The mathematical expressions for bias and mean square error of proposed the estimator are derived under large sample approximation. Many other generalized ratio and product-type estimators are obtained from the proposed estimator using different choices of scalar constants. Some special cases are also discussed in which the proposed generalized estimator reduces to the usual mean, classical ratio, product, and regression type estimators. Mathematical conditions are obtained for which the proposed estimator will perform more precisely than the challenging estimators mentioned in this article. The efficiency of the proposed estimator is evaluated using four populations. Results showed that the proposed estimator is efficient and useful for survey sampling in comparison to the other existing estimators.

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2

Rather, Khalid Ul Islam, Eda Gizem Koçyiğit, Ronald Onyango, and Cem Kadilar. "Improved regression in ratio type estimators based on robust M-estimation." PLOS ONE 17, no. 12 (December 12, 2022): e0278868. http://dx.doi.org/10.1371/journal.pone.0278868.

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In this article, a new robust ratio type estimator using the Uk’s redescending M-estimator is proposed for the estimation of the finite population mean in the simple random sampling (SRS) when there are outliers in the dataset. The mean square error (MSE) equation of the proposed estimator is obtained using the first order of approximation and it has been compared with the traditional ratio-type estimators in the literature, robust regression estimators, and other existing redescending M-estimators. A real-life data and simulation study are used to justify the efficiency of the proposed estimators. It has been shown that the proposed estimator is more efficient than other estimators in the literature on both simulation and real data studies.

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3

Khan, Mursala, and Rajesh Singh. "Estimation of Population Mean in Chain Ratio-Type Estimator under Systematic Sampling." Journal of Probability and Statistics 2015 (2015): 1–5. http://dx.doi.org/10.1155/2015/248374.

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A chain ratio-type estimator is proposed for the estimation of finite population mean under systematic sampling scheme using two auxiliary variables. The mean square error of the proposed estimator is derived up to the first order of approximation and is compared with other relevant existing estimators. To illustrate the performances of the different estimators in comparison with the usual simple estimator, we have taken a real data set from the literature of survey sampling.

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4

Malik, Sachin, and Rajesh Singh. "Some Improved Multivariate-Ratio-Type Estimators Using Geometric and Harmonic Means in Stratified Random Sampling." ISRN Probability and Statistics 2012 (August 26, 2012): 1–7. http://dx.doi.org/10.5402/2012/509186.

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Auxiliary variable is commonly used in survey sampling to improve the precision of estimates. Whenever there is auxiliary information available, we want to utilize it in the method of estimation to obtain the most efficient estimator. In this paper using multiauxiliary information we have proposed estimators based on geometric and harmonic mean. It was also shown that estimators based on harmonic mean and geometric mean are less biased than Olkin (1958) and Singh (1967) estimators under certain conditions. However, the MSE of Olkin (1958) estimator and geometric and harmonic estimators are same up to the first order of approximations.

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5

Subramani, J., and G. Kumarapandiyan. "A Class of Modified Ratio Estimators for Estimation of Population Variance." Journal of Applied Mathematics, Statistics and Informatics 11, no. 1 (May 1, 2015): 91–114. http://dx.doi.org/10.1515/jamsi-2015-0006.

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Abstract In this paper we have proposed a class of modified ratio type variance estimators for estimation of population variance of the study variable using the known parameters of the auxiliary variable. The bias and mean squared error of the proposed estimators are obtained and also derived the conditions for which the proposed estimators perform better than the traditional ratio type variance estimator and existing modified ratio type variance estimators. Further we have compared the proposed estimators with that of the traditional ratio type variance estimator and existing modified ratio type variance estimators for certain natural populations.

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6

Olufadi, Yunusa, and Cem Kadilar. "A Study on the Chain Ratio-Type Estimator of Finite Population Variance." Journal of Probability and Statistics 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/723982.

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We suggest an estimator using two auxiliary variables for the estimation of the unknown population variance. The bias and the mean square error of the proposed estimator are obtained to the first order of approximations. In addition, the problem is extended to two-phase sampling scheme. After theoretical comparisons, as an illustration, a numerical comparison is carried out to examine the performance of the suggested estimator with several estimators.

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7

Olasunkanmi Muili, Jamiu, and A. Audu. "Estimation of Finite Population Mean of Median Based Using Power Transformation." Oriental Journal of Physical Sciences 6, no. 1-2 (February 28, 2022): 26–31. http://dx.doi.org/10.13005/ojps06.01-02.05.

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This paper deals with the assessment of finite population mean. An estimator is suggested for estimation of finite population mean of study variable. The purpose of this study is to evolve a ratio-type estimator to enhance the proficiency of the existing estimators considered in the study in sample random sampling without replacement using information of auxiliary variable. Expressions of the bias and mean square error (MSE) of the proposed estimator was derived by Taylor series method. The efficiency conditions under which the proposed ratio-type estimator is better than sample mean, ratio estimator, and other estimators considered in this study have been established. Theoretical and empirical findings are incentive and brace the robustness of the proposed estimator for mean estimation. The empirical results shown that the suggested estimator is more efficient than the sample mean, ratio estimator and other estimators.

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8

Bhushan, Shashi, Anoop Kumar, Amer Ibrahim Al-Omari, and Ghadah A. Alomani. "Mean Estimation for Time-Based Surveys Using Memory-Type Logarithmic Estimators." Mathematics 11, no. 9 (April 30, 2023): 2125. http://dx.doi.org/10.3390/math11092125.

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This article examines the issue of population mean estimation utilizing past and present data in the form of an exponentially weighted moving average (EWMA) statistic under simple random sampling (SRS). We suggest memory-type logarithmic estimators and derive their properties, such as mean-square error (MSE) and bias up to a first-order approximation. Using the EWMA statistic, the conventional and novel memory-type estimators are compared. Real and artificial populations are used as examples to illustrate the theoretical findings. According to the empirical findings, memory-type logarithmic estimators are superior to the conventional mean estimator, ratio estimator, product estimator, logarithmic-type estimator, and memory-type ratio and product estimators.

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9

RATHER, KHALID UL ISLAM, M. IQBAL JEELANI, and AFSHAN TABASSUM. "OPTIMUM SEPARATE RATIO -TYPE EXPONENTIAL ESTIMATOR FOR COMPUTATION OF POPULATION MEAN IN STRATIFIED RANDOM SAMPLING." Journal of Science and Arts 22, no. 2 (June 30, 2022): 331–42. http://dx.doi.org/10.46939/j.sci.arts-22.2-a07.

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In this manuscript, we study the problem of separate type exponential ratio estimator for estimation of population mean with their properties. The MSE and Bias up to the first degree of approximation for the suggested estimator are computed. The suggested estimator is proven to be more efficient than estimators mentioned in the literature under stratified random technique. An empirical investigation was done to assess the suggested estimator. Also, the percent relative efficiency is to be remarkable for the proposed estimator.

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10

Yunusa, Mojeed Abiodun, Ahmed Audu, and Awwal Adejumobi. "Logarithmic-Product-Cum-Ratio Type Estimator for Estimating Finite Population Coefficient of Variation." Oriental Journal of Physical Sciences 7, no. 2 (January 10, 2023): 82–87. http://dx.doi.org/10.13005/ojps07.02.05.

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Estimation of population parameters have been a challenging aspect in sample survey for sometimes and many efforts have been made to enhance the exactness of the parameters of these estimators. We suggested the logarithmic-product-cum-ratio type estimator. Expression of the MSE of the intended estimator originated using the Taylor series technique. A numerical illustration was conducted and the results revealed that the modified work is ameliorated than sample means with other estimators observed.

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11

Rabiu, Adam, Abubakar Yahaya, and Muhammad Abdulkarim. "MODIFICATION OF SEPARATE RATIO TYPE EXPONENTIAL ESTIMATOR: A POST-STRATIFICATION APPROACH." FUDMA JOURNAL OF SCIENCES 5, no. 2 (July 10, 2021): 404–12. http://dx.doi.org/10.33003/fjs-2021-0502-629.

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In this research, modification of separate ratio type exponential estimator introduced in an earlier study is proposed. Expressions for the bias and mean square error (MSE) of the proposed estimator up to first degree of approximation are derived. The optimum value of the constant which minimize the MSE of the suggested estimator is also obtained. In the same vein, efficiency comparisons between the proposed estimator and some related existing ones under the case of post-stratification is conducted. Empirical studies have been conducted to demonstrate the efficiencies of the suggested estimators over other considered estimators. The proposed MSE and Percentage Relative Efficiency (PRE) were used to evaluate the achievement of the modified estimator.

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12

Mittal, Alisha, and Manoj Kumar. "Two new estimators of finite population variance under random non-response: An application." Model Assisted Statistics and Applications 18, no. 1 (March 24, 2023): 73–84. http://dx.doi.org/10.3233/mas-221361.

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In this paper, an attempt has been made to study the estimation of finite population variance in simple random sampling without replacement (SRSWOR) in presence of non-response by proposing two estimators. The two estimators (dual to ratio and ratio cum dual to ratio type) have been proposed on the basis of availability and non-availability of auxiliary information. The properties such as bias and mean square error of the proposed estimators have also been studied up to first order of approximation. The proposed estimators are compared with some existing estimators and are also mutually compared. An empirical study, based on both vegetable crop data and simulated data, has been performed to find out the best estimator. It has been seen that out of the two proposed estimators, the ratio cum dual to ratio type estimator performed better than dual to ratio estimator.

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13

Muhammad, Isah, Yahaya Zakari, and Ahmed Audu. "An Alternative Class of Ratio-Regression-Type Estimator under Two-Phase Sampling Scheme." Central Bank of Nigeria Journal of Applied Statistics 12, no. 2 (March 30, 2022): 1–26. http://dx.doi.org/10.33429/cjas.12221.1/5.

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In this study, a new exponential ratio-regression estimator is developed using an auxiliary variable for estimating the finite population mean under a two-phase sampling system. The Bias and Mean Square Error (MSE) of the proposed estimator are derived and compared with some of the estimators in extant literature. Thus, the conditions under which the proposed estimator is better than some existing estimators are provided. Empirically, using four real datasets and simulation study, the proposed estimator performs better than the classical ratio, classical regression, exponential ratio, and exponential regression cum ratio estimator when compared using the criteria of bias, mean square error and percentage relative efficiency. The proposed estimator can be used to estimate the averages of economic variables such as inflation, exchange rate, and standard of living for policy formulation.

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14

Muhammad, Isah, Yahaya Zakari, and Ahmed Audu. "An Alternative Class of Ratio-Regression-Type Estimator under Two-Phase Sampling Scheme." Central Bank of Nigeria Journal of Applied Statistics 12, no. 2 (March 30, 2022): 1–26. http://dx.doi.org/10.33429/cjas.12221.1/5.

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Анотація:

In this study, a new exponential ratio-regression estimator is developed using an auxiliary variable for estimating the finite population mean under a two-phase sampling system. The Bias and Mean Square Error (MSE) of the proposed estimator are derived and compared with some of the estimators in extant literature. Thus, the conditions under which the proposed estimator is better than some existing estimators are provided. Empirically, using four real datasets and simulation study, the proposed estimator performs better than the classical ratio, classical regression, exponential ratio, and exponential regression cum ratio estimator when compared using the criteria of bias, mean square error and percentage relative efficiency. The proposed estimator can be used to estimate the averages of economic variables such as inflation, exchange rate, and standard of living for policy formulation.

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15

Muhammad, Isah, Yahaya Zakari, and Ahmed Audu. "An Alternative Class of Ratio-Regression-Type Estimator under Two-Phase Sampling Scheme." Central Bank of Nigeria Journal of Applied Statistics 12, no. 2 (March 30, 2022): 1–26. http://dx.doi.org/10.33429/cjas.12221.1/5.

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Анотація:

In this study, a new exponential ratio-regression estimator is developed using an auxiliary variable for estimating the finite population mean under a two-phase sampling system. The Bias and Mean Square Error (MSE) of the proposed estimator are derived and compared with some of the estimators in extant literature. Thus, the conditions under which the proposed estimator is better than some existing estimators are provided. Empirically, using four real datasets and simulation study, the proposed estimator performs better than the classical ratio, classical regression, exponential ratio, and exponential regression cum ratio estimator when compared using the criteria of bias, mean square error and percentage relative efficiency. The proposed estimator can be used to estimate the averages of economic variables such as inflation, exchange rate, and standard of living for policy formulation.

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16

Mittal, Alisha, and Manoj Kumar. "GENERALISED EXPONENTIAL RATIO-TYPE ESTIMATOR FOR FINITE POPULATION VARIANCE UNDER RANDOM NON-RESPONSE." International Journal of Advanced Research 9, no. 01 (January 31, 2021): 589–96. http://dx.doi.org/10.21474/ijar01/12332.

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In this research paper an effort has been made for the estimation of population variance of the study variable by using information on certain known parameters of the auxiliary variable under non-response for scheme I and II given by Singh and Joarder (1998). Generalized exponential ratio-type estimator has been proposed and their properties have been studied under non response techniques and conditions were found when the family of proposed estimators identified by using different choices for (P, Q) performed better than the usual unbiased estimator. It was also observed that for different values of Î± âˆˆ (0.0, 1.0), the estimators and were found to be best under numerical illustration.

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17

Kamal, Asifa, Nimra Amir, and Huma Dastagir. "Some Exponential Type Predictive Estimators of Finite Population Mean in Two-Phase Sampling." STATISTICS, COMPUTING AND INTERDISCIPLINARY RESEARCH 2, no. 1 (June 30, 2020): 51–57. http://dx.doi.org/10.52700/scir.v2i1.10.

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This study is designed for predictive estimation of finite population mean in two phase sampling using two auxiliary variables. Two phase exponential ratio type estimator and exponential chain ratio type estimator are proposed under predictive approach suggested by Bahl & Tuteja (1991). The expressions of bias and mean square error of both suggested estimators have been carried out for theoretical comparison. The numerical study on real life data sets as well as simulation study has been conducted to examine the performance of suggested estimators. Finally, it is demonstrated that the suggested exponential ratio estimators are more efficient than competitive estimators in support of numerical and simulation study as well.

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18

Ijaz, Muhammad, Syed Muhammad Asim, Atta ullah, and Ibrahim Mahariq. "Flexible Robust Regression-Ratio Type Estimators and Its Applications." Mathematical Problems in Engineering 2022 (September 28, 2022): 1–6. http://dx.doi.org/10.1155/2022/8977392.

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In real-world situations, the data set under examination may contain uncommon noisy measurements that unreasonably affect the data’s outcome and produce incorrect model estimates. Practitioners employed robust-type estimators to reduce the weight of the noisy measurements in a data set in such a scenario. Using auxiliary information that will produce reliable estimates, we have looked at a few flexible robust-type estimators in this study. In order to estimate the population mean, this study presents unique flexible robust regression type ratio estimators that take into account the data from the midrange and interdecile range of the auxiliary variables. Up to the first order of approximate computation, the bias and mean square were calculated. In order to compare the flexibility of the proposed estimator to those of the existing estimators, theoretical conditions were also obtained. We took into account data sets containing outliers for empirical computation, and it was found that the suggested estimators produce results with higher precision than the existing estimators.

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19

Yunusa, Mojeed Abiodun, Jamiu Olasunkanmi Muili, Ahmed Audu, and Ran Vijay Kumar Singh. "A Sine Type Median Based Estimator for the Estimation of Population Mean." Oriental Journal of Physical Sciences 8, no. 1 (July 15, 2023): 21–26. http://dx.doi.org/10.13005/ojps08.01.05.

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In the literature, there are numerous estimators for estimating population means when auxiliary information is provided. Subramani suggested ratio median based estimator when the median of the study variable is available and the regression estimator was shown to be significantly less efficient than the estimator. In this research, we suggested an estimator for the population mean of the studied variable based on a sine type median. Using Taylor series expansion, the bias and mean square error of the estimator were obtained up to the first order of approximation. The condition under which the proposed estimator is more efficient than the existing estimators was established. An empirical investigation was done to compare the suggested estimator's efficiency to that of the existing estimators, and the numerical findings showed that the proposed estimator is more efficient.

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20

Sharma, Prayas, and Rajesh Singh. "Improved Ratio Type Estimator Using Two Auxiliary Variables under Second Order Approximation." Mathematical Journal of Interdisciplinary Sciences 2, no. 2 (March 3, 2014): 179–90. http://dx.doi.org/10.15415/mjis.2014.22014.

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21

Agbebia, C. S., and E. I. Enang. "Calibration Approach Ratio Estimators of Population Median in Stratified Random Sampling Design." Asian Journal of Probability and Statistics 21, no. 4 (March 29, 2023): 64–77. http://dx.doi.org/10.9734/ajpas/2023/v21i4472.

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Median as a measure of location gives a more robust estimate than the mean when dealing with heavy tailed or skewed distributions. It can also be used in cases of qualitative variables and open end intervals. Calibration, an approach that adjusts the original design weight by incorporating auxiliary information is employed using the chi square distance measure on a ratio median estimator under stratified random sampling to propose some estimators of population median. These proposed estimators are: the regression and ratio-type calibrated estimators with one constraint and the regression and ratio-type calibrated estimators with two constraints. The estimators of variance of these proposed estimators are also obtained. Empirical investigations on the performance of these estimators are carried out using R software simulated data set under underlying distributional assumptions of Cauchy and Lognormal, for sample sizes of 10%, 20% and 25%. The results showed that the proposed regression and ratio-type calibrated estimators with one constraint and the regression-type calibrated estimator with two constraints were more efficient than the existing ratio estimator and the proposed ratio-type calibrated estimator under two constraints for both Cauchy and the lognormal distributions.

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22

Rather, K. Ul Islam, M. Iqbal Jeelani, M. Younis Shah, S. E. H. Rizvi, and M. Sharma. "A new ratio type estimator for computation of population mean under post-stratification." Journal of Applied Mathematics, Statistics and Informatics 18, no. 1 (May 1, 2022): 29–42. http://dx.doi.org/10.2478/jamsi-2022-0003.

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Abstract In this study, the difficulty of estimating the population mean in the situation of post-stratification is discussed. The case of post-stratification is presented for ratio-type exponential estimators of finite population mean. Mean-squared error of the proposed estimator is obtained up to the first degree of approximation. In the instance of post-stratification, the proposed estimator was compared with the existing estimators. An empirical study by using some real data and further, simulation study has been carried out to demonstrate the performance of the proposed estimator.

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23

Subramani, J. "Generalized Modified Ratio Type Estimator for Estimation of Population Variance." Sri Lankan Journal of Applied Statistics 16, no. 1 (May 20, 2015): 69. http://dx.doi.org/10.4038/sljastats.v16i1.7807.

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24

Onyango, Ronald, Brian Oduor, and Francis Odundo. "Mean Estimation of a Sensitive Variable under Nonresponse Using Three-Stage RRT Model in Stratified Two-Phase Sampling." Journal of Probability and Statistics 2022 (April 22, 2022): 1–14. http://dx.doi.org/10.1155/2022/4530120.

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The present study addresses the problems of mean estimation and nonresponse under the three-stage RRT model. Auxiliary information on an attribute and variable is used to propose a generalized class of exponential ratio-type estimators. Expressions for the bias, mean squared error, and minimum mean squared error for the proposed estimator are derived up to the first degree of approximation. The efficiency of the proposed estimator is studied theoretically and numerically using two real datasets. From the numerical analysis, the proposed generalized class of exponential ratio-type estimators outperforms ordinary mean estimators, usual ratio estimators, and exponential ratio-type estimators. Furthermore, the efficiencies of the mean estimators are observed to decrease with an increase in the sensitivity level of the survey question. As the inverse sampling rate and nonresponse rate go up, so does the efficiency of the mean estimators, which makes them more accurate.

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25

Magnussen, Steen, and Thomas Nord-Larsen. "A Jackknife Estimator of Variance for a Random Tessellated Stratified Sampling Design." Forest Science 65, no. 5 (March 12, 2019): 543–47. http://dx.doi.org/10.1093/forsci/fxy070.

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Abstract Semisystematic sampling designs—in which a population area frame is tessellated into cells, and a randomly located sample is taken from each cell—affords random tessellated stratified (RTS) Horvitz–Thompson-type estimators. Forest inventory applications with RTS estimators are rare, possibly because of computational complexities with the estimation of variance. To reduce this challenge, we propose a jackknife estimator of variance for RTS designs. We demonstrate an application with a model-assisted ratio of totals estimator and data from the Danish National Forest Inventory. RTS estimators of standard error were, as a rule, smaller than comparable estimates obtained under the assumption of simple random sampling. The proposed jackknife estimator performed well.

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26

Raghav, Yashpal Singh. "Neutrosophic Generalized Exponential Robust Ratio Type Estimators." International Journal of Analysis and Applications 21 (May 1, 2023): 41. http://dx.doi.org/10.28924/2291-8639-21-2023-41.

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Estimators proposed under classical statistics fail if data are vague or indeterminate. Neutrosophic Statistics are the only alternative because its deal with indeterminacy. Extensive reserch has been conducted in this field because of its wide applicability. This study aimed to further develop the theory of neutosophic simple random sampling without replacement. In this study, a generalized neutrosophic exponential robust ratio-type estimator was proposed, and five of its member neutrosophic estimators were developed. Derivations of the bias and Mean Square Error were provided up to the first-order approximation. To demonstrate the high efficiency of the proposed neutrosophic estimators an empirical study on the stock price of Moderna and four simulation studies have been conducted, and the results show that the proposed neutrosophic estimators are more efficient than similar existing ratio type estimators discussed in this paper in neutrosophic as well as classical forms.

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27

Ali, Muhammad, Muhammad Khalil, Muhammad Hanif, Nasir Jamal, and Usman Shahzad. "An Improved Ratio-Type Variance Estimator by Using Linear Combination of Diferent Measures of Location." Oriental Journal of Physical Sciences 3, no. 1 (June 25, 2018): 24–32. http://dx.doi.org/10.13005/ojps03.01.05.

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Анотація:

In this research study, modified family of estimators is proposed to estimate the population variance of the study variable when the population variance, quartiles, median and the coefficient of correlation of auxiliary variable are known. The expression of bias and mean squared error (MSE) of the proposed estimator are derived. Comparisons of the proposed estimator with the other existing are conducted estimators. The results obtained were illustrated numerically by using primary data sets. Theoretical and numerical justification of the proposed estimator was done to show its dominance.

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28

Shabbir, Javid, Shakeel Ahmed, Aamir Sanaullah, and Ronald Onyango. "Measuring Performance of Ratio-Exponential-Log Type General Class of Estimators Using Two Auxiliary Variables." Mathematical Problems in Engineering 2021 (October 1, 2021): 1–12. http://dx.doi.org/10.1155/2021/5245621.

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Анотація:

In this paper, a ratio-exponential-log type general class of estimators is proposed in estimating the finite population mean using two auxiliary variables when population parameters of the auxiliary variables are known. From the proposed estimator, some special estimators are identified as members of the proposed general class of estimators. The mean square error (MSE) expressions are obtained up to the first order of approximation. This study finds that the proposed general class of estimators outperforms as compared to the conventional mean estimator, usual ratio estimators, exponential-ratio estimators, log-ratio type estimators, and many other competitor regression type estimators. Four real-life applications are used for efficiency comparison.

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29

Suleiman, Sikiru A., and Amos A. Adewara. "Improved Modified Ratio Estimation of Population Mean Using Information on Size of the Sample." Tanzania Journal of Science 47, no. 5 (December 29, 2021): 1753–65. http://dx.doi.org/10.4314/tjs.v47i5.22.

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Анотація:

In sample surveys, auxiliary information is used for estimation to improve the eﬃciency of estimators. Increased precision can be obtained when the variable under study is highly correlated with auxiliary information. In this study, the sample size has been used as information for improved estimation of population mean of the main variable under study. A new modified generalized ratio type estimator of population mean has been proposed and the efficiency was examined using Murthy (1967) and Mukhopadhyay (2009) dataset. The large sample properties, the bias and the mean squared error of the newly proposed modified ratio estimator were obtained up to first order of approximation. The optimum value of the characterizing scalar which minimizes the mean squared error was obtained and the minimum value of the mean squared error of the proposed modified ratio estimator for this optimum value was also obtained. A theoretical comparison of the proposed modified ratio estimators was made with the other existing related estimators of population mean using auxiliary information. The conditions under which the proposed modified ratio estimators perform better than the other existing estimators of population mean are given. A numerical study was also carried out to see the performances of the proposed modified ratio estimators and some existing related ratio estimators of population mean and verify the conditions under which the proposed modified ratio estimators are better than some other existing related ratio estimators considered. It was shown that the proposed modified ratio estimators perform better than some existing related ratio estimators as they are having lower mean squared errors. Keywords: Ratio Estimator, Sample size, Bias, Mean Squared Error, Efficiency

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30

IJAZ, MUHAMMAD, ATTA ULLAH, and TOLGA ZAMAN. "ON THE DEVELOPMENT OF RATIO TYPE ESTIMATORS USING AUXILIARY INFORMATION." Journal of Science and Arts 21, no. 1 (March 30, 2021): 163–70. http://dx.doi.org/10.46939/j.sci.arts-21.1-a14.

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Анотація:

The paper produces some new modified forms of the ratio estimators using the auxiliary information. The large sample properties, that is, the bias and mean squared error up to the first order of approximation are determined. The comparison is made with other existing estimators by using an applied data. It has been observed that the proposed estimators have a fewer mean squared error and leads to the efficient results as compared to the classical ratio estimator, Sisodia and Dwivedi, Singh and Kakran, Upadhyaya and Singh estimators.

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31

Panda, K. B., M. Sen, and P. Das. "Efficient Ratio-type Exponential Estimator for Population Variance." International Journal of Scientific Research in Mathematical and Statistical Sciences 5, no. 3 (June 30, 2018): 129–32. http://dx.doi.org/10.26438/ijsrmss/v5i3.129132.

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32

Ali, Asad, Muhammad Moeen Butt, and Muhammad Zubair. "Generalized Chain Regression-cum-Chain Ratio Estimator for Population Mean under Stratified Extreme-cum-Median Ranked Set Sampling." Mathematical Problems in Engineering 2022 (January 4, 2022): 1–13. http://dx.doi.org/10.1155/2022/9556587.

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Estimation of population mean of study variable Y suffers loss of precision in the presence of high variation in the data set. The use of auxiliary information incorporated in construction of an estimator under ranked set sampling scheme results in efficient estimation of population mean. In this paper, we propose an efficient generalized chain regression-cum-chain ratio type estimator to estimate finite population mean of study variable under stratified extreme-cum-median ranked set sampling utilizing information on two auxiliary variables. Mean square error (MSE) of the proposed generalized estimator is derived up to first order of approximation. The applications of the proposed estimator under symmetrical and asymmetrical probability distributions are discussed using simulation study and real-life data set for comparisons of efficiency. It is concluded that the proposed generalized estimator performs efficiently as compared to some existing estimators. It is also observed that the efficiency of the proposed estimator is directly proportional to the correlations between the study variable and its auxiliary variables.

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APANTAKU, F. S., O. M. OLAYIWOLA, A. O. AJAYI, and O. S. JAIYEOLA. "A MODIFIED GENERALIZED CHAIN RATIO IN REGRESSION ESTIMATOR." Journal of Natural Sciences Engineering and Technology 19, no. 1 (December 2, 2021): 1–7. http://dx.doi.org/10.51406/jnset.v19i1.2087.

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Generalized Chain ratio in regression type estimator is efficient for estimating the population mean. Many authors have derived a Generalized Chain ratio in regression type estimator. However, the computation of its Mean Square Error (MSE) is cumbersome based on the fact that several iterations have to be done, hence the need for a modified generalized chain ratio in regression estimator with lower MSE. This study proposed a modified generalized chain ratio in regression estimator which is less cumbersome in its computation. Two data sets were used in this study. The first data were on tobacco production by tobacco producing countries with yield of tobacco (variable of interest), area of land and production in metric tonnes as the auxiliary variables. The second data were the number of graduating pupils (variable of interest) in Ado-Odo/Ota local government, Ogun state with the number of enrolled pupils in primaries one and five as the auxiliary variables. The mean square errors in the existing and proposed estimators for various values of alpha were derived and relative efficiency was determined. The MSE for the existing estimator of tobacco production gave six values 0.0080, 0.0079, 0.0080, 0.0082, 0.0087 and 0.0093 with 0.0079 as the minimum while the proposed estimator gave 0.0054. The MSEs for the existing estimator for the graduating pupils were 20.73, 11.08, 7.49, 9.96, 18.50 and 33.10 with 7.49 as the minimum while the proposed was 6.52. The results of this study showed that the proposed estimator gave lower MSE for the two data sets, hence it is more efficient.

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Zaman, Tolga, Emre Dünder, Ahmed Audu, David Anekeya Alilah, Usman Shahzad, and Muhammad Hanif. "Robust Regression-Ratio-Type Estimators of the Mean Utilizing Two Auxiliary Variables: A Simulation Study." Mathematical Problems in Engineering 2021 (September 3, 2021): 1–9. http://dx.doi.org/10.1155/2021/6383927.

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Many authors defined the modified version of the mean estimator by using two auxiliary variables. These proposed estimators highly depend on the calculated regression coefficients. In the presence of outliers, these estimators do not give satisfactory results. In this study, we improve the suggested estimators using several robust regression techniques while obtaining the regression coefficients. We compared the efficiencies between the suggested estimators and the estimators presented in the literature. We used two numerical examples and a simulation study to support these theoretical results. Empirical results show that the modified ratio estimator performs well in the presence of outliers when adopting robust regression techniques.

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35

Chodjuntug, Kanisa, and Nuanpan Lawson. "A Chain Ratio Exponential-Type Compromised Imputation for Mean Estimation: Case Study on Ozone Pollution in Saraburi, Thailand." Journal of Probability and Statistics 2020 (December 5, 2020): 1–6. http://dx.doi.org/10.1155/2020/8864412.

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Due to its impact on health and quality of life, Thailand’s ozone pollution has become a major concern among public health investigators. Saraburi Province is one of the areas with high air pollution levels in Thailand as it is an important industrialized area in the country. Unfortunately, the August 2018 Pollution Control Department (PCD) report contained some missing values of the ozone concentrations in Saraburi Province. Missing data can significantly affect the data analysis process. We need to deal with missing data in a proper way before analysis using standard statistical techniques. In the presence of missing data, we focus on estimating ozone mean using an improved compromised imputation method that utilizes chain ratio exponential technique. Expressions for bias and mean square error (MSE) of an estimator obtained from the proposed imputation method are derived by Taylor series method. Theoretical finding is studied to compare the performance of the proposed estimator with existing estimators on the basis of MSE’s estimators. In this case study, the results in terms of the percent relative efficiencies indicate that the proposed estimator is the best under certain conditions, and it is then applied to the ozone mean estimation for Saraburi Province in August 2018.

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36

Younis, Faryal, and Javid Shabbir. "Generalized ratio-type and ratio-exponential-type estimators for population mean under modified Horvitz-Thompson estimator in adaptive cluster sampling." Journal of Statistical Computation and Simulation 89, no. 8 (March 4, 2019): 1505–15. http://dx.doi.org/10.1080/00949655.2019.1586905.

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37

RATHER, KHALID UL ISLAM, M. IQBAL JEELANI, M. YOUNIS SHAH, AFSHAN TABASSUM, and S. E. H. RIZVI. "DIFFERENCE-CUM-EXPONENTIAL EFFICIENT ESTIMATOR OF POPULATION VARIANCE." Journal of Science and Arts 22, no. 2 (June 30, 2022): 367–74. http://dx.doi.org/10.46939/j.sci.arts-22.2-a10.

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In the current investigation, we have suggested a Difference Cum-Exponential Type Efficient Estimator of Population variance of the study variable using information on the auxiliary variable. Up to the first order of approximation, the proposed estimator's bias and mean square error (MSE) expressions are derived and suggested optimum estimator is also found, with its optimal qualities are investigated. The suggested estimator is proven to be more competent than sample variance, classic ratio estimators based on Isaki , Singh et al. and Kadilar and Cingi estimators in [1-3]. Numerical study is also carried out by using real data sets.

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38

Bacanlı, Sevil. "Horvitz-Thomson Ratio Type Estimator in Estimating Population Mean." SOP Transactions on Statistics and Analysis 2015, no. 1 (January 31, 2015): 1–7. http://dx.doi.org/10.15764/stsa.2015.01001.

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39

Ahmad, Sohaib, Sardar Hussain, Kalim Ullah, Erum Zahid, Muhammad Aamir, Javid Shabbir, Zubair Ahmad, Huda M. Alshanbari, and Wejdan Alajlan. "A simulation study: Improved ratio-in-regression type variance estimator based on dual use of auxiliary variable under simple random sampling." PLOS ONE 17, no. 11 (November 18, 2022): e0276540. http://dx.doi.org/10.1371/journal.pone.0276540.

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In this article, we proposed an improved finite population variance estimator based on simple random sampling using dual auxiliary information. Mathematical expressions of the proposed and existing estimators are obtained up to the first order of approximation. Two real data sets are used to examine the performances of a new improved proposed estimator. A simulation study is also recognized to assess the robustness and generalizability of the proposed estimator. From the result of real data sets and simulation study, it is examining that the proposed estimator give minimum mean square error and percentage relative efficiency are higher than all existing counterparts, which shown the importance of new improved estimator. The theoretical and numerical result illustrated that the proposed variance estimator based on simple random sampling using dual auxiliary information has the best among all existing estimators.

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40

Chen, Yingbing, John A. Kershaw, Yung-Han Hsu, and Ting-Ru Yang. "Carbon estimation using sampling to correct LiDAR-assisted enhanced forest inventory estimates." Forestry Chronicle 96, no. 01 (May 2020): 9–19. http://dx.doi.org/10.5558/tfc2020-003.

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Light Detection and Ranging (LiDAR) scanning has been increasingly applied in forest ecosystem surveys. Data from LiDAR describe forest structure and provide attribute information for forest inventory. These attributes can potentially aid in the estimation of biomass and carbon by providing sampling covariates. Therefore, this study explored the accuracy of estimating carbon storage by calibrating LiDAR attributes using list sampling with a ratio estimator. Standing tree carbon and down woody debris carbon were estimated across 10 broad forest types. LiDAR-derived gross total volume was used as a listing factor and big BAF samples to collect field data. Gross total volumes were “corrected” using a ratio estimator. The results show that standing tree carbon was 58.5 Mg C × ha-1 (± 2.9% SE), and dead woody debris carbon 1.8 Mg C × ha-1 (± 7.2% SE). With the exception of one forest type, these estimates were comparable to those derived from the carbon budget model of the Canadian forest sector (CBM-CFS3).

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41

Singh, B. K. "Improved Exponential Dual to Ratio Type Imputation for Missing Data under Two-Phase Sampling." International Journal for Research in Applied Science and Engineering Technology 9, no. 8 (August 31, 2021): 2338–48. http://dx.doi.org/10.22214/ijraset.2021.37772.

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Abstract: In this paper, authors have proposed a class of exponential dual to ratio type compromised imputation technique and corresponding point estimator in two-phase sampling design. Two different sampling designs in two-phase sampling are compared under imputed data. The bias and M.S.E. of suggested estimator is derived in the form of population parameters using the concept of large sample approximation. Numerical study is performed over two populations using the expressions of bias and M.S.E. and efficiency compared with existing estimators. Keywords: Missing data, Bias, Mean squared error (M.S.E), Two-phase sampling, SRSWOR, Compromised Imputation (C.I.).

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42

Chadyšas, V. "Estimation of a Distribution function under Sampling on Two Occasions." Nonlinear Analysis: Modelling and Control 14, no. 3 (July 20, 2009): 315–31. http://dx.doi.org/10.15388/na.2009.14.3.14498.

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Estimation of the distribution function under sampling on two occasions with a simple random sampling design on each occasion is investigated. Composite regression and ratio type estimators are considered, using values of the study variable as auxiliary information obtained on the first occasion. The optimal estimator, in the sense of minimal variance, is also obtained. A simulation study, based on the real population data, is performed and the proposed estimators are compared by a simple estimator for a distribution function.

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43

Zoramthanga, R. "Estimation of current population mean using two-occasion successive sampling with one auxiliary variable." Science Vision 18, no. 2 (June 30, 2018): 74–77. http://dx.doi.org/10.33493/scivis.18.02.05.

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In this study, two-occasion successive sampling for ratio-to-regression estimator was used to determine the current estimate of the population mean using only the matched part and one auxiliary variable, which is available on both the occasions. The data used were based on the total number of female workers in villages in Mizoram with the total number of literate female in villages in Mizoram as an auxiliary variables. The data were gotten from Census of India 2001 and 2011. The optimum mean square error of the combined ratio-to-regression and ratio estimator has been compared with (i) the optimum mean square error of the chain-type ratio estimator (ii) mean per unit estimator and (iii) combined estimator when no auxiliary information is used at any occasion. This result showed that the combined ratio-to-regression and ratio estimator is more efficient than the other three existing estimators.

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44

Tailor, Rajesh, and Sunil Chouhan. "Ratio Type Estimator of Ratio of Two Population Means in Stratified Random Sampling." Journal of Modern Applied Statistical Methods 11, no. 1 (May 1, 2012): 279–83. http://dx.doi.org/10.22237/jmasm/1335846300.

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45

Srivnstava, Rani S., S. P. Srivastava, and B. B. Khare. "Chain ratio type estimator for ratio of two population m3ans using auxiliary characters." Communications in Statistics - Theory and Methods 18, no. 10 (January 1989): 3917–26. http://dx.doi.org/10.1080/03610928908830131.

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46

Mehta, Nitu, and V. L. Mandowara. "Some Efficient Methods to Remove Bias in Ratio and Product Types Estimators in Ranked Set Sampling." International Journal of Bio-resource and Stress Management 13, no. 3 (March 31, 2022): 276–82. http://dx.doi.org/10.23910/1.2022.2771a.

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Ranked set sampling is one method to potentially increase precision and reduce costs by using quantitative or qualitative information to obtain a more representative sample. Use of auxiliary information has shown its significance in improvement of efficiency of estimators of unknown population parameters. Ratio estimator is used when auxiliary information in the form of population mean of auxiliary variable at estimation stage for the estimation of population parameters when study and auxiliary variable are positively correlated. In case of negative correlation between study variable and auxiliary variable, Product estimator is defined for the estimation of population mean. This paper proposed the problem of reducing the bias of the ratio and product estimators of the population mean in ranked set sampling (RSS). This paper suggested several type unbiased estimators of the finite population mean using information on known population parameters of the auxiliary variable in ranked set sampling. An important objective in any statistical estimation procedure is to obtain the estimators of parameters of interest with more precision. The Variance of the proposed unbiased ratio and product estimators are obtained up to first degree of approximation. Theoretically, it is shown that these suggested estimators are more efficient than the unbiased estimators in Simple random sampling. A numerical illustration is also carried out to demonstrate the merits of the proposed estimators using RSS over the usual estimators in SRS.

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47

Ijaz, Muhammad, Atta Ullah Khan, Syed Muhammad Asim, Yousaf Hayat, Syed Habib Shah, Muhammad Farooq, Kashif Ali, Neelam, and Seema Zubair. "A NEW RATIO TYPE ESTIMATOR TO ESTIMATE THE POPULATION MEAN USING AUXILIARY INFORMATION." Advances and Applications in Statistics 63, no. 1 (July 5, 2020): 97–108. http://dx.doi.org/10.17654/as063010097.

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48

Parichha, P., K. Basu, A. Bandyopadhyay, and P. Mukhopadhyay. "Development of Efficient Estimation Technique for Population Mean in Two Phase Sampling Using Fuzzy Tools." Journal of Applied Mathematics, Statistics and Informatics 13, no. 2 (December 20, 2017): 5–28. http://dx.doi.org/10.1515/jamsi-2017-0006.

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Abstract The present investigation deals with the problem of estimation of population mean in two-phase (double) sampling. Utilizing information on two auxiliary variables, one chain exponential ratio and regression type estimator has been proposed and its properties are studied under two different structures of twophase sampling. To make the estimator practicable, unbiased version of the proposed strategy has also been developed. The dominance of the suggested estimator over some contemporary estimators of population mean has been established through numerical illustrations carried over the data set of some natural population and artificially generated population. Categorization of the dominance ranges of the proposed estimation strategies are deployed through defuzzification tools, which are followed by suitable recommendations.

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49

Oh, Jungtaek, and Key-Il Shin. "A study on the ratio type estimator in survey sampling." Survey Research 18, no. 4 (November 30, 2017): 105–25. http://dx.doi.org/10.20997/sr.18.4.5.

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50

Patel, P. A., and F. H. Shah. "Two-phase Ratio-type Estimator of a Finite Population Mean." International Journal of Scientific Research in Mathematical and Statistical Sciences 5, no. 5 (October 31, 2018): 199–203. http://dx.doi.org/10.26438/ijsrmss/v5i5.199203.

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