scholarly journals An Improved Ratio-Type Variance Estimator by Using Linear Combination of Diferent Measures of Location

2018 ◽  
Vol 3 (1) ◽  
pp. 24-32
Author(s):  
Muhammad Ali ◽  
Muhammad Khalil ◽  
Muhammad Hanif ◽  
Nasir Jamal ◽  
Usman Shahzad
Keyword(s):  
Research Study ◽  
Mean Squared Error ◽  
Auxiliary Variable ◽  
The Other ◽  
Primary Data ◽  
Data Sets ◽  
Variance Estimator ◽  
Population Variance ◽  
Study Variable ◽  
Squared Error

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.

scholarly journals A Class of Modified Ratio Estimators for Estimation of Population Variance

2015 ◽  
Vol 11 (1) ◽  
pp. 91-114 ◽  
Author(s):  
J. Subramani ◽  
G. Kumarapandiyan
Keyword(s):  
Mean Squared Error ◽  
Natural Populations ◽  
Auxiliary Variable ◽  
Variance Estimator ◽  
Population Variance ◽  
Study Variable ◽  
Variance Estimators ◽  
Squared Error ◽  
Ratio Estimators ◽  
Better Than

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.

Computation of Improved Searls Estimation of Population Variance Using Robust Auxiliary Parameters

2020 ◽  
Vol 13 ◽  
Author(s):  
S. K. Yadav ◽  
Dinesh Sharma ◽  
Julius Alade
Keyword(s):  
Mean Squared Error ◽  
Natural Populations ◽  
Auxiliary Variable ◽  
Efficient Estimation ◽  
Data Sets ◽  
Population Variance ◽  
Practical Applications ◽  
Squared Error ◽  
Natural Data ◽  
R Programming

Introduction: Variation is an inherent phenomenon whether in nature made things or man made. Thus, it looks important to estimate this variation. Various authors have worked in the direction of improved estimation of population variance utilizing the known auxiliary parameters for better policy making. Methods: In this article, a new searls ratio type class of estimator is suggested for elevated estimation of population variance of main variable. As the suggested estimator is biased, so its bias and mean squared error (MSE) have been derived up to the approximation of order-one. The optimum values for the Searls characterizing scalars are obtained. The minimum MSE of the introduced estimator is obtained for the optimum Searls characterizing scalars. A theoretical comparison between suggested estimator and the competing estimators has been made through their mean squared errors. The efficiency conditions of suggested estimator over competing estimators are also obtained. These theoretical conditions are verified using some natural data sets. The computation of R codes for the biases and MSEs of the suggested and competing estimators are developed and are used for three natural populations in Naz et al. (2019). The estimator with least MSE is recommended for practical utility. The empirical study has been done using R programming. Results: The MSEs of different competing and the suggested estimators are obtained for three natural populations. The estimator under comparison with the least MSE is recommended for practical applications. Discussion: The aim to search for the most efficient estimation for improved estimation, is fulfilled through the proper use of the auxiliary parameters obtained from the known auxiliary variable. The suggested estimator may be used for elevated estimation of population variance. Conclusion: The introduced estimator is having least MSE as compared to competing estimators of popularion variance for all three natural populations. Thus it may be recommended for the application in various fields.

scholarly journals Improved Estimator of Population Variance Using Measure of Dispersion of Auxiliary Variable

2018 ◽  
Vol 3 (1) ◽  
pp. 33-39
Author(s):  
Muhammad Khalil ◽  
Muhammad Ali ◽  
Usman Shahzad ◽  
Muhammad Hanif ◽  
Nasir Jamal
Keyword(s):  
Standard Deviation ◽  
Empirical Study ◽  
Research Study ◽  
Secondary Data ◽  
Auxiliary Variable ◽  
Data Sets ◽  
Mean Square ◽  
Population Variance ◽  
Study Variable ◽  
Class Of Estimators

This research study is designed to obtain a more precise class of estimators of a population variance by taking advantage of relation between auxiliary variable and study variable. Here a class of new modified ratio type estimators of population variance by using coefficient of variation (CV), standard deviation, mean and median of auxiliary variable. Further empirical study is made to compare bias and mean square error (MSE) of proposed estimators with the existing estimators. Expressions for bias and MSE are obtained. Few secondary data sets are used to check the efficiency of proposed estimators of population variance.

scholarly journals Variance Estimator Using Tri-mean and Inter Quartile Range of Auxiliary Variable

2017 ◽  
Vol 1 ◽  
pp. 83-91
Author(s):  
S.K. Yadav ◽  
Sheela Misra ◽  
S.S. Mishra ◽  
Shankar Prasad Khanal
Keyword(s):  
Mean Squared Error ◽  
Natural Populations ◽  
Auxiliary Variable ◽  
Population Parameter ◽  
Variance Estimator ◽  
Population Variance ◽  
Inter Quartile Range ◽  
First Order ◽  
Squared Error ◽  
Quartile Range

Background: Whenever the population is large and it is very time taking and costly to take observation on each unit of the population then sampling is the only way to get the appropriate estimate of the population parameter under consideration. Many authors have given many estimators for estimating population variance with greater efficiency.Objective: The objective of the study is to search for more efficient estimator than the competing estimators of population variance of study variable.Materials and Methods: The estimator utilizing information on tri-mean and inter quartile range of auxiliary variable has been is developed. The expressions for the bias and mean squared error (MSE) of the proposed estimator have been derived up to the first order of approximation. A theoretical comparison of the proposed estimator has been made with the competing estimators of population variance.Results: The theoretical findings have been justified with the help of numerical example from some natural populations. It has been found that the proposed estimator is best among the competing estimators of population variance as it has least mean squared error among them.Conclusion: Since the proposed estimator is best among the competing estimator of the population variance, therefore it must be used for the improved estimation of population variance.Nepalese Journal of Statistics, 2017, Vol. 1, 83-91

scholarly journals Almost Unbiased Ratio cum Product Estimator for Finite Population Mean with Known Median in Simple Random Sampling

2017 ◽  
Vol 1 ◽  
pp. 1-14
Author(s):  
Subramani Jambulingam ◽  
Ajith S. Master
Keyword(s):  
Random Sampling ◽  
Mean Squared Error ◽  
Numerical Study ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Study Variable ◽  
Population Mean ◽  
Squared Error ◽  
Product Estimator ◽  
Almost Unbiased

Introduction: In sampling theory, different procedures are used to obtain the efficient estimator of the population mean. The commonly used method is to obtain the estimator of the population mean is simple random sampling without replacement when there is no auxiliary variable is available. There are methods that use auxiliary information of the study characteristics. If the auxiliary variable is correlated with study variable, number of estimators are widely available in the literature.Objective: This study deals with a new ratio cum product estimator is developed for the estimation of population mean of the study variable with the known median of the auxiliary variable in simple random sampling.Materials and Methods: The bias and mean squared error of proposed estimator are derived and compared with that of the existing estimators by analytically and numerically.Results: The proposed estimator is less biased and mean squared error is less than that of the existing estimators and from the numerical study, under some known natural populations, the bias of proposed estimator is approximately zero and the mean squared error ranged from 6.83 to 66429.21 and percentage relative efficiencies ranged from 103.65 to 2858.75.Conclusion: The proposed estimator under optimum conditions is almost unbiased and performs better than all other existing estimators.Nepalese Journal of Statistics, 2017, Vol. 1, 1-14

scholarly journals Improved Estimator of Finite Population Variance Using Coefficient of Quartile Deviation

2018 ◽  
pp. 1-6
Author(s):  
Komal Javed ◽  
Nasir Jamal ◽  
Muhammad Hanif ◽  
Muhammad Ali ◽  
Usman Shahzad ◽  
...  
Keyword(s):  
Finite Population ◽  
Secondary Data ◽  
Auxiliary Variable ◽  
Data Sets ◽  
Population Variance ◽  
Study Variable ◽  
Variance Estimators ◽  
Class Of Estimators ◽  
Efficiency Comparison ◽  
Variable Bias

This study introduces a new, better, class of ratio estimators for the estimation of population variance of the study variable by using the coefficient of quartile deviation of auxiliary variable. Bias and mean square error of the proposed class of estimators are also derived. The conditions of efficiency comparison are also obtained. Simulation and different secondary data sets are used to evaluate the efficiency of proposed class of variance estimators over existing class of estimators. The empirical study shows that the suggested class of estimators is more efficient the existing class of estimators for the population variance.

scholarly journals Thematic Maps for the Variation of Bearing Capacity of Soil Using SPTs and MATLAB

Geosciences ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 329
Author(s):  
Mahdi O. Karkush ◽  
Mahmood D. Ahmed ◽  
Ammar Abdul-Hassan Sheikha ◽  
Ayad Al-Rumaithi
Keyword(s):  
Bearing Capacity ◽  
Mean Squared Error ◽  
Ground Level ◽  
The Other ◽  
Thematic Maps ◽  
First Order ◽  
Squared Error ◽  
Order Polynomial ◽  
Interpolation Polynomials ◽  
Penetration Tests

The current study involves placing 135 boreholes drilled to a depth of 10 m below the existing ground level. Three standard penetration tests (SPT) are performed at depths of 1.5, 6, and 9.5 m for each borehole. To produce thematic maps with coordinates and depths for the bearing capacity variation of the soil, a numerical analysis was conducted using MATLAB software. Despite several-order interpolation polynomials being used to estimate the bearing capacity of soil, the first-order polynomial was the best among the other trials due to its simplicity and fast calculations. Additionally, the root mean squared error (RMSE) was almost the same for the all of the tried models. The results of the study can be summarized by the production of thematic maps showing the variation of the bearing capacity of the soil over the whole area of Al-Basrah city correlated with several depths. The bearing capacity of soil obtained from the suggested first-order polynomial matches well with those calculated from the results of SPTs with a deviation of ±30% at a 95% confidence interval.

Finite Sample Properties of Several Predictors From an Autoregressive Model

1987 ◽  
Vol 3 (3) ◽  
pp. 359-370 ◽  
Author(s):  
Koichi Maekawa
Keyword(s):  
Maximum Likelihood ◽  
Sample Size ◽  
Asymptotic Expansions ◽  
Autoregressive Model ◽  
Mean Squared Error ◽  
The Other ◽  
Finite Sample ◽  
Squared Error ◽  
Distributional Properties ◽  
Finite Sample Properties

We compare the distributional properties of the four predictors commonly used in practice. They are based on the maximum likelihood, two types of the least squared, and the Yule-Walker estimators. The asymptotic expansions of the distribution, bias, and mean-squared error for the four predictors are derived up to O(T−1), where T is the sample size. Examining the formulas of the asymptotic expansions, we find that except for the Yule-Walker type predictor, the other three predictors have the same distributional properties up to O(T−1).

A Class of Estimators of the Population Mean Using Multi­Auxiliary Information

1983 ◽  
Vol 32 (1-2) ◽  
pp. 47-56 ◽  
Author(s):  
S. K. Srivastava ◽  
H. S. Jhajj
Keyword(s):  
Mean Squared Error ◽  
Broad Class ◽  
Auxiliary Variable ◽  
Population Parameters ◽  
Auxiliary Variables ◽  
Sample Mean ◽  
Squared Error ◽  
Class Of Estimators ◽  
The Mean ◽  
Asymptotic Mean Squared Error

For estimating the mean of a finite population, Srivastava and Jhajj (1981) defined a broad class of estimators which we information of the sample mean as well as the sample variance of an auxiliary variable. In this paper we extend this class of estimators to the case when such information on p(> 1) auxiliary variables is available. The estimators of the class involve unknown constants whose optimum values depend on unknown population parameters. When these population parameters are replaced by their consistent estimates, the resulting estimators are shown to have the same asymptotic mean squared error. An expression by which the mean squared error of such estimators is smaller than those which use only the population means of the auxiliary variables, is obtained.

scholarly journals Gaining competitive advantage through business analytics

2013 ◽  
Vol 61 (7) ◽  
pp. 2779-2785 ◽  
Author(s):  
Peter Sprongl
Keyword(s):  
Information Management ◽  
Statistical Tests ◽  
The Other ◽  
Primary Data ◽  
Sense Making ◽  
Data Sets ◽  
Business Analytics ◽  
A Value ◽  
Organisational Factors ◽  
Analytical Tools

The industry for business analytics within the BI sphere is growing significantly and the distinction in organizations between transactional information systems and decision-oriented systems breaks down. Firms need to understand both the opportunity and the potential of business analytics. Reporting, which is getting a handle on what happened in organizations, is complemented by analytics that is rather explanatory and predictive. Leveraging business analytics means to use analytics applications in order to analyse business problems and produce related business recommendations to improve business process performance. Business analytics must but be a part of a value creating process operating together with other systems and organisational factors in a synergistic manner, including people, processes, knowledge and relationship assets, culture, structure, and policies. In order for companies to be efficient, they need to automate processes, workflows and make rules. Effectiveness, on the other hand, is about making better decisions, perhaps using the same data that their competitors may have. What matters is not necessarily the technologies deployed, but emerging competence that the firm uses to support its business. A specific “mindset” needs to be installed for companies to invest into business analytics. Organisations need to better understand how best to exploit their data and convert them into information and sense-making capabilities. Business capabilities can be enhanced not only by exploitation of analytical tools, but also by the sophisticated use of information. This leads to a truly sense-making capability or “analytical mindset”. The primary data covers 398 data sets, where firms have been asked about the specifics of their information management. The data is used as input to statistical tests and the value of business analytics is being analyzed in an empirical way.

Sign in / Sign up

Export Citation Format

Share Document