Efficient Estimation of a Scale Parameter of Bivariate Lomax Distribution by Ranked Set Sampling

2021 ◽  
pp. 000806832199252
Author(s):  
Rohan D. Koshti ◽  
Kirtee K. Kamalja
Keyword(s):  
Scale Parameter ◽  
Real Life ◽  
Auxiliary Variable ◽  
Ranked Set Sampling ◽  
Efficient Estimation ◽  
Study Variable ◽  
Variable Formula ◽  
Lomax Distribution ◽  
Efficiency Comparison ◽  
Ams Classification

Ranked set sampling (RSS) is an efficient technique for estimating parameters and is applicable whenever ranking on a set of sampling units can be done easily by a judgment method or based on an auxiliary variable. In this paper, we assume [Formula: see text]to have bivariate Lomax distribution where a study variable [Formula: see text]is difficult and/or expensive to measure and is correlated with an auxiliary variable [Formula: see text] which is readily measurable. The auxiliary variable is used to rank the sampling units. In this article, we propose an estimator for the scale parameter of bivariate Lomax distribution using some of the modified RSS schemes. Efficiency comparison of the proposed estimators is performed numerically as well as graphically. A simulation study is also performed to demonstrate the performance of the proposed estimators. Finally, we implement the results to real-life datasets. AMS classification codes: 62D05, 62F07, 62G30

scholarly journals Generalized Chain Regression-cum-Chain Ratio Estimator for Population Mean under Stratified Extreme-cum-Median Ranked Set Sampling

2022 ◽  
Vol 2022 ◽  
pp. 1-13
Author(s):  
Asad Ali ◽  
Muhammad Moeen Butt ◽  
Muhammad Zubair
Keyword(s):  
Real Life ◽  
Auxiliary Information ◽  
Ranked Set Sampling ◽  
Efficient Estimation ◽  
Ratio Estimator ◽  
Auxiliary Variables ◽  
Study Variable ◽  
Data Set ◽  
Population Mean ◽  
Median Ranked Set Sampling

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.

scholarly journals ENHANCING EFFICIENCY OF RATIO ESTIMATOR OF POPULATION MEDIAN BY CALIBRATION TECHNIQUES

2020 ◽  
Vol 9 (8) ◽  
pp. 14-23
Keyword(s):  
Real Life ◽  
Auxiliary Variable ◽  
Survey Sampling ◽  
Ratio Estimator ◽  
Chi Square ◽  
Life Data ◽  
Real Life Data ◽  
Efficiency Comparison ◽  
Calibration Techniques ◽  
Better Than

The use of calibration estimation techniques in survey sampling have been found to improve the precision of estimators. This paper adopts the calibration approach with the assumption that the population median of the auxiliary variable is known to obtain a more efficient ratio-type estimator in estimating population median in stratified sampling. Conditions necessary for efficiency comparison have been obtained which show that the proposed estimator will always perform better than the existing asymptotically unbiased separate estimators in stratified random sampling. Numerical evaluations have been carried out through simulation and real-life data to compliment the theoretical claims. Results from the simulation study carried out under three distributional assumptions, namely the chi square, lognormal and Cauchy distributions with different sample settings showed that the new estimator provided better estimate of the median with greater gain in efficiency. In addition, result from the real-life data further supports the superiority of the proposed estimator over the existing ones considered in this study.

RATIO ESTIMATION OF THE POPULATION MEAN USING AUXILIARY INFORMATION UNDER THE OPTIMAL SAMPLING DESIGN

2020 ◽  
pp. 1-12
Author(s):  
Chunxian Long ◽  
Wangxue Chen ◽  
Rui Yang ◽  
Dongsen Yao
Keyword(s):  
Sampling Design ◽  
Auxiliary Information ◽  
Cost Effective ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Ranked Set Sampling ◽  
Study Variable ◽  
Population Mean ◽  
Optimal Sampling Design ◽  
Extreme Ranked Set Sampling

Cost-effective sampling design is a problem of major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time-consuming. In this article, we investigate ratio-type estimators of the population mean of the study variable, involving either the first or the third quartile of the auxiliary variable, using ranked set sampling (RSS) and extreme ranked set sampling (ERSS) schemes. The properties of the estimators are obtained. The estimators in RSS and ERSS are compared to their counterparts in simple random sampling (SRS) for normal data. The numerical results show that the estimators in RSS and ERSS are significantly more efficient than their counterparts in SRS.

scholarly journals Even Order Ranked Set Sampling with Auxiliary Variable

2020 ◽  
Vol 18 (2) ◽  
Author(s):  
Muhammad Tayyab ◽  
Muhammad Noor ul-Amin ◽  
Muhammad Hanif
Keyword(s):  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Ranked Set Sampling ◽  
Sampling Scheme ◽  
Ratio Estimator ◽  
Study Variable ◽  
Median Ranked Set Sampling ◽  
Even Order ◽  
Efficient Alternative ◽  
The One

Even order ranked set sampling (EORSS) is a novel proposed ranked set sampling scheme connected with an auxiliary variable correlated with the study variable. This scheme quantifies only the one sampling unit which is at even position from each ranking set by employing specific criteria. The performance of the ratio estimator under EORSS is compared to its contemporary estimators in simple random sampling (SRS), ranked set sampling (RSS), median ranked set sampling (MRSS) and quartile ranked set sampling (QRSS) exploiting the same number of quantified units. The simulation results proved that EORSS is an efficient alternative sampling scheme for ratio estimation than SRS, RSS, MRSS and QRSS.

scholarly journals The Efficiency Comparison and Application of Proposed Rhombus Ranked Set Sampling

2021 ◽  
pp. 65-78
Author(s):  
Mishal Choudri ◽  
Nadia Saeed ◽  
Kanwal Saleem
Keyword(s):  
Probability Distributions ◽  
Real Life ◽  
Secondary Data ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Population Means ◽  
Zn Concentration ◽  
The Family ◽  
Efficiency Comparison ◽  
Extreme Ranked Set Sampling

A new scheme ‘Rhombus Ranked Set Sampling’ (RRSS) is developed in this research together with its properties for estimating the population means. Mathematical validation along with the simulation evaluation is presented. The proposed method is an addition to the family of different sampling methods and generalization of ‘Folded Ranked Set Sampling’ (FRSS). For the simulation process, nine probability distributions are considered for the efficiency comparison of proposed scheme from which four are symmetric and rest are asymmetric among which Weibull and beta distributions which are used twice, unlike parametric values. (Al-Naseer, 2007 and Bani-Mustafa, 2011). Through simulation processes, it is observed that RRSS is competent and more reliable relative to simple random sampling (SRS), ranked set sampling (RSS) and folded ranked set sampling (FRSS). It is noted that for all the underlying distributions, an increase in the efficiency of Rhombus Ranked Set Sampling (RRSS) is achieved via increasing the size of the sample ‘p’. Besides the efficiency comparison, consistency of the proposed method is also valued by using Co-efficient of Variation (CV).  Secondary data on zinc (Zn) concentration and lead (Pb) contamination in different parts and tissues of freshwater fish was collected to illustrate the evaluation of RRSS against SRS, RSS, FRSS and ERSS (extreme ranked set sampling). The results obtained through real life illustration defend the simulation study and hence indicates that the RRSS estimator is efficient substitute for existing methods (Al-Omari, 2011).

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.

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

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.

scholarly journals Modified ratio estimators of population mean using linear combination of co-efficient of skewness and quartile deviation

2013 ◽  
Vol 31 (1) ◽  
pp. 39 ◽  
Author(s):  
M. Iqbal Jeelani ◽  
S. Maqbool
Keyword(s):  
Linear Combination ◽  
Auxiliary Variable ◽  
Degree Of Approximation ◽  
Linear Combinations ◽  
Study Variable ◽  
Population Mean ◽  
Mean Squared Errors ◽  
Ratio Estimators ◽  
Coefficient Of Skewness ◽  
Better Than

The present paper deals with the estimation of population mean of the study variable using the linear combination of known population values of coefficient of skewness and quartile deviation of auxiliary variable. Two modified ratio estimators for estimation of population mean of the study variable involving the above linear combinations are being used. Mean squared errors and biases up to the first degree of approximation are derived and compared with the proposed modified ratio estimators. The proposed modified ratio estimators perform better than the existing ratio estimators. The empirical study has been carried out in support of the results.

Using Weibull Distribution for Modeling Bimodal Diffusion Curves: A Naive Framework to Study Product Life Cycle

2019 ◽  
Vol 16 (07) ◽  
pp. 1950050
Author(s):  
Adarsh Anand ◽  
Richie Aggarwal ◽  
Ompal Singh
Keyword(s):  
Weibull Distribution ◽  
Product Life Cycle ◽  
Scale Parameter ◽  
Functional Model ◽  
Real Life ◽  
Step Function ◽  
Unknown Parameters ◽  
Consumer Durables ◽  
Study Product ◽  
Better Than

With the purpose of understanding differing shapes of sales curve (unimodal and bimodal) this paper discusses a naive way for viewing the diffusion process for consumer durables. In this paper, a step functional model involving two-step Weibull distribution with four unknown parameters is characterized wherein the shape of the density function of the models depends upon the shape and scale parameter of Weibull distribution. Empirical analysis on real life sales datasets indicates that the Weibull step function model is more flexible and fits better than the other models.

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