Finite population distribution function estimation with dual use of auxiliary information under simple and stratified random sampling

Abstract

The main purpose of this paper is to propose two new estimators for estimating the finite population distribution function under simple and stratified random sampling schemes using supplementary information on the distribution function, mean and ranks of the auxiliary variable. The mathematical expressions for the bias and mean squared error of the proposed estimators are derived under the first order of approximation. The theoretical and empirical studies showed that the proposed estimators uniformly perform better than the existing estimators in terms of the percentage relative efficiency.

Use of auxiliary information in estimation of the finite population mean: An exponential type of estimator

“…Bhal and Tuteja l (1991) proposed an exponential product estimator for the scenario when study and auxiliary variable are negatively correlated and proposed a simple exponential ratio estimator, in the case when a positive correlation exists between Y and X. There are some similarities between the procedures in this paper and Hussain et al 2020, however the target Hussain et al, (2020 is estimation of population distribution function. This paper primarily focuses on the development of a new estimation procedure capable of more competent incorporation of supplementary information in estimating the finite population mean.…”

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

“…Stratification improves efficiency when the variance between strata is much larger than the variances within strata as stated by Zaman and Kadilar [1]. More studies regarding population mean using auxiliary variables are Hussain et al [2], Aladag and Cingi [3], Grover and Kaur [4], Shabbir and Gupta [5], Rao [6], Singh et al [7], Kadilar and Cingi [8], Khalid [9,10], Zaman and Bulut [11], Al-Marzouki [12], and Aamir et al [13,14].…”

“…erefore, the rank of the auxiliary variable can be treated as a new auxiliary variable, and it is useful to increase the effectiveness of an estimator. By taking motivation from Hussain et al [2], we developed a new family of estimators of 􏽥 Y which needed a helping variable on the sample mean and rank of the auxiliary variable. Moreover, some members of our proposed and existing estimates are also presented in Table 1.…”

Estimation of finite population distribution function with dual use of auxiliary information under non-response

“…The optimum values of k 5 , k 6 and k 7 , determined by minimizing (26), are It is clear thatF 9 ðyÞ is more precise thanF 4 ðyÞ.…”

“…Dong et al [ 21 ] investigating the differences of single-vehicle and multi-vehicle accident probability using mixed logit model, Chen et al [ 22 ] worked on analysis of hourly crash likelihood using unbalanced panel data mixed logit model and real-time driving environmental big data, Zeng et al [ 23 ] suggested a jointly modeling area-level crash rates by severity and Zeng et al [ 24 ] used spatial joint analysis for zonal daytime and night time crash frequencies using a bayesian bivariate conditional autoregressive model. Hussain et al [ 25 ] proposed two new families of estimators using the supplementary information on auxiliary variable and exponential function for the population distribution functions in case of non-response under simple random sampling, and Hussain et al [ 26 ] two new families of estimators for estimating the finite population distribution function are proposed under simple and stratified random sampling schemes using supplementary information on the distribution function, mean and ranks of the auxiliary variable.…”