Sharma, Manish Kr.Bhat, Arshid Ahmad2023-11-142023-11-142023-10-27preferred for your work.………https://krishikosh.egranth.ac.in/handle/1/5810201146In sample surveys there are the cases when the population is rare and clustered. The sampling method used to obtain the sample in these cases is known as Adaptive Cluster Sampling. Adaptive cluster sampling (ACS) refers to the design in which an initial unit is selected by probability sampling procedure namely Simple Random Sampling without replacement and whenever the variable of interest of a selected unit satisfies a given pre-defined condition, additional units in the neighborhood of that unit are added to form the sample. The present investigation entitled “Modified Ratio and Product Type Estimators under Adaptive Cluster Sampling” has been undertaken with the objectives to develop some generalized ratio and product type estimators for estimating the population mean under ACS. The additional information used in order to improve the efficiency of the ratio and product type estimators is known as auxiliary information. The large sample property of mean square error (MSE) for the proposed estimators have been derived up to first order of approximation and are compared with the conventional and existing estimators both theoretically as well as empirically. The generalized class of ratio type estimators (t_(p,q)^ri) under ACS has been developed on the basis of linear combinations of mean, variance, skewness, kurtosis and correlation both at unit and network level at different values of i, p,q where i = 1, 2, 3, 4, p and q are the constants to be determined in order to improve the efficiency of the proposed estimators. All the cases developed with the different combinations of i, p and q are found efficient than the existing estimators taken in the literature. Among the developed cases the different values of p and q have been determined and the estimators namely 〖 t〗_2,2^r1,t_5,10^r2,t_8,9^r3 and t_2,2^r4 are found most efficient theoretically and empirically than the existing estimators as proposed by Cochran (1940), Sisodia and Dwivedi (1981), Upadhyay and Singh (1999), Singh and Tailor (2003), Kadilar and Cingi (2003), Dryver and Chao (2007), Yan and Tian (2010), Chutiman (2013), Yadav et al. (2016). The generalized class of product type estimators (t_(k,k')^pi), (t^p4) and (t_(k,k')^p5) under ACS have also been developed on the basis of linear combinations of mean, variance, skewness, kurtosis and correlation both at unit and network level at different values of i, k, k ' where i = 1, 2, 3,k and k ' are the constants to be determined in order to improve the efficiency of the proposed estimators. All the cases developed with the different combinatioIn sample surveys there are the cases when the population is rare and clustered. The sampling method used to obtain the sample in these cases is known as Adaptive Cluster Sampling. Adaptive cluster sampling (ACS) refers to the design in which an initial unit is selected by probability sampling procedure namely Simple Random Sampling without replacement and whenever the variable of interest of a selected unit satisfies a given pre-defined condition, additional units in the neighborhood of that unit are added to form the sample. The present investigation entitled “Modified Ratio and Product Type Estimators under Adaptive Cluster Sampling” has been undertaken with the objectives to develop some generalized ratio and product type estimators for estimating the population mean under ACS. The additional information used in order to improve the efficiency of the ratio and product type estimators is known as auxiliary information. The large sample property of mean square error (MSE) for the proposed estimators have been derived up to first order of approximation and are compared with the conventional and existing estimators both theoretically as well as empirically. The generalized class of ratio type estimators (t_(p,q)^ri) under ACS has been developed on the basis of linear combinations of mean, variance, skewness, kurtosis and correlation both at unit and network level at different values of i, p,q where i = 1, 2, 3, 4, p and q are the constants to be determined in order to improve the efficiency of the proposed estimators. All the cases developed with the different combinations of i, p and q are found efficient than the existing estimators taken in the literature. Among the developed cases the different values of p and q have been determined and the estimators namely 〖 t〗_2,2^r1,t_5,10^r2,t_8,9^r3 and t_2,2^r4 are found most efficient theoretically and empirically than the existing estimators as proposed by Cochran (1940), Sisodia and Dwivedi (1981), Upadhyay and Singh (1999), Singh and Tailor (2003), Kadilar and Cingi (2003), Dryver and Chao (2007), Yan and Tian (2010), Chutiman (2013), Yadav et al. (2016). The generalized class of product type estimators (t_(k,k')^pi), (t^p4) and (t_(k,k')^p5) under ACS have also been developed on the basis of linear combinations of mean, variance, skewness, kurtosis and correlation both at unit and network level at different values of i, k, k ' where i = 1, 2, 3,k and k ' are the constants to be determined in order to improve the efficiency of the proposed estimators. All the cases developed with the different combinations of i, k and k' are found efficient than the existing estimators. Among the developed cases the proposed values of k and k ' have been determined from those estimators and the estimators namely〖 t〗_4,8^p1,〖 t〗_(-1,-2)^p2,t_(-1,-2)^p3, t^p4 , t_(1,-1)^p5 and are found the most efficient theoretically and empirically than the estimators proposed by Robson (1957), Bahl and Tuteja (1991), Shahzad and Hanif (2016), Panda and Samantary (2018) and Hussain et al. (2021). Thus the proposed generalized ratio and product type estimators under ACS are superior over existing estimators theoretically as well as empirically. ns of i, k and k' are found efficient than the existing estimators. Among the developed cases the proposed values of k and k ' have been determined from those estimators and the estimators namely〖 t〗_4,8^p1,〖 t〗_(-1,-2)^p2,t_(-1,-2)^p3, t^p4 , t_(1,-1)^p5 and are found the most efficient theoretically and empirically than the estimators proposed by Robson (1957), Bahl and Tuteja (1991), Shahzad and Hanif (2016), Panda and Samantary (2018) and Hussain et al. (2021). Thus the proposed generalized ratio and product type estimators under ACS are superior over existing estimators theoretically as well as empirically.EnglishThesis