Several Problems In The Systematic Sampling Study

System sampling compared with other sampling methods, the implementation ofsimple and convenient operation, easily accepted by practitioners. However, when thepopulation size N is not the integer times of sample size n, sample mean is not theunbiased estimator of the population mean, actual sample mean variance is not easy toobtain. To do this by introducing a modified equidistant line sampling, circular systemsampling, etc. Get the unbiased estimator of the population mean. But even so, theestimator variance is still not easy to obtain, in order to solve this problem, we useunequal probability Horvitz-Thompson as systematic sampling estimator of populationmean. Thus, the first include probability, the second order includes probability that canbe obtained, will become the key to solve the problem. This paper introduces the newsystem sampling, mixed random systematic sampling, etc., by defining any two differentunit of distance, the nonzero probability of first, second order contain will be obtainedafter the division of the population units. Range to use the estimator variance ofHorvitz-Thompson to realize the calculation of system sampling sample mean variance.Under the linear trend the population units arrangement, the precision of the systemsampling than simple random sampling. Diagonal system sampling is put forward bySubramani, this is an unequidistant systematic sampling method, implementation isrelatively simple, and the population units arrangement under a linear trend, the estimatorvariance sampling efficiency is higher than the average system. Through theimprovement of others, the population size N is the integer times of sample size n,diagonal systematic sampling is a good systematic sampling design, and the efficiency isbetter than the average systematic sampling. When the population size N is not theinteger times of sample size n, this paper puts forward two new diagonal systemsampling method: remainder diagonal linear systematic sampling method, afterpopulation division, one part with diagonal system sampling, another part with generalsystematic sampling; Remainder diagonal systematic sampling, the population division,part with diagonal systematic sampling, the other part with also diagonal systematicsampling. By using a mixture of diagonal systems and general linear systematic sampling to produce new estimator, also calculate first include probability and the second orderprobability, by using the estimator variance of Horvitz-Thompson to realize thecalculation of system sampling sample mean variance. This population N will no longerbe limited by sample size n, it is a very good development of diagonal systematicsampling and added. In addition, this article also put forward a new systematic samplingsupplemented by simple random sampling, sample size n divisible by population size N,It can press equidistant systematic sampling to implement, and this provides a newmethod when the population size N is not integer times of sample size n.This article partly discussed the systematic sampling method, this paper mainlysolves the implement of systematic sampling method when the population size N is not arestricted integer, it has important value for actual worker to reference.