Analyzing radiation data using an optimal memory-type mean estimator under PPS sampling

Abstract

In the last few years, memory-type estimators of population parameters have received a wide popularity among researchers due to their improved efficiency over simple estimators. The available memory-type estimators use the traditional equal probability sampling designs. A drawback of the traditional sampling methods is that they employ the assumption of equal chances of selection for all population units, which is generally not applicable in real-life problems. In situations in which the units of the population have unequal selection probabilities, PPS (probability proportional to size) design is the appropriate method for sample selection. This paper presents an optimal memory-type mean estimator under PPS sampling. Different mathematical properties have been derived and assessed in the case of PPS sampling. Real-world populations related to food irradiation methods have been considered to assess the efficiency of the competing estimators. The comparative analysis reveals that the new memory-type estimator works better than the competitor estimators in efficiency, which makes the new estimator suitable for practical applications.