Generalized class of estimators under PPS Sampling: Application on solar radiation

The estimation of the population means is a crucial aspect of environmental studies in many cases including situations where the population is skewed or there is a high variability of the auxiliary data. Solar radiation is a major parameter in renewable energy planning and climate model, which tends to be spatially and temporally heterogeneous. This variability can be inefficiently estimated under Probability Proportional to Size (PPS) sampling due to inefficiencies caused by a biased ineffective estimator. In this work article we find the finite population mean of solar radiation by use of probability proportional to size (PPS) sampling. The estimators incorporate the auxiliary information into the computations in a more flexible way to increase the estimation of the population mean in PPS sampling schemes. The foremost objective of the study is to formulate, generalized and boosted estimators to attain the minimum mean squared error (MSE) and higher percentage relative efficiency (PRE) than conventional estimators. The real application to focus on is solar radiation data where the range of the auxiliary variables location, altitude, and atmospheric conditions, has a considerable impact on the value. The results show that the estimators consistently given by the generalized boosted estimators have minimum MSE and drastically high PRE as compared to their standard existing estimators. This implies that the suggested class of estimators provides a better and more efficient tool of means estimation in complex populations. Finally, the paper has added a highly flexible and valid estimation procedure in the context of a PPS sample, an application of which can be found in environmental monitoring, assessment of solar energy, and statistical surveys.