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In survey research, various types of estimators have been suggested that consider only the current sample information to compute the unknown population parameters. Therefore, we utilize the past sample information along with the current sample information in the form of hybrid exponentially weighted moving averages to suggest the memory type logarithmic estimators for time-based surveys. The expression of the mean square error of the suggested estimators is determined to the first order of approximation. A relative comparison of the suggested estimators with the existing estimators is performed and efficiency conditions are obtained. Further, a simulation study is accomplished using a hypothetically rendered population and a real data illustration to improve the theoretical results. The results of the simulation study and the real data application exhibit that the consideration of past and current sample information meliorates the efficiency of the suggested estimators.

In this paper, the main aim is to define a statistical distribution that can be used to model COVID-19 data in Mexico and Canada. Using the method of exponentiation on the gull alpha exponential distribution introduces a new distribution with three parameters called the exponentiated gull alpha power exponential (EGAPE) distribution. The distribution has the benefit of being able to represent monotonic and nonmonotonic failure rates, both of which are often seen in dependability issues. It is possible to determine the quantile function as well as the skewness, kurtosis, and order statistics of the suggested distribution. The approach of maximum likelihood is used in order to calculate the parameters of the model, and the RMSE and average bias are utilised in order to evaluate how successful the strategy is. In conclusion, the flexibility of the new distribution is demonstrated by modeling COVID-19 data. From the practical application, we can conclude that the proposed model outperformed the competing models and therefore can be used as a better option for modeling COVID-19 and other related datasets.