A novel stereographic semi-circular distribution and enhanced analysis of the posterior corneal curvature of eye.

Circular distributions within the radians range describe two-dimensional directions by mapping points onto a unit circle. These distributions are vital in diverse fields such as medicine, ecology, and environmental studies, where measurements are expressed in terms of angles. However, when these distributions involve measuring angles within the radians range, they constitute axial or semi-circular data instead of circular data.

Properties, quantile regression, and application of bounded exponentiated Weibull distribution to COVID-19 data of mortality and survival rates.

Well-known continuous distributions such as Beta and Kumaraswamy distribution are useful for modeling the datasets which are based on unit interval [0,1]. But every distribution is not always useful for all types of data sets, rather it depends on the shapes of data as well. In this research, a three-parameter new distribution named bounded exponentiated Weibull (BEW) distribution is defined to model the data set with the support of unit interval [0,1].

Efficient estimation of population variance of a sensitive variable using a new scrambling response model.

This study introduces a pioneering scrambling response model tailored for handling sensitive variables. Subsequently, a generalized estimator for variance estimation, relying on two auxiliary information sources, is developed following this novel model. Analytical expressions for bias, mean square error, and minimum mean square error are meticulously derived up to the first order of approximation, shedding light on the estimator's statistical performance.