Abstract
This paper is devoted to deriving a new lifetime distribution based on a sine function to model different initial symptoms of Covid-19 patients that initially present as muscle weakness with increased Creatinine Kinase (CK), without fever or respiratory symptoms. The new distribution is called Sinusoidal Exponential Distribution. Among its interesting properties, it has the feature of possessing a periodic hazard rate function. Some of its mathematical properties are studied, including moments, moment generating function, hazard rate function, mean residual life function, reversed failure rate and Lorenz and Bonferroni Curves. The estimation of its parameter is investigated using the maximum likelihood estimation. A simulation study is carried out to assess the performance of the obtained estimators for small and large samples. Areal-life data set is considered to illustrate the usefulness and the flexibility of the proposed distribution.