On Fitting Live-Streaming Data: A Level Three Polynomial Component Probability Model Development

A new probability distribution termed Stream distribution is proposed and studied. This distribution is a mathematical combination of level three polynomial components and exponential distribution. The mathematical and statistical properties of the development are studied, with empirical emphasis: on the inequality relationship within the measures of central tendency, and the coefficient of variation. The model parameter was estimated using the method of maximum likelihood, where the asymptotic and consistent properties are numerically studied as well. The flexibility of Stream distribution is shown, through an application to a Live-Streaming data set and showed high efficiency in the inferential performance. The distribution is therefore recommended for forecasting needs in the light of live online audience engagement.