We produce an alternate proof of the extended binomial theorem by solving a first order linear ordinary differential equation with a given initial condition. The method is easy to follow and the ...

The beta-binomial distribution is extended to allow negative correlations among binary variates within an experimental unit. Regression models are proposed for both the binary variate response rate ...

This study extends the Poisson binomial distribution by introducing correlation and dependence between binomial events, enhancing its ability to capture complex event types and improving model ...