Abstract
Zero-inflated negative binomial distribution is characterized in this paper through a linear differential equation satisfied by its probability generating function.
Highlights
Zero-inflated discrete distributions have paved ways for a wide variety of applications, especially count regression models
Zero-inflated negative binomial distribution is characterized in this paper via a differential equation satisfied by its pgf
The probability generating function of X is given by f= (s) E ( )= sX ∑p (s) sx, 0 < s < 1 x=0
Summary
Zero-inflated discrete distributions have paved ways for a wide variety of applications, especially count regression models. Nanjundan [1] has characterized a subfamily of power series distributions whose probability generating function (pgf) f (s) satisfies the differential equation (a + bs) f ′(s) = cf (s) , where f ′(s) is the first derivative of f (s) . This subfamily includes binomial, Poisson, and negative binomial distributions. Nanjundan and Sadiq Pasha [2] have characterized zero-inflated Poisson distribution through a differential equation.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
