Abstract
We model the interaction between a qubit and optical radiation field (ORF) using an excited binomial distribution (EBD) and excited negative binomial distribution (ENBD). The explicit form of the density matrix of the qubit-ORF system is given in terms of the photon number distribution. The Mandel parameter is used to quantify the statistical properties of the ORF during the interaction. We derive the relation between the tomographic entropy and the quantum Fisher information of the estimators of model parameters in the EBD and ENBD. We also explore the properties and dynamics of these statistical quantities.