Let \(P=\{(p_1,p_2,\dots,p_n),\;0\leq p_i\leq 1,\;\sum_{i=1}^np_i=1\}\) be a finite discrete probability distribution of a set of \(n\) events \(E(E_1,E_2,\dots,E_n)\) on the basis of an experiment whose predicted probability distribution is \[ Q=\{(q_1,q_2,\dots,q_n),\;0\leq q_i\leq 1,\sum_{i=1}^nq_i=1\} \] and the utility distribution is \(U=\{(u_1,u_2,\dots,u_n),\;u_i\geq 0\}\). Under a set of certain axioms the author develops a generalized weighted information measure \(I_n^{(\alpha,\beta)}[P;Q;U]\) depending on real parameters \(\alpha\) and \(\beta\). These parameters represent factors which affect the diversity in plants and the developed model is applicable when the law of population growth is not exponential. The particular cases of this model reduce to well known measures such as Kullback’s relative information and Kerridge’s inaccuracy.