Comments on “Estimating the parameter of the population selected from discrete exponential family”

We provide counter-examples to the statements claimed in Theorems 3.1-3.3 of Vellaisamy and Jain [Vellaisamy, P., Jain, S., 2008. Estimating the parameter of the population selected from discrete exponential family. Statist. Probab. Lett. 78, 1076-1087].