A note on the unimodality and log-concavity of the exponentiated Teissier distribution.

Recently, Sharma et al. (Exponentiated Teissier distribution with increasing, decreasing and bathtub hazard functions, J. Appl. Stat. 49 (2022), pp. 371-393) introduced the exponentiated Teissier distribution. Unfortunately, the proof given for the log-concavity of the probability density function and log-concave for α ≥ 1 only, are incorrect. Also, the information related to the unimodality of the distribution is incomplete. In this note, numerically, graphically and analytically, the necessary corrections have been made.