Recently, Poonia and Azad (Theor Appl Climatol 149(1–2):339–353, 2022) studied the Alpha power exponentiated Teissier distribution and presented four applications related to the climate datasets. Unfortunately, the results of the statistical data analysis section are not correct. Therefore, the correct results for the scaled data (used by Poonia and Azad (Theor Appl Climatol 149(1–2):339–353, 2022)) are presented in this note and it is pointed out that the maximum likelihood estimates given by them for the Alpha power exponentiated Teissier distribution is not unique. Also, results for the actual datasets with a new local minimum of negative log-likelihood are provided. Few cases of identifiability is proved and few examples of non-identifiability is also given.
