We present a new set of distributions for positive data based on a skewnormalalpha-power (PSN) model including a new parameter which in turnmakes the log-skew-normal alpha-power (LPSN) model more flexible thanboth the log-normal (LN) model and log-skew-normal (LSN) model. TheLPSN model contains the LN model and LSN model as special cases. Furthermore,it models positive data with asymmetry and kurtosis larger thanthe one permitted by the LN distribution. Precipitation data illustrates theusefulness of the LPSN model being less influenced by outliers.