We introduce two new general families of continuous distributions, generated by a distribution F and
two positive real parameters α and β which control the skewness and tail weight of the distribution. The
construction is motivated by the distribution of k-record statistics and can be derived by applying the inverse
probability integral transformation to the log-gamma distribution. The introduced families are suitable for
modelling the data with a significantly skewed and heavy-tailed distribution. Various properties of the
introduced families are studied and a number of estimations and data fitness on real data are given to
illustrate the results.