We introduce a new family of continuous distributions
called the beta transmuted-H family which extends the
transmuted family pioneered by Shaw and Buckley .
Some of its mathematical properties including explicit expressions for the ordinary moments, quantiles, generating
functions and order statistics are derived. Some special models of the new family are provided. The maximum likelihood
method is used for estimating the model parameters, and the
finite sample performance of the estimators is assessed by
simulation. The importance and flexibility of the proposed
family are illustrated by applications to two real data sets.