  The paper considers the problem of modeling a univariate random variable.
Main contributions: (i) Suggested a new family of distributions with quantile
defined by a linear combination of some basis quantiles. This family of
distributions has a high shape flexibility and covers commonly used
distributions. (ii) Proposed an efficient estimation method by constrained
linear regression (linearity with respect to the parameters). Various types of
constraints and regularizations are readily available to reduce model
flexibility and improve out-of-sample performance for small datasets . (iii)
Proved that the estimator is asymptotically a minimum Wasserstein distance
estimator and is asymptotically normal. The estimation method can also be
viewed as the best fit in quantile-quantile plot. (iv) Case study demonstrated
numerical efficiency of the approach (estimated distribution of historical
drawdowns of SP500 Index).
