  We propose a structure of a semiparametric two-component mixture model when
one component is parametric and the other is defined through L-moments
conditions. Estimation of a two-component mixture model with an unknown
component is very difficult when no particular assumption is made on the
structure of the unknown component. A previous work was proposed to incorporate
a prior linear information concerning the distribution function of the unknown
component such as moment constraints. We propose here to incorporate a prior
linear information about the quantile function of the unknown component
instead. This information is translated by L-moments constraints. L-moments
hold better information about the tail of the distribution and are considered
as good alternatives for moments especially for heavy tailed distributions
since they can be defined as soon as the distribution has finite expectation.
The new semiparametric mixture model is estimated using $\varphi-$divergences
which permit to build feasible algorithms. Asymptotic properties of the
resulting estimators are studied and proved under standard assumptions.
Simulations on data generated by several mixtures models demonstrate the
viability and the interest of our novel approach and the gain from using
L-moment constraints in comparison to the use of moments constraints.
