ISEE observations indicate that after prolonged quiet periods, the saturated equatorial density decreases exponentially with the radial distance in the plasmasphere. No hydrostatic barometric models fit the saturated equatorial density profiles, since those obtained with barometric maxwellian or lorentzian kinetic models decrease more slowly with the radial distance. Orbits of trapped particles are in complete thermal equilibrium with the escaping and ballistic ones only when the Coulomb collision time is much smaller than the inter-hemispheric flight time of the ions and electrons. At large radial distances and in the outermost flux tubes (i.e. for large L-parameters), this condition is not always fulfilled. It is shown that hydrostatic exospheric models with an unsaturated and L-dependent population of trapped particles can be used to fit the observed density profiles. Such hydrostatic exospheric models with unsaturated population of trapped particles can therefore be used to construct empirical 3D models of the density distribution in the plasmasphere. At small L and low altitudes, trapped orbits are saturated, while at large distances, these orbits are almost completely depleted. The fraction η(L) of required trapped particles necessary to obtain a good fit to observed equatorial density profiles is a function of L. We have determined this function by fitting our hydrostatic theoretical equatorial electron density profiles to that observed by Carpenter and Anderson (1992) from L=2 to 8 after a prolonged period of quiet conditions. Differences between maxwellian and lorentzian hydrostatic barometric models and exospheric hydrostatic models for different values of the kappa index are presented.