  Real projective structures on $n$-orbifolds are useful in understanding the
space of representations of discrete groups into $\mathrm{SL}(n+1, \mathbb{R})$
or $\mathrm{PGL}(n+1, \mathbb{R})$. A recent work shows that many hyperbolic
manifolds deform to manifolds with such structures not projectively equivalent
to the original ones. The purpose of this paper is to understand the structures
of properly convex ends of real projective $n$-dimensional orbifolds. In
particular, these have the radial or totally geodesic ends. For this, we will
study the natural conditions on eigenvalues of holonomy representations of ends
when these ends are manageably understandable. In this paper, we only study the
properly convex ends. The main techniques are the Vinberg duality and a
generalization of the work of Goldman, Labourie, and Margulis on flat
Lorentzian $3$-manifolds. Finally, we show that a noncompact strongly tame
properly convex real projective orbifold with generalized lens-type or
horospherical ends satisfying some topological conditions always has a strongly
irreducible holonomy group.
