  There exist only a few known examples of subordinators for which the
transition probability density can be computed explicitly along side an
expression for its L\'evy measure and Laplace exponent. Such examples are
useful in several areas of applied probability, for example, they are used in
mathematical finance for modeling stochastic time change, they appear in
combinatorial probability to construct sampling formulae, which in turn is
related to a variety of issues in the theory of coalescence models, moreover,
they have also been extensively used in the potential analysis of subordinated
Brownian motion in dimension greater than or equal to 2. In this paper, we show
that Kendall's classic identity for spectrally negative L\'evy processes can be
used to construct new families of subordinators with explicit transition
probability semigroups. We describe the properties of these new subordinators
and emphasise some interesting connections with explicit and previously unknown
Laplace transform identities and with complete monotonicity properties of
certain special functions.
