  In this article, the compound Poisson processes of order $k$ (CPPoK) is
introduced and its properties are discussed. Further, using mixture of tempered
stable subordinator (MTSS) and its right continuous inverse, the two
subordinated CPPoK with various distributional properties are studied. It is
also shown that space and tempered space fractional versions of CPPoK and PPoK
can be obtained, which generalize the results in the literature.
