Summary: In this paper, we use the emergent property of the ultra weak multidimensional coupling of \(p\) 1-dimensional dynamical chaotic systems which leads from chaos to randomness.{ } Efficient Chaotic Pseudo Random Number Generators (CPRNG) have been recently introduced. They use the ultra weak multidimensional coupling of \(p\) 1-dimensional dynamical systems which preserve the chaotic properties of the continuous models in numerical experiments. Together with chaotic sampling and mixing processes, ultra weak coupling leads to families of (CPRNG) which are noteworthy.{ }In this paper we improve again these families using a double threshold chaotic sampling instead of a single one.{ }We analyze numerically the properties of these new families and underline their very high qualities and usefulness as CPRNG when very long series are computed. Moreover, a determining property of such improved CPRNG is the high number of parameters used and the high sensitivity to the parameters value which allows choosing it as cipher-keys. It is why we call these families multiparameter chaotic pseudo-random number generators (M-p CPRNG).