When the observations reflect a multimodal, asymmetric or truncated construction or a combination of them, using usual unimodal and symmetric distributions leads to misleading results. Therefore, distributions with ability of modeling skewness, multimodality and truncation have been in the core of interest in statistical literature, always. There are different methods to contract a distribution with these abilities, which using the weighted distribution is one of these methods. In this paper, it is shown that by using a weight function one can create such desired abilities in the corresponding weighted distribution.