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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.