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The normal distribution plays an important role in statistical analysis‎. ‎However‎, ‎a researcher may also wish to construct another symmetric distributions which fit the data better than the normal distribution‎. ‎For this purpose‎, ‎more flexible distributions have been introduced‎. ‎In this thesis‎, ‎we introduce some of such distributions‎. ‎We first introduce the slash distribution as a family of mixed-normal scale distributions‎. ‎The slash distribution can be used instead of normal distribution‎, ‎in many situations‎. ‎We also introduce Skew-slash‎. ‎Then‎, ‎a new modified-slash distribution is discussed‎. ‎We also study a modified Skew-slash distribution‎. ‎Some properties of the distributions discussed in this thesis are given‎. ‎In particular‎, ‎we present the stochastic representations‎, ‎density functions and moments of the distributions‎.