The Characteristic Function from a Family of Truncated Normal Distributions

The Characteristic Function from a Family of Truncated Normal Distributions -- Solution proposed by Karim Abadir and Tassos Magdalinos. The posers of the problem have raised an important question. We can offer a solution to a more general problem, which covers characteristic functions of continuous distributions. We then use these results to obtain formulae for the moments, whose existence is guaranteed because of double truncation. We give alternative formulae for the characteristic function (and also for the moments) because some are easier to apply than others in different circumstances. We illustrate some of the general formulae with two common distributions