Abstract:

Based on background in genetic analysis, this paper proposes a class of mean-mixture  of normal distribution. It is different from the variance-mixture of normal distribution,  which is discussed in several bibliographies in general. We principally consider the  properties of statistics of the mean-mixture of normal distribution. It is shown that  those statistics which are invariant under translational transformation are robust in  the class of mean-mixture of normal distribution, that is, these statistics have the   same properties as those of normal distribution. Then the   mean-mixture of normal distribution has the advantage of easily transferring properties enjoyed by
 normal distribution. Besides, the distributions of several other statistics are discussed.

Key words: Mean-mixture of normal distribution, Variance-mixture of normal distribution, Translational transformation, Scaling transformation, Robust