The Properties Of Statistics Of The Mean-mixture Of Normal Distribution

Based on background in genetic analysis, this paper proposes a class of mean-mixture of normal distribution:where be a density of , be a weighting function. It is different from the variance-mixture of normal distribution:where be a density of , be a weighting func-tion.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 ,such as X and are discussed.