Many properties of distribution functions can be characterized in terms of their characteristic functions

Аннотация

Many properties of distribution functions can be characterized in terms of their characteristic functions. This suggests that statistical inference about such properties might utilize the characteristic function. This requires that some means be found to gather information about the characteristic function from a random sample. In this investigation, the empirical characteristic function is proposed to do this. Key words: empirical characteristic function, characteristic function, probability space, independent and identically distributed random variables.