Moment Bounds for A y li Dis rete and Continuous Phase Type Distributions of Se ond Order
نویسنده
چکیده
The problem of mat hing moments to phase type (PH) distributions o urs in many appli ations. Often, low dimensions of the sele ted distributions are desired. On the other hand, it is obvious that the three parameters of a y li PH distributions of se ond order be they ontinuous (ACPH(2)) or dis rete (ADPH(2)) an be tted to three given moments provided that these are feasible. For both types of PH distributions, this paper provides the pre ise permissible ranges by giving the immanent lower and upper (if existing) bounds for the rst three moments. For moments whi h obey these bounds an exa t and minimal (with respe t to the dimension of the representation) analyti mapping of three moments into ACPH(2) or ADPH(2) is presented.
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