【摘要】 X(m)和Y(k)服从参数(m,λ)和(k,μ)的Erlang分布且相互独立.证明了在X(m)<Y(k)<X(m+n)条件下,Y(k)的条件分布为n个参数(m+i+k,λ+μ)的Erlang分布的混合,其中i=0,1,…,n-1,这一结果是条件Erlang分布双参数加法定理的一个推广.它对研究复杂排队系统中顾客等待时间分布起着重要作用.更多还原

【Abstract】 Let X(m) and Y(k) be Erlang distribution with parameter(m,λ) and,X(m) and Y(k) are mutually independent.In this paper,we prove that the conditional distribution of Y(k) is a mixture of Erlang distributions with parameter(m+i+k,λ+μi=0,1,…,n-1 under the condition X(m)<Y(k)<X(m+n).We call this result as the extension of biparametric additive theorem of conditional Erlang distribution.It plays an important role in deriving waiting time distribution in multi-server queuing system.更多还原