Delayed Renewal Process

In many practical situation one may face a situation where the first interarrival time has a different distribution from subsequent values. Thus as per the definition given  is a sequence of independent non-negative random variables with  having the distribution , while ,  has the distribution. Let , , , then we define , such that the stochastic process  is called a general or a delayed renewal process.

Properties of delayed renewal process

Note
When , then we have the normal renewal process.