On the statistical analysis of a random number of observations (Q1824972)

Let \((X_ n\), \(n\geq 1)\) be a sequence of real-valued (for simplicity) random variables, and \((T_ n\), \(n\geq 1)\) a strictly increasing sequence of nonnegative random variables. The double sequence \((T_ n,X_ n\), \(n\geq 1)\) is called a marked point process. In a fixed observation interval [0,t], we get a sequence of mark observations \((X_ n\), \(1\leq n\leq N(t))\). On the basis of this model, we shall evaluate the common probability distribution of the variables \(X_ n\), if they are identically distributed, and estimate moments of this distribution.