Another Look At Laplace Transform With Applications

Bartoszewicz (1999) pointed out L_X(s) may be considered as a survival function of some nonnegative random variable (denoted by (?)(X) ). Base on this new look, we studied some properties of (?)(X) and established a new stochastic order: differentiated Laplace transform ratio order. Then we give some detailed investigations on its properties. Finally, we give its some applications in the insurance pricing model, the well known Frailty models and reliability.