A general approximation formula for the moment-generating function of random variables with broadly distributed logarithms is derived using a saddle-point expansion of the defining integral. As a special case, a simple and accurate approximation formula for the momentgenerating function of log-normal distributions is obtained. For 4.3 dB spread it reaches 0.5% accuracy and improves rapidly as t...


 We are mainly concerned with kernel-type estimators for the moment-generating function in present paper. More precisely, we establish central limit theorem characterization of bias and variance nonparametric recursive under some mild conditions censored data setting. Finally, investigate methodology’s performance small samples through a short simulation study.

we consider an m/g/1 queue with regular and optional phase vacation and withstate dependent arrival rate. the vacation policy is after completion of service if there are no customers in the system, the server takes vacation consisting of k -phases, each phase is generally distributed. here the first phase is compulsory where as the other phases are optional. for this model the supplementary var...

A new expression for the characteristic function of log-spot in Heston model is presented. This expression more clearly exhibits its properties as an analytic characteristic function and allows us to compute the exact domain of the moment generating function. This result is then applied to the volatility smile at extreme strikes and to the control of the moments of spot. We also give a factoriz...

We present a novel mathematical approach that for the first time allows for calculating the moment generating function of mutual information of Rayleigh fading MIMO channels with arbitrary fading correlation at transmitter and receiver. Specifically, we make use of certain hypergeometric functions of matrix argument, which are frequently used in multivariate statistics. This allows for a concis...

Hidden Markov Processes (HMP) is one of the basic tools of the modern probabilistic modeling. The characterization of their entropy remains however an open problem. Here the entropy of HMP is calculated via the cycle expansion of the zeta-function, a method adopted from the theory of dynamical systems. For a class of HMP this method produces exact results both for the entropy and the moment-gen...

We consider a two-dimensional semimartingale reflecting Brownian motion (SRBM) in the nonnegative quadrant. The data of the SRBM consists of a two-dimensional drift vector, a 2×2 positive definite covariance matrix, and a 2×2 reflection matrix. Assuming the SRBM is positive recurrent, we are interested in tail asymptotic of its marginal stationary distribution along each direction in the quadra...