Moment-generating function and characteristic function

2012 ◽  
pp. 185-210
Author(s):  
Hisashi Kobayashi ◽  
Brian L. Mark ◽  
William Turin
Keyword(s):  
Characteristic Function ◽  
Generating Function ◽  
Moment Generating Function

The BMAP/GI/1 queue with server set-up times and server vacations

1993 ◽  
Vol 25 (01) ◽  
pp. 235-254 ◽  
Author(s):  
Josep M. Ferrandiz
Keyword(s):  
Characteristic Function ◽  
Generating Function ◽  
Queue Length ◽  
Queueing System ◽  
Moment Generating Function ◽  
Server Vacations ◽  
Service Completion ◽  
Set Up ◽  
Vacation Period ◽  
Completion Times

Using Palm-martingale calculus, we derive the workload characteristic function and queue length moment generating function for the BMAP/GI/1 queue with server vacations. In the queueing system under study, the server may start a vacation at the completion of a service or at the arrival of a customer finding an empty system. In the latter case we will talk of a server set-up time. The distribution of a set-up time or of a vacation period after a departure leaving a non-empty system behind is conditionally independent of the queue length and workload. Furthermore, the distribution of the server set-up times may be different from the distribution of vacations at service completion times. The results are particularized to the M/GI/1 queue and to the BMAP/GI/1 queue (without vacations).

The BMAP/GI/1 queue with server set-up times and server vacations

1993 ◽  
Vol 25 (1) ◽  
pp. 235-254 ◽  
Author(s):  
Josep M. Ferrandiz
Keyword(s):  
Characteristic Function ◽  
Generating Function ◽  
Queue Length ◽  
Queueing System ◽  
Moment Generating Function ◽  
Server Vacations ◽  
Service Completion ◽  
Set Up ◽  
Vacation Period ◽  
Completion Times

Using Palm-martingale calculus, we derive the workload characteristic function and queue length moment generating function for the BMAP/GI/1 queue with server vacations. In the queueing system under study, the server may start a vacation at the completion of a service or at the arrival of a customer finding an empty system. In the latter case we will talk of a server set-up time. The distribution of a set-up time or of a vacation period after a departure leaving a non-empty system behind is conditionally independent of the queue length and workload. Furthermore, the distribution of the server set-up times may be different from the distribution of vacations at service completion times. The results are particularized to the M/GI/1 queue and to the BMAP/GI/1 queue (without vacations).

The Cumulant Generating Function Estimation Method

1997 ◽  
Vol 13 (2) ◽  
pp. 170-184 ◽  
Author(s):  
John L. Knight ◽  
Stephen E. Satchell
Keyword(s):  
Characteristic Function ◽  
Density Function ◽  
Generating Function ◽  
Estimation Method ◽  
Empirical Characteristic Function ◽  
Function Estimation ◽  
Asymptotic Equivalence ◽  
Cumulant Generating Function ◽  
Worked Example ◽  
Step Procedure

This paper deals with the use of the empirical cumulant generating function to consistently estimate the parameters of a distribution from data that are independent and identically distributed (i.i.d.). The technique is particularly suited to situations where the density function is unknown or unbounded in parameter space. We prove asymptotic equivalence of our technique to that of the empirical characteristic function and outline a six-step procedure for its implementation. Extensions of the approach to non-i.i.d. situations are considered along with a discussion of suitable applications and a worked example.

scholarly journals Performance Analysis Of Cooperative Relaying In Nakagami-M Fading Channels

1970 ◽  
Vol 6 (2) ◽  
pp. 1-5
Author(s):  
B Barua ◽  
MZI Sarkar
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Fading Channels ◽  
Generating Function ◽  
Error Probability ◽  
Moment Generating Function ◽  
Cooperative Relaying ◽  
Relay Network ◽  
Symbol Error Probability

This paper is concerned with the analysis of exact symbol error probability (SEP) for cooperative diversity using amplify-and-forward (AF) relaying over independent and non-identical Nakagami-m fading channels. The mathematical formulations for Probability Density Function (pdf) and Moment Generating Function (MGF) of a cooperative link have been derived for calculating symbol error probability with well-known MGF based approach taking M-ary Phase Shift Keying (MPSK) signals as input. The numerical results obtained from this research have been compared with different fading conditions. It is observed that the existence of the diversity link in a relay network plays a dominating role in error performance. Keywords: Symbol Error Probability; Probability Density Function; Moment Generating Function; Nakagami-m fading. DOI: http://dx.doi.org/10.3329/diujst.v6i2.9338 DIUJST 2011; 6(2): 1-5

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