scholarly journals Extension of Ostrowki type inequality via moment generating function

2020 ◽  
Keyword(s):  
Generating Function ◽  
Type Inequality ◽  
Moment Generating Function

On the Power Series Expansion of the Moment Generating Function

1974 ◽  
Vol 28 (2) ◽  
pp. 58
Author(s):  
Roch Roy ◽  
Yves Lepage ◽  
Marc Moore
Keyword(s):  
Power Series ◽  
Series Expansion ◽  
Generating Function ◽  
Power Series Expansion ◽  
Moment Generating Function ◽  
The Moment

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

scholarly journals Moments of the weighted Cantor measures

2019 ◽  
Vol 52 (1) ◽  
pp. 256-273
Author(s):  
Steven N. Harding ◽  
Alexander W. N. Riasanovsky
Keyword(s):  
Probability Measure ◽  
Generating Function ◽  
Exponential Decay ◽  
Legendre Polynomials ◽  
Borel Probability Measure ◽  
Moment Generating Function ◽  
Unit Interval ◽  
Uniform Error ◽  
Natural Case ◽  
Borel Probability

AbstractBased on the seminal work of Hutchinson, we investigate properties of α-weighted Cantor measures whose support is a fractal contained in the unit interval. Here, α is a vector of nonnegative weights summing to 1, and the corresponding weighted Cantor measure μα is the unique Borel probability measure on [0, 1] satisfying {\mu ^\alpha }(E) = \sum\nolimits_{n = 0}^{N - 1} {{\alpha _n}{\mu ^\alpha }(\varphi _n^{ - 1}(E))} where ϕn : x ↦ (x + n)/N. In Sections 1 and 2 we examine several general properties of the measure μα and the associated Legendre polynomials in L_{{\mu ^\alpha }}^2 [0, 1]. In Section 3, we (1) compute the Laplacian and moment generating function of μα, (2) characterize precisely when the moments Im = ∫[0,1]xm dμα exhibit either polynomial or exponential decay, and (3) describe an algorithm which estimates the first m moments within uniform error ε in O((log log(1/ε)) · m log m). We also state analogous results in the natural case where α is palindromic for the measure να attained by shifting μα to [−1/2, 1/2].

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