Non-conformability of the Moment Generating Function: Rayleigh Probability Function Case
A. T. Adeniran *
Department of Statistics, University of Ibadan, Ibadan, Oyo State, Nigeria.
R. O. Olatunbosun
Department of Statistics, University of Ibadan, Ibadan, Oyo State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Non-existence has been highlighted in literature as the major limitation of the moment generating function (MGF) for some random variables (e.g. Log-Normal, Cauchy) due to divergence in their series. This study investigates (with focus on the Rayleigh probability function) the case where MGF exists but not conforming with the traditional method of deriving moments (μ′r and or μr). Results show that the MGF of a Rayleigh random variable exists, uniformly continuous, infinitely differentiable, converge absolutely, and M(0) = 1, yet moments derived from MGF are in-homogeneous with the orthodox moment method.
Keywords: Moment generating function, rayleigh probability function, non-existence, log-Normal distribution, moments