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- Title
On Distribution of Rice–Middleton Model.
- Authors
Górska, Katarzyna; Horzela, Andrzej; Maširević, Dragana Jankov; Pogány, Tibor K.
- Abstract
The probability density function in Rice–Middleton model, which describes the behavior of the single sinusoidal random signal combined with Gaussian noise is expressed in three mutually independent ways: firstly, with the aid of an integral representation of the modified Bessel function of the first kind of integer order; secondly, by a hyperbolic cosine differential operator and thirdly, applying the Grünwald–Letnikov fractional derivative. The cumulative distribution functions are also described in all these cases, and also using the Nuttall Q–function. An associated, seemingly new, probability distribution is introduced which cumulative distribution function and the raw moments of general real order are obtained whilst the characteristic function's power series form is inferred. The exposition ends with a discussion in which by–product summations are given for the considered Neumann series of the second type built by modified Bessel functions of the second kind having integer order.
- Subjects
CUMULATIVE distribution function; PROBABILITY density function; DIFFERENTIAL operators; CHARACTERISTIC functions; BESSEL functions; RANDOM noise theory
- Publication
Results in Mathematics / Resultate der Mathematik, 2024, Vol 79, Issue 3, p1
- ISSN
1422-6383
- Publication type
Article
- DOI
10.1007/s00025-024-02141-3