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# Article

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Summary:
The knowledge of the relations between the distribution of a random vibratory process and that of its envelope is required in many engineering applications. Under the assumption that the vibratory process is of narrow band type and the phase is uniformly distributed over the interval $(0, 2\pi)$, the integral transform giving the relation between the two distributions in question may be derived considering that the distribution of the envelope is known and the distribution function of the vibratory process is to be estimated. The aim of the paper is to summarize some most useful types of distribution functions which are important in the technical practice. Analytical expressions for the distributions of the corresponding vibratory processes are given for ten one-parametric distributions and for distributions with threeshold values, all related to the envelope processes. Approximate analytical description using the Gram-Charlier series may be used for cases where the analytical solution is inaccessible. This procedure is shown for three two-parametric distributions and for the generalized three- and four-parametric gamma-distributions.
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