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October 15, 2025Open Access

Sums of Mixed Independent Positive Random Variables: A Unified Framework

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This framework derives PDFs and CDFs for sums of fading variates, highlighting Gaussian and non-Gaussian characteristics.

The framework streamlines obtaining exact solutions for the PDF and CDF of mixed independent random variables.
Novel expressions for the PDF and CDF are derived for both Gaussian-class and non-Gaussian-class fading distributions.
The approach accommodates various types of sums, including independent and identically distributed, and mixed-type sums.
Introduction of the new α-μ mixture distribution unifies all Gaussian-class fading models and expands application scope.

García et al. (2025) studied this question.

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