Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.09866 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- We derive a fully analytical, one-line closed-form expression for the cumulative distribution function (CDF) of the product of two correlated zero-mean normal random variables, avoiding any series representation. This result complements the well-known compact density formula with an equally compact and computationally practical CDF representation. Our main formula expresses the CDF in terms of Humbert's confluent hypergeometric function $Φ_1$ and modified Bessel functions $K_ν$, offering both theoretical elegance and computational efficiency. High-precision numerical experiments confirm pointwise agreement with Monte Carlo simulations and other benchmarks to machine accuracy. The resulting representation provides a tractable tool for applications in wireless fading channel modeling, nonlinear signal processing, statistics, finance, and applied probability.