A Lightweight Neural Inference Engine for Real Time Parameter Estimation of the Modified Inverse Generalized Exponential Distribution

Abstract

The Modified Inverse Generalized Exponential (MIGE) distribution is a very useful probability distribution used in lifetime data analysis. Classical parameter estimation methods (maximum likelihood, least squares, Cramer-von-Mises) are iterative, slow (~200 ms per sample) and limiting real‑time applications. This study presents a lightweight neural network that learns the direct mapping from sample quantiles to MIGE parameters. The network has only 32 hidden neurons and 419 trainable weights which is small enough to run on edge devices. Training it on 20,000 synthetic datasets (with input/output scaling and hyperparameter tuning), achievements of the neural estimator inference times of 0.0001 seconds per sample (size 100) which is 2,000× faster than maximum likelihood when used on a standard Intel i5 CPU. The neural estimates (α = 23.91, β = 0.2366, λ = 15.90) are nearly close to the maximum likelihood estimates (α = 30.78, β = 0.1942, λ=14.83), having a Kolmogorov–Smirnov statistic of 0.0789 (below the 5% critical value of 0.171, which indicates an acceptable fit) on the benchmark carbon fiber strength dataset. Bootstrap standard errors for α=3.83, β=0.0694, λ=2.93, reveals uncertainty quantification. Over 100 test sets of simulation study show a speed‑accuracy trade‑off has negligible bias (α = -1.79, β = -0.0059, λ = -0.097), and the neural estimator perform better than method of moments and quantile matching in accuracy during retaining speed. This study discusses how a computer engineer could further decrease MSE by implementing deeper networks (using TensorFlow Lite), deploying on FPGA/edge TPU, or quantizing weights. All codes used are open source. This study helps in bridging statistical reliability modeling with efficient embedded inference.