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This note reconsiders the marginal density of a threshold moving average process and proposes a simple yet effective numerical algorithm to implement that by solving an associated integral equation. This algorithm can also be applied to calculate stationary probability density or distribution functions of a few other types of nonlinear stationary stochastic processes numerically.

Background Large-volume fluid resuscitation remains irreplaceable in the early-stage management of severe burns. We aimed to explore the relationship between fluid volume and other indicators. Method Data of severe burn patients with successful resuscitation in the early stage was collected. Correlation and linear regression analyses were performed. Multiple linear regression models, related goodness-of-fit assessment (adjusted R-square and Akaike Information Criterion), scatter plots and paired t-test for two models, and a likelihood ratio test were performed. Results 96 patients were included. The median of total burn area (TBA) was 70%TBSA, with full thickness burn area (FTBA)/TBA of 0.4, a resuscitation volume of 1.93 mL/kg/%TBSA. Among volume-correlated indicators, two linear regression models were established (Model 1: TBA × weight and tracheotomy; and Model 2: FTBA × weight, partial thickness burn area (PTBA) × weight, and tracheotomy). For these models, close values of Akaike Information Criterion, adjusted R-squares, outliers of the prediction range, and the result of paired t-test, all suggest similarity between two models estimations, while the likelihood ratio test for coefficients of FTBA × weight and PTBA × weight showed a statistical difference. Conclusion inhalational injury and decompression surgery only correlated with volume, while Tracheotomy, TBA × weight, FTBA × weight, and PTBA × weight correlated with and were accepted in linear models of volume. Although FTBA and PTBA differed statistically, there may be no need to distinguish them when estimating the resuscitation volume requirements in this patient set. Further study about different depths fluid should be conducted.