Introduction: Length of stay in hospital is one of the effective factors in determining the cost of hospitalized patients and one of the high-cost departments is the pediatric intensive care unit (PICU). Knowing how long patients stay in hospital beds can be effective. The purpose of this study was to provide the most appropriate statistical distribution of patients 'stay in PICU wards to predict patients' hospital stay.

Methods: In this paper, in addition to investigating the diagnoses presented to patients admitted to the PICU ward, it has been attempted to use the best statistical models in survival studies such as the inverse Weibull distribution family or its combinations to determine the best statistical model for pediatric hospitalization. To determine the pediatric intensive care unit of three hospitals in Mashhad in 2018 based on these
distributions, the first, second and third quartiles of survival time are identified and the best statistical distribution is determined for patients' residence time. R statistical software version 3.5.2 was also used for data analysis and statistical modeling of the population. Finally, maximum likelihood, Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC) were used to identify the appropriate model.

Results: Based on the data from these three hospitals, several statistical distributions suitable for survival data were fitted to patients' survival times in the PICU wards studied, and the distribution parameters along with intermediate indices and first and third quartiles were reported. After fitting the composite statistical Weibull and Generalized Reverse Weibull statistical distributions to the length of hospital stay in the PICU ward, the best distribution was the logistic regression Weibull series distribution with the highest likelihood.

Conclusion: Generalized inverse Weibull logarithmic series and Inverse Weibull Geometric distribution had a good fit for patients’ bed time in PICU department of reviewed hospitals.