Analysis and Modeling of the Neonatal Mortality Rate by Fitting Probabilistic Distributions: Comparison of HLPKD, Weibull, Gamma, Lindley and Gompertz Models

This study compares five probabilistic distributions whose HLPKD, Weibull, Gamma, Gompertz and Lindley for modeling annual neonatal mortality rates in Burkina Faso over the period 1969-2023. The objective is to identify the most appropriate model for describing the distribution of this indicator and to evaluate estimator stability through simulation. Parameters were estimated using the maximum likelihood method based on data compiled by the United Nations Inter-agency Group for Child Mortality Estimation (UN IGME), accessible via the CEIC database. Monte Carlo simulations were conducted using R software (version 4.3.2) with $N=500$ replications for sample sizes $n=40,80,120,160,200$ . Performance criteria included bias, relative bias, mean squared error (MSE), root mean squared error (RMSE), average confidence interval lengths (AL₉₀ and AL₉₅) and coverage probabilities (CP₉₀ and CP₉₅). For the real data, goodness-of-fit was assessed using log-likelihood (lnL), Akaike information criterion (AIC), Bayesian information criterion (BIC), the Kolmogorov-Smirnov test (KS), mean absolute error (ASAE), the Cramér-von Mises test ($W$ ) and the Anderson-Darling test ($A$ ). Bootstrap-corrected p-values were also computed to account for parameter estimation uncertainty. The simulations showed that the Weibull, Gamma, Gompertz and Lindley models converge rapidly to stable estimates, whereas HLPKD requires larger sample sizes to achieve comparable precision. The application to real data identified the Gamma and HLPKD models as the best-fitting, with high p-values (0.8431 for Gamma and 0.9050 for HLPKD) and small discrepancies between theoretical distributions and observations. The Gamma model stands out for its parsimony (two parameters) and estimation stability, while HLPKD, despite its flexibility, suffers from greater uncertainty in its parameter $\theta$ . Bootstrap-corrected tests confirmed that Gamma and HLPKD are the only models not rejected at the 5% level. The Gamma model emerges as the most reliable for describing the distribution of