A Cox-Weibull Convoluted Proportional Hazard Model with Constrained Parameters for Modelling Short-Term and Long-Term Survival Risks

O. Faweya — 2026-03-31

Survival analysis comprises a set of statistical techniques used to investigate the time duration until occurrence of a specific event.it undergone significant methodological advancement since the introduction of the classical Cox proportional hazards model. The Cox model, by virtue of its semi-parametric formulation, provided researchers with a flexible tool to model time-to-event data without making strict assumptions about the baseline hazard function. However, its flexibility has proven insufficient in many real-world applications, especially where complex hazard dynamics such as dual risk, long-term survivorship, or structural heterogeneity are present, have advanced survival modeling but fall short of addressing the dual risk of hazard: the distinct short-term and long-term risk patterns that may coexist within survival processes. This limitation is particularly problematic in criminological studies of recidivism, where individuals face heightened risk immediately after release, followed by a different pattern of risk in the longer term. Conventional models such as the Cox proportional hazards (PH) model or parametric survival distributions are often too restrictive to capture these complexities. The present study addresses this methodological gap by proposing a convoluted proportional hazard model with constrained parameters. The literature, therefore, has evolved toward mixture cure models, split‐population models, and hybrid specifications that allow simultaneous modeling of short‐term and long‐term risks. Survival analysis has undergone significant methodological advancement but the dual risk of hazard where short-term and long-term risks follow different trajectories remains unaccounted for many approach. This study convoluted proportional hazard model with constrained parameters, This approach integrates the semi-parametric flexibility of the Cox model with the parametric structure of the Weibull distribution, to predicting the probability of recidivism and identify factors that influence the risk of recidivism and study also offers significant improvement by combining Weibull distribution and Cox model by introducing two additional constrained parameters to capture both short term and long term risk of recidivism. The addition of parameter constraints enhances parsimony, stabilty and interpretability. Maximum Likelihood estimation approach was used to estimate the parameter of the newly developed Cox-Weibull model.

Panel Vector Error Correction Modeling of the Impacts of Demographic Indicators on Human Development in Nigeria

Elizabeth Ishagba Aniah-Betiang — 2026-04-01

This study examined the impact of key demographic indicators on human development in Nigeria using an advanced panel econometric framework. Annual panel data covering the period 1994-2024 across Nigeria’s six geopolitical regions were employed to analyze how life expectancy at birth (LEB), fertility rate (FR), urbanization rate (UR), dependency ratio (DR), and female labour force participation (FLP) influence the Human Development Index (HDI). The study employed descriptive statistics, first- and second-generation panel unit root tests, Johansen Fisher panel cointegration tests, Dynamic Panel Fully Modified Ordinary Least Squares (FMOLS), Panel Vector Error Correction Models (VECM), and Dumitrescu–Hurlin as well as panel pairwise Granger causality tests. Descriptive statistics revealed considerable volatility and non-stationary behaviour in the level series of all variables. However, stationarity was achieved after first differencing, indicating integration of order one, I(1). This was confirmed by both first-generation (IPS) and second-generation (CCE-ADF) unit root tests. The Johansen Fisher panel cointegration results provided strong evidence of a stable long-run equilibrium relationship between HDI and the demographic variables. Long-run estimates obtained through dynamic panel FMOLS showed that life expectancy at birth and female labour force participation exert significant positive effects on human development, while fertility rate, urbanization rate, and dependency ratio have negative long-run impacts. These findings highlight the growth-enhancing role of improved health outcomes and women’s economic participation, alongside the development constraints imposed by high fertility, demographic dependency, and unplanned urban expansion. Short-run dynamics analyzed through the Panel VECM revealed that increases in life expectancy and female labour participation immediately enhance HDI, whereas higher fertility and dependency ratios reduce human development in the short term. Urbanization exhibited mixed effects, with negative contemporaneous impacts but positive lagged effects, suggesting that rapid urban growth initially strains infrastructure and social services but contributes to development once adjustment occurs. The error-correction term was negative and highly significant, indicating a strong annual convergence speed of about 70% toward long-run equilibrium. Finally, Dumitrescu-Hurlin panel causality tests revealed strong unidirectional causality from all demographic indicators to HDI, alongside bidirectional causality between HDI and both life expectancy and female labour force participation. The study concluded that demographic factors played a critical and enduring role in shaping Nigeria’s human development path and recommended improvement in health investment, gender-inclusive labour policies, fertility reduction, strategic urban planning, and effective management of demographic dependency for sustainable development.

Asian Journal of Probability and Statistics

A Cox-Weibull Convoluted Proportional Hazard Model with Constrained Parameters for Modelling Short-Term and Long-Term Survival Risks

Panel Vector Error Correction Modeling of the Impacts of Demographic Indicators on Human Development in Nigeria