Probabilistic distributions applied to the lifespan of tilapia

a simulation study in the R Statistical Environment

Abstract

Understanding the behavior of continuous variables is highly useful for modeling natural phenomena. The longevity of fish, whether in natural or controlled environments, is a variable of interest in ecological and environmental management studies. The objective of this work was to study and fit continuous probability distributions to a dataset of Tilapia lifespan. To achieve this, the lifespan (in months) of Tilapia in a reservoir was simulated. Initially, an exploratory data analysis was conducted, revealing positive skewness and the presence of extreme values (outliers) associated with individuals with longer lifespans. The variable of interest was then modeled using probability distributions such as Exponential, Gamma, Weibull, and Normal. Parameter estimates for the models were obtained using the maximum likelihood method, and model comparison was based on the Akaike Information Criterion (AIC) and graphical analysis. The Weibull distribution provided the best fit to the fish lifespan data, with the lowest AIC and the best graphical performance. The Gamma distribution also showed excellent fit, making it a viable alternative. All analyses were performed using the R statistical environment.