A weighted Weibull detection model for line transect sampling: application on wooden stake perpendicular distance data

Abstract

AbstractThe line transect survey method is commonly used to estimate the population size. However, recent developments in this field have tended to prefer practical mathematical models for this purpose. In this study, a new model called the weighted Weibull detection model was introduced to specifically address certain criteria related to line transect data. This study thoroughly explored the characteristics of this new model, including its shapes, moments, and probability density functions. The maximum likelihood estimation and Bayesian estimation methods were employed to ensure accurate parameter estimation. To gauge the performance of this model, population size estimates were generated and compared with various existing parametric estimation methods that are commonly used in the field. Through simulations, the resulting estimates were assessed and compared to widely adopted approaches for estimating population size. Additionally, this mathematical model was applied to real-world data involving perpendicular distances, allowing for a direct comparison of its performance against both traditional and contemporary methods using various measures of goodness of fit. Moreover, the study calculates statistical metrics, such as the variance–covariance matrix, parameter confidence intervals, and estimated population size, were obtained using the proposed detection model. These metrics provide valuable insights into the precision and uncertainty associated with estimated parameters and population size estimates. Confidence intervals offer a range of plausible parameter values, whereas the variance–covariance matrix quantifies the relationships and uncertainties between the estimated parameters.

Keywords

• Weibull distribution
• line transect sampling
• shoulder condition
• Zude Zhou, Wuhan University of Technology, China
• Applied Mathematics; Statistics & Probability; Material Science