A New Detection Function Model for Distance Sampling Based on the Burr XII Model

Abstract

One of the most used techniques for determining animal abundance is distance sampling. The distance sampling framework depends on the idea of a detection function, and a number of options have been suggested. In this paper, we provide a new flexible parametric model based on the Burr XII distribution. To be more specific, we use the survival function of the Burr XII distribution for novel purposes in this context. The proposed model is appealing because it meets all of the requirements for a reliable detection function model, such as being monotonically decreasing and having a shoulder at the origin. It also has the features of having various asymmetric properties and a heavy right tail, which are rare properties in this setting. In the first part, we provide its key characteristics, such as shapes and moments. Then, the inferential aspect of the model is investigated. The maximum likelihood estimation method is used to estimate the parameters in a data-fitting scenario. The estimates of population abundance are derived and compared with some existing parametric estimates. A simulation is run to assess how well the resulting estimates perform in comparison to other widely applied estimates from the literature. The model is then tested using two real-world data sets. Based on the famous goodness-of-fit statistics, we show that it is preferable to some of the well-established models.

Introduction to the Special Issue in Symmetry Titled “Symmetry in Statistics and Data Science”

“…11. The eleventh article, "A New Detection Function Model for Distance Sampling Based on the Burr XII Model" by Alanzi et al [11], provides a new flexible parametric model based on the functionalities of the Burr XII distribution. The inferential aspect of the model is investigated and tested using two real-world data sets.…”