A Bimodal Discrete Shifted Poisson Distribution. A Case Study of Tourists’ Length of Stay

Abstract

Although the Poisson distribution is appropriate for modelling equi-dispersed distributions, it reflects bimodality less well. In this paper, we propose a distribution which is more suitable for the latter purpose. It can be fitted to both positively and negatively skewed data and appears to represent overdispersion phenomena correctly in count data models obtained using a Poisson distribution. Furthermore, the distribution can be normalised in terms of its mean value, and therefore covariates can be included. Our empirical results are based on tourists’ length of stay in the Canary Islands (Spain), a popular holiday destination. The study analyses data supplied by the Canary Islands Tourist Expenditure Survey. Our findings show that the model presented is valid and that the fit obtained is reasonably good.

Modelling Bimodal Data Using a Multivariate Triangular-Linked Distribution

“…Other examples of such distributions include the alpha-skew Laplace distribution [20], the alpha-skew-logistic distribution [21,22], bimodal skew-elliptical distributions [23], flexible generalized skew normal and t distributions [24], as well as some multivariate skewed distributions presented in [25][26][27]. See also [28][29][30][31][32][33][34][35][36][37] for other related work. Skewed distributions have also been used in the construction of mixture models.…”

Flexible Power-Normal Models with Applications

“…An approach typically used for fitting multimodal data is the mixture of normal or asymmetric-normal models, which present difficulties such as identifiability problems (see McLachlan and Peel [3]; Marin et al [4]) and complicated numerical implementation. Bimodal distributions generated from skew-symmetric distributions can be found in Azzalini and Capitanio [5], Ma and Genton [6], Arellano-Valle et al [7], Kim [8], Lin et al [9,10], Elal-Olivero et al [11], Arnold et al [12,13], Gómez et al [14], Braga et al [15], Venegas et al [16] and Gómez-Déniz et al [17], among others.…”

Bimodal length of stay in the accommodation sharing economy

“…The other specific feature of length of stay is excess dispersion, which indicates that the mean is lower than the variance. Both are important characteristics in the fit of the distribution of tourist length of stay and in the study of its determinants ( Gómez-Déniz and Pérez-Rodríguez, 2019 ; Gómez-Déniz et al, 2020b ).…”