NU. International Journal of Science 2018; 15(2) : 25-42 25 The zero-distorted Topp-Leone geometric distribution: some properties and its applications with biological data Areeya Sudsuk, Winai Bodhisuwan* and Boonorm Chomtee Department of Statistics, Faculty of Science, Kasetsart University, P.O.Box 1086, Chatuchak, Bangkok, 10900, Thailand *Corresponding author. E-mail: fsciwnb@ku.ac.th ABSTRACT In this paper, the zero-distorted Topp-Leone geometric distribution is introduced. It belongs to the k-distorted generalized discrete family of distributions. This family is useful to fit both zero-inflated and zero-deflated data. In addition, the proposed distribution has many special cases including the Topp-Leone geometric, the discrete zero-truncated Topp-Leone geometric, the zero-deflated Topp-Leone geometric and the zero-inflated Topp-Leone geometric distributions. We also derive the first four moments and index of dispersion for the zero-distorted Topp-Leone geometric distribution. For parameter estimation, the most well- known method called the maximum likelihood estimation is utilized. In application study, we apply the proposed model to fit with three biological datasets. Furthermore, the fitted results of zero-distorted Topp-Leone geometric distribution are compared with the Topp-Leone geometric, the zero-distorted generalized geometric and the negative binomial distributions. In conclusion, the Anderson-Darling test statistic for discrete distributions shows that the zero-distorted Topp-Leone geometric distribution is the most appropriate model for these datasets. Keywords: zero-distorted distributions, geometric distribution, zero-inflated, maximum likelihood estimation, biological data, T-X family INTRODUCTION Count data frequently occur in many research problems. For example, the number of plant in biological study (Bliss and Fisher, 1953), the number of automobile claims in actuarial application (Gómez-Déniz et al., 2011), and the number of hospitalizations per family member in clinical trials (Klugman et al., 2012) are recorded in the form of count data. Basically, these phenomena can be described by the Poisson distribution. However, the Poisson distribution restricts values of mean and variance to be equal. Frequently, observed data do not meet that restriction as count data exhibits either overdispersion, i.e., the variance is greater than the mean or zero-inflated, i.e., the presence of a high percentage of zero values (Gómez-Déniz et al., 2011). In addition, the observed overdispersion may be the result of excessive zeros in the distribution (Perumean-Chaney et al., 2013). Some