Abstract:
The analysis and modeling of zero truncated count data is of primary interest in many fields such as engineering, public health, sociology, psychology, epidemiology. Therefore, in this article we have proposed a new and simple structure model, named a zero truncated discrete Lindley distribution. The distribution contains some sub models and represents a two-component mixture of a zero truncated geometric distribution and a zero truncated negative binomial distribution with certain parameters. Several properties of the distribution are obtained such as mean residual life function, probability generating function, moments of residual life function, raw moments, estimation of parameters, Shannon and Rényi entropies, a characterization, and stress-strength parameter. Moreover, the collective risk model is discussed by considering the proposed distribution as primary distribution and exponential and Erlang distributions as secondary ones. Test and evaluation statistics as well as three real-life data applications are considered to assess the performance of the distribution among the most frequently zero truncated discrete probability models.
Keywords:
Characterization
,
Zero truncated generalized Poisson distribution
,
Mean residual life
,
Estimation