AN ALTERNATIVE DISCRETE ANALOGUE OF THE HALF-LOGISTIC DISTRIBUTION

Abstract

A discrete version of the continuous half-logistic distribution is introduced, which is based on the minimization of the Cramer distance between the corresponding continuous and step-wise cumulative distribution functions. The expression of the probability mass function is derived in analytic form and some properties of the distribution are discussed, as well as sample estimation. A comparison is also made with a discrete version already proposed in the literature, which is based on a different rationale. An application to real data is finally presented.

Keywords

• discretization
• distance minimization
• survival function

References

1. N. Balakrishnan, Order statistics from the half logistic distribution, J. Stat. Comput. Simul. 20(4) (1985) 287–309.
2. A. Barbiero and A. Hitaj, A discrete analogue of the half-logistic distribution, in 2020 International Conference on Decision Aid Sciences and Application (DASA), 2020, pp. 64–67.
3. A. Barbiero and A. Hitaj, A new method for building a discrete analogue to a continuous random variable based on minimization of a distance between distribution functions, in 2021 International Conference on Data Analytics for Business and Industry (ICDABI), 2021, pp.338–341.
4. M. S. Ridout and P. Besbeas, An empirical model for underdispersed count data, Stat.Model. 4(1) (2004) 77–89.
5. S. Chakraborty and R. D. Gupta, Exponentiated geometric distribution: another generalization of geometric distribution, Comm. Statist. Simulation Comput. 44(6) (2015) 1143–1157.
6. A. Barbiero, A. Hitaj, An alternative discrete analogue of the half-logistic distribution, in Abstract Book of ICMS 2023, p.84.