Page 79 - programme book

ST-009
A New One-Parameter Underdispersed Size-Biased Poisson Distribution
for Count Data

Razik Ridzuan Mohd Tajuddin 1, a) and Noriszura Ismail 1, b)

1 Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia,
43600 UKM Bangi, Selangor, Malaysia.

a) Corresponding author: razikridzuan@siswa.ukm.edu.my
b) ni@ukm.edu.my

Abstract. This paper proposes a new one-parameter discrete distribution for positive count data,
named as underdispersed size-biased Poisson distribution as an alternative to modeling underdispersed
positive count data. Several properties and measures such as moment about origins, variance,
skewness, kurtosis, index of dispersion, coefficient of variation and recurrence relationship are
presented. Estimator based on two estimation techniques, i.e., maximum likelihood and moment
method are developed as well. It was found that both estimation techniques yield an identical estimator
which is unique, positively biased, consistent and asymptotically normal. A dataset is fitted to the
proposed distribution to verify the ability of the proposed distribution in explaining real dataset with
comparison to a known size-biased distribution.

Keywords: two-component mixture distribution, underdispersion, weighted distribution