A New Skewed Discrete Model: Properties, Inference, and Applications

Abstract

In this paper, a new probability discrete distribution for analyzing over-dispersed count data encountered in biological sciences was proposed. The new discrete distribution, with one parameter, has a log-concave probability mass function and an increasing hazard rate function, for all choices of its parameter. Several properties of the proposed distribution including the mode, moments and index of dispersion, mean residual life, mean past life, order statistics and L- moment statistics have been established. Two actuarial or risk measures were derived. The numerical computations for these measures are conducted for several parametric values of the model parameter. The parameter of the introduced distribution is estimated using eight frequentist estimation methods. Detailed Monte Carlo simulations are conducted to explore the performance of the studied estimators. The performance of the proposed distribution has been examined by three over-dispersed real data sets from biological sciences.

A Discrete Analogue of Complementary Exponentiated-G Poisson Family of Distributions: Properties and Estimation

“…The second data set refers to survival times of 44 patients suffering from head and neck cancer who retreated using a combination of radio therapy. This data is given by Afify et al [40]. The data are: The third data set is displayed in Table 10.…”

Bayesian Estimation and Prediction for Discrete Zubair Weibull Distribution under Type-II Censoring Scheme

“…The second data set refers to the survival times of 44 patients suffering from head and neck cancer who retreated using a combination of radiotherapy. These data are proposed by Afify et al (2021). The data are: 12, 32, 37, 24, 24, 74, 81, 26, 41, 58, 63, 68, 78, 47, 55, 84, 155, 159, 92, 94, 110, 127, 130, 133, 140, 112, 119, 146, 173, 179, 194, 195, 339, 432, 209, 249, 281, 319, 469, 725, 817, 519, 633, and 1776.…”