A Study on Discrete Bilal Distribution with Properties and Applications on Integer-Valued Autoregressive Process

This study proposes a new one-parameter discrete distribution, called a discrete Bilal distribution. The structural properties of the proposed distribution, including the shape of the probability mass function, mode, moments, skewness, kurtosis, index of dispersion, mean deviation, stress-strength reliability, and order statistics, are derived. These properties are expressed in closed-forms. The maximum likelihood and method of moments estimation methods are considered to estimate the unknown model parameter. An extensive simulation study is carried out to examine the finite sample performance of estimation methods. The usefulness of the proposed model is illustrated in the first-order integer-valued autoregressive process. The empirical importance of the proposed models is proved through three real data applications.