Comparison of estimation and prediction methods for a zero-inflated geometric INAR(1) process with random coefficients.

This study explores zero-inflated count time series models used to analyze data sets with characteristics such as overdispersion, excess zeros, and autocorrelation. Specifically, we investigate the process, a first-order stationary integer-valued autoregressive model with random coefficients and a zero-inflated geometric marginal distribution. Our focus is on examining various estimation and prediction techniques for this model.

Some developments on seasonal INAR processes with application to influenza data.

Influenza epidemic data are seasonal in nature. Zero-inflation, zero-deflation, overdispersion, and underdispersion are frequently seen in such number of cases of disease (count) data. To explain these counts' features, this paper introduces a flexible model for nonnegative integer-valued time series with a seasonal autoregressive structure.

Unit upper truncated Weibull distribution with extension to 0 and 1 inflated model - Theory and applications.

A two-parameter unit distribution and its regression model plus its extension to 0 and 1 inflation is introduced and studied. The distribution is called the unit upper truncated Weibull (UUTW) distribution, while the inflated variant is called the inflated unit upper truncated Weibull (ZOIUUTW) distribution. The UUTW distribution has an increasing and a J-shaped hazard rate function.

A versatile model for lifetime of a component under stress.

In this study, a versatile model, called [Formula: see text]-monotone inverse Weibull distribution ([Formula: see text]IW), for lifetime of a component under stress is introduced by using the [Formula: see text]-monotone concept. The [Formula: see text]IW distribution is also expressed as a scale-mixture between the inverse Weibull distribution and uniform distribution on (0, 1). The [Formula: see text]IW distribution includes [Formula: see text]-monotone inverse exponential and [Formula: see text]-monotone inverse Rayleigh distributions as submodels and converenges to the inverse Weibull, inverse exponential, and inverse Rayleigh distributions as limiting cases.

Statistical modelling of COVID-19 and drug data via an INAR(1) process with a recent thinning operator and cosine Poisson innovations.

In this paper, we propose the first-order stationary integer-valued autoregressive process with the cosine Poisson innovation, based on the negative binomial thinning operator. It can be equi-dispersed, under-dispersed and over-dispersed. Therefore, it is flexible for modelling integer-valued time series.