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. Some probabilistic properties of the model are discussed for general seasonal INAR(p) model and three estimation methods are used to estimate the model parameters for its special case seasonal INAR(1) model. The performance of the estimation procedures has been studied using simulation. The proposed model is applied to analyze weekly influenza data from the Breisgau- Hochschwarzwald county of Baden-Württemberg state, Germany. The empirical findings show that the suggested model performs better than existing models.

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. Also, slash Weibull, slash Rayleigh, and slash exponential distribuitons can be obtained under certain variable transformation and parameter settings. The [Formula: see text]IW distribution is characterized by its hazard rate function and characterizing conditions are provided as well. Maximum likelihood, maximum product of spacing, and least squares methods are used to estimate distribution parameters. A Monte-Carlo simulation study is conducted to compare the efficiencies of the considered estimation methods. In the application part, two practical data sets, Kevlar 49/epoxy and Kevlar 373/epoxy, are modeled via the [Formula: see text]IW distribution. Modeling performance of the [Formula: see text]IW distribution is compared with its rivals by means of some well-known goodness-of-fit statistics and results show that [Formula: see text]IW distribution performs better modeling than them. Results of comparison also indicate that obtaining the [Formula: see text]IW distribution by using the [Formula: see text]-monotone concept is cost effective since the new shape parameter added to the distribution by using the [Formula: see text]-monotone concept significantly increases the modeling capability of the IW distribution. As a result of this study, it is shown that the [Formula: see text]IW distribution can be an alternative to the well-known and recently-introduced distributions for modeling purposes.