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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 $ {\rm ZIGINAR}_{RC}(1) $ ZIGINAR RC (1) 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. We employ estimation methods, including Whittle, Taper Spectral Whittle, Maximum Empirical Likelihood, and Sieve Bootstrap estimators for parameter estimation. Additionally, we propose forecasting approaches, such as median, Bayesian, and Sieve Bootstrap methods, to predict future values of the series. We assess the performance of these methods through simulation studies and real-world data analysis, finding that all methods perform well, providing 95% highest predicted probability intervals that encompass the observed data. While Bayesian and Bootstrap methods require more time for execution, their superior predictive accuracy justifies their use in forecasting. [ABSTRACT FROM AUTHOR]

In this article, classical and Bayes interval estimation procedures have been discussed for the reliability characteristics, namely mean time to system failure, reliability function, and hazard function for the power Lindley model and its special case. In the classical part, maximum likelihood estimation, maximum product spacing estimation are discussed to estimate the reliability characteristics. Since the computation of the exact confidence intervals for the reliability characteristics is not directly possible, then, using the large sample theory, the asymptotic confidence interval is constructed using the above-mentioned classical estimation methods. Further, the bootstrap (standard-boot, percentile-boot, students t-boot) confidence intervals are also obtained. Next, Bayes estimators are derived with a gamma prior using squared error loss function and linex loss function. The Bayes credible intervals for the same characteristics are constructed using simulated posterior samples. The obtained estimators are evaluated by the Monte Carlo simulation study in terms of mean square error, average width, and coverage probabilities. A real-life example has also been illustrated for the application purpose. [ABSTRACT FROM AUTHOR]

In this paper, a first-order integer-valued autoregressive (INAR(1)) model with zero-and-one inflated Poisson–Lindley distributed innovations is presented. It is shown that the model represents a mixture of zero-and-one inflated geometric INAR(1) process and zero-and-one inflated negative binomial INAR(1) process. Moreover, some basic and conditional properties of this model are obtained. The distribution of the runs (the lengths of zeros and ones) is investigated. Some estimation methods are used to estimate the unknown parameters of the model and the asymptotic properties of the estimators are obtained. Using the conditional maximum likelihood estimation method, the model is fitted to a set of practical data, and the model is validated by some goodness-of-fit criteria. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a flexible extension of the Maxwell distribution for modeling various practical data with non-monotone failure rate. Some main properties of this distribution are obtained, and then the estimation of the parameters for the proposed distribution has been addressed by maximum likelihood estimation method and Bayes estimation method. The Bayes estimators have been obtained under gamma prior using squared error loss function. Also, a simulation study is gained to assess the estimates performance. A real-life applications for the proposed distribution have been illustrated through different lifetime data. [ABSTRACT FROM AUTHOR]