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In the present paper, we concentrate on an INAR(1) model with flexible binomial-discrete Poisson Lindley innovations (BDPLINAR(1)), which describes several attractive properties. The applicability of the proposed process is evaluated by the daily counts of the COVID-19 data sets that indicate the superiority of the BDPLINAR(1) model among some competitor models. The model adequacy checking using Pearson residuals indicates that the BDPLINAR(1) model is appropriate for modeling the COVID-19 data. Several forecasting approaches, such as the classic, mode, probability function, and modified Sieve Bootstrap methods, are considered for the COVID-19 data under the BDPLINAR(1) model. [ABSTRACT FROM AUTHOR]

In this paper, a discrete one-parameter distribution called the semi-Poisson distribution is introduced, which is based on a set of non-negative integers. It is seen that this distribution captures over-dispersion and zero-inflation scenarios well. A few properties of the proposed distribution, such as moments, the probability-generating function, index of dispersion, recurrence relation for the moments, and negative moments are presented. The distribution is applied to two real-life datasets related to insurance claims and parasite counts, where it is noted to perform better than many of the existing discrete distributions based on Z + , including some of the recently introduced ones. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new integer valued autoregressive model of order one. The specificity of this model is based on its non-linear structure. The autoregressive component is defined through the binomial thinning operator. Also, an additional process is introduced into the autoregressive component. This random process controls how the previous value influences the next value of the observed series. For such a model, the main properties are derived and the unknown parameters of the model are estimated using the conditional maximum likelihood method. The practical aspect of the model is discussed on real data sets. [ABSTRACT FROM AUTHOR]

INAR models have the great advantage of being able to capture the conditional distribution of a count time series based on their past observations, thus allowing it to be tailored to meet the unique characteristics of count data. This paper reviews the two-parameter Poisson extended exponential (PEE) distribution and its corresponding INAR(1) process. Then the INAR of order p (INAR(p)) model that incorporates PEE innovations is proposed, its statistical properties are presented, and its parameters are estimated using conditional least squares and conditional maximum likelihood estimation methods. Two practical data sets are analyzed and compared with competing INAR models in an effort to gauge the performance of the proposed model. It is found that the proposed model performs better than the competitors. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

As a statistical and computational technique, independent component analysis (ICA) is employed to separate the source variables into statistically independent components. ICA methods have received growing attention as effective data mining tools. In this paper, two novel ICA-based approaches are proposed to identify the clusters of variables. The identified clusters reduce the dimensionality of the data in a natural way. The first approach, namely "Estimated Mixing Coefficients," is based on the sum of squares of mixing coefficients, and the second approach, namely "Ranked R ¯ 2 ," uses the ranking pattern of R ¯ 2 of the original and reconstructed series at predefined threshold levels. The proposed techniques are applied to financial time series data to validate their effectiveness. The main focus of the study is on the clustering of multivariate time series datasets using two new proposed approaches based on independent component analysis. The internal and external structures of clusters are also explored using different metrics. Both proposed techniques are compared with some existing clustering techniques. The experimental evaluation results show that the performance of the proposed techniques is better than the existing techniques. [ABSTRACT FROM AUTHOR]

Lifetime distributions that have bathtub-shaped failure rates with low and long constant region at the mid-time period are more realistic for modelling failure time datasets with similar failure rates. In this paper, we introduce a new model named flexible additive Chen–Gompertz distribution. The model has increasing and bathtub-shaped failure rate with or without low and long constant region, and can be adequately used in reliability context. Some distributional properties of the model are obtained. We present a complete Bayesian analysis of the proposed model for censored and non-censored datasets and provide the Bayes estimators of the model parameters using the Metropolis–Hastings algorithm by utilizing the square error loss function. We have also given the maximum likelihood estimators of the model parameters for complete and right-censored datasets and performed simulations on the two methods for different settings of the parameters and sample sizes. The applicability of the proposed distribution is demonstrated by fitting three different failure time datasets each with bathtub failure rate from reliability and survival analysis. The results of the applications illustrate that the model provides a good fit to all the three datasets compared to the other well-known Chen and Weibull extended distributions as evidenced by some goodness-of-fit tests. • Proposed a new extension of Chen distribution for one and two failure modes systems. • Has bathtub-shaped failure rate with or without low and long constant region. • Present a complete Bayesian analysis of the proposed model for complete and right-censored datasets. • Obtained maximum likelihood estimators for complete and right-censored datasets. • Demonstrate the model performance in modelling reliability and survival datasets. [ABSTRACT FROM AUTHOR]

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., (© 2023. The Author(s).)

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 0 - 1 inflated unit upper truncated Weibull (ZOIUUTW) distribution. The UUTW distribution has an increasing and a J-shaped hazard rate function. The parameters of the proposed models are estimated by the method of maximum likelihood estimation. For the UUTW distribution, two practical examples involving household expenditure and maximum flood level data are used to show its flexibility and the proposed distribution demonstrates better fit tendencies than some of the competing unit distributions. Application of the proposed regression model demonstrates adequate capability in describing the real data set with better modeling proficiency than the existing competing models. Then, for the ZOIUUTW distribution, the CD34+ data involving cancer patients are analyzed to show the flexibility of the model in characterizing inflation at both endpoints of the unit interval., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2023 The Author(s).)