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This work considers the infinite multi-server Markovian queueing model with balking and catastrophes where the rates of arrivals, service, balking, and catastrophes are time dependent. The catastrophes arrive as negative customers to the system. The arrival of negative customers to a queueing system removes the positive customers. The catastrophes may come either from another service station or from outside the system. In this paper, we obtained the transient solution of this model using the approach of probability-generating function. Also, we derived an expression of transient probabilities in terms of Volterra equation of the second kind. Furthermore, we obtained a measure for time-dependent expected number of customers in the system.

In this paper, a new Kumaraswamy generalized family is proposed. Four sub-models of the proposed family accommodate symmetrical, left-skewed, bimodal, right-skewed unimodal, and reverse-J densities, as well as increasing, modified bathtub, decreasing, bathtub, upside down bathtub, reverse J and J shaped hazard rates. Its fundamental properties are derived. The maximum likelihood method and seven other methods are used for estimating the model parameters. Numerical simulations are performed to explore the performance of these estimation methods. Three real-life data sets from medicine, agriculture and engineering are fitted to illustrate the flexibility of the proposed family. The proposed family is a good alternative to the Kumaraswamy-G, beta-G, and Topp-Leone-G families. [ABSTRACT FROM AUTHOR]

To understand the dynamic relationship of discrete time series processes, we adopted copula directional dependence via beta regression model applied with generalized autoregressive conditional heteroscedasticity (INGARCH) marginals. To validate the proposed method, we completed simulations of two INGARCH processes from asymmetric bivariate copula function with members such as Gaussian and Plackett copula functions. The simulations show that the proposed method is consistent for deriving directional dependent measurements regardless of the choice of the symmetric members. The proposed method is applied to the bivariate discrete time series data of the monthly counts of sandstorms and dust haze phenomena in Saudi Arabia. [ABSTRACT FROM AUTHOR]

Count time series data with excess zeros are observed in several applied disciplines. When these zero-inflated counts are sequentially recorded, they might result in serial dependence. Ignoring the zero-inflation and the serial dependence might produce inaccurate results. In this paper, Markov zero-inflated count time series models based on a joint distribution on consecutive observations are proposed. The joint distribution function of the consecutive observations is constructed through copula functions. First- and second-order Markov chains are considered with the univariate margins of zero-inflated Poisson (ZIP), zero-inflated negative binomial (ZINB), or zero-inflated Conway–Maxwell–Poisson (ZICMP) distributions. Under the Markov models, bivariate copula functions such as the bivariate Gaussian, Frank, and Gumbel are chosen to construct a bivariate distribution of two consecutive observations. Moreover, the trivariate Gaussian and max-infinitely divisible copula functions are considered to build the joint distribution of three consecutive observations. Likelihood-based inference is performed and asymptotic properties are studied. To evaluate the estimation method and the asymptotic results, simulated examples are studied. The proposed class of models are applied to sandstorm counts example. The results suggest that the proposed models have some advantages over some of the models in the literature for modeling zero-inflated count time series data. [ABSTRACT FROM AUTHOR]

We study a new continuous distribution called the Marshall-Olkin modified Burr III distribution. The density function of the proposed model can be expressed as a mixture of modified Burr III densities. A comprehensive account of its mathematical properties is derived. The model parameters are estimated by the method of maximum likelihood. The usefulness of the derived model is illustrated over other distributions using a real data set. [ABSTRACT FROM AUTHOR]

In this paper, we propose a flexible family called the exponentiated alpha-power-G (EAP-G) family. The benefits of the proposed family include its analytical simplicity and its ability to confer flexibility to the baseline distributions in survival analysis. Based on the proposed approach, a three-parameter extension of the exponential distribution called the exponentiated alpha-power exponential (EAPE) distribution is studied in detail. Maximum likelihood is used to estimate the EAPE parameters, and its performance is evaluated via a simulation study. Furthermore, two real-world survival data are used to demonstrate the applicability and examine the flexibility of the proposed distribution. The EAPE distribution is compared to other competing generalizations of the exponential distribution. The real data analysis shows that the proposed model performed better among the competitors and could potentially be very adequate in describing and modeling a wide range of survival data. [ABSTRACT FROM AUTHOR]