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Article Citation - WoS: 27Citation - Scopus: 30The Distributions of Sum, Minima and Maxima of Generalized Geometric Random Variables(Springer, 2015) Tank, Fatih; Eryilmaz, SerkanGeometric distribution of order as one of the generalization of well known geometric distribution is the distribution of the number of trials until the first consecutive successes in Bernoulli trials with success probability . In this paper, it is shown that this generalized distribution can be represented as a discrete phase-type distribution. Using this representation along with closure properties of phase-type distributions, the distributions of sum, minima and maxima of two independent random variables having geometric distribution of order are obtained. Numerical results are presented to illustrate the computational details.Article Afthd: Bayesian Accelerated Failure Time Model for High-Dimensional Time-To Data(Springernature, 2025) Kumari, Pragya; Bhattacharjee, Atanu; Vishwakarma, Gajendra K.; Tank, FatihAnalyzing high-dimensional (HD) data with time-to-event outcomes poses a formidable challenge. The accelerated failure time (AFT) model, an alternative to the Cox proportional hazard model in survival analysis, lacks sufficient R packages for HD time-to-event data under the Bayesian paradigm. To address this gap, we develop the R package afthd. This tool facilitates advanced AFT modeling, offering Bayesian analysis for univariate and multivariable scenarios. This work includes diagnostic plots and an open-source R code for working with HD data, extending the conventional AFT model to the Bayesian framework of log-normal, Weibull, and log-logistic AFT models. The methodology is rigorously validated through simulation techniques, yielding consistent results across parametric AFT models. The application part is also performed on two different real HD liver cancer datasets, which reveals the proposed method's significance by obtaining inferences for survival estimates for the disease. Our developed package afthd is competent in working with HD time-to-event data using the conventional AFT model along with the Bayesian paradigm. Other aspects, like missing values in covariates within HD data and competing risk analysis, are also covered in this article.
