Exponentiality Test Based on the Progressive Type II Censoring via Cumulative Entropy

In this article, we use cumulative residual Kullback-Leibler information (CRKL) and cumulative Kullback-Leibler information (CKL) to construct two goodness-of-fit test statistics for testing exponentiality with progressively Type-II censored data. The power of the proposed tests are compared with the power of goodness-of-fit test for exponentiality introduced by Balakrishnan et al. (2007 Balakrishnan, N., Habibi Rad, A., Arghami, N.R. (2007). Testing exponentiality based on Kullback-Leibler information with progressively type-II censored data. IEEE Transactions on Reliability 56(2):301–307.[Crossref], [Web of Science ®] , [Google Scholar]). We show that when the hazard function of the alternative is monotone decreasing, the test based on CRKL has higher power and when the hazard function of the alternative is non-monotone, the test based on CKL has higher power. But, when it is monotone increasing the power difference between test based on CKL and their proposed test is not so remarkable. The use of the proposed tests is shown in an illustrative example.     

On the distribution of the sum of independent uniform random variables

Motivated by an application in change point analysis, we derive a closed form for the density function of the sum of n independent, non-identically distributed, uniform random variables.     

Strong Gaussian Approximations of Product-Limit and Quantile Processes for Strong Mixing and Censored Data

In this article, we consider the product-limit quantile estimator of an unknown quantile function under a censored dependent model. This is a parallel problem to the estimation of the unknown distribution function by the product-limit estimator under the same model. Simultaneous strong Gaussian approximations of the product-limit process and product-limit quantile process are constructed with rate O[(log n)^?λ] for some λ > 0. The strong Gaussian approximation of the product-limit process is then applied to derive the laws of the iterated logarithm for product-limit process.     

ML and Bayes estimation in a two-phase tandem queue with a second optional service and random feedback

ABSTRACT

In this article, we consider a two-phase tandem queueing model with a second optional service and random feedback. The first phase of service is essential for all customers and after the completion of the first phase of service, any customer receives the second phase of service with probability α, feedback to the tail of the first queue with probability β if the service is not successful and leaves the system with probability 1 ? α ? β. In this model, our main purpose is to estimate the parameters of the model, traffic intensity, and mean system size, in the steady state, via maximum likelihood and Bayesian methods. Furthermore, we find asymptotic confidence intervals for mean system size. Finally, by a simulation study, we compute the confidence levels and mean length for asymptotic confidence intervals of mean system size with a nominal level 0.95.     

A generalized binomial exponential 2 distribution: modeling and applications to hydrologic events

Developing statistical methods to model hydrologic events is always interesting for both statisticians and hydrologists, because of its importance in hydraulic structures design and water resource planning. Because of this, a flexible 3-parameter generalization of the exponential distribution is introduced based on the binomial exponential 2 (BE2) distribution [2 H.S. Bakouch, M. Aghababaei Jazi, S. Nadarajah, A. Dolati, and R. Roozegar, A lifetime model with increasing failure rate, Appl. Math. Model. 38 (2014), pp. 5392–5406. doi: 10.1016/j.apm.2014.04.028[Crossref], [Web of Science ®] , [Google Scholar]]. The proposed distribution involving the exponential, gamma and BE2 distributions as submodels; and it exhibits decreasing, increasing and bathtub-shaped hazard rates, so it turns out to be quite flexible for analyzing non-negative real life data. Some statistical properties, parameters estimation and information matrix of the distribution are investigated. The proposed distribution, Gumbel, generalized Logistic and other distributions are utilized to model and fit two hydrologic data sets. The distribution is shown to be more appropriate to the data than the compared distributions using the selection criteria: average scaled absolute error, Akaike information criterion, Bayesian information criterion and Kolmogorov–Smirnov statistics. As a result, some hydrologic parameters of the data are obtained such as return level, conditional mean, mean deviation about the return level and the rth moments of order statistics.     

Change Point Detection in a General Class of Distributions

ABSTRACT

We consider the change point problem in a general class of distributions, and derive a test statistic T _n which reduces to the statistic obtained by Kander and Zacks (1966 Kander , Z. , Zacks , S. ( 1966 ). Test procedure for possible changes in parameter of statistical distributions occurring at unknown time points. Ann. Math. Statist. 37 : 1196 – 1210 . [CSA] [Crossref] , [Google Scholar]) for the exponential family. Properties of the test, including its asymptotic distribution, are discussed.     

A comparison of parametric and semi-parametric survival models with artificial neural networks

Survival models are used to examine data in the event of an occurrence. These are discussed in various types including parametric, non-parametric and semi-parametric models. Parametric models require a clear distribution of survival time, and semi-parametric models assume proportional hazards. Among these models, the non-parametric model of artificial neural network has the fewest assumptions and can be often replaced by other models. Given the importance of distribution Weibull survival models in this study of simulation shape parameter of the Weibull distribution have been assumed as 1, 2 and 3, and also the average rate at levels of 0%–75% have been censored. The values predicted by the neural network forecasting model with parametric survival and Cox regression models were compared. This comparison considering levels of complexity due to the hazard model using the ROC curve and the corresponding tests have been carried out.     

Estimation of the Parameters of a Two-phase Tandem Queue with a Second Optional Service

In this article, we consider a two-phase tandem queueing model with a second optional service. In this model, the service is done by two phases. The first phase of service is essential for all customers and after the completion of the first phase of service, any customer receives the second phase of service with probability α, or leaves the system with probability 1 ? α. Also, there are two heterogeneous servers which work independently, one of them providing the first phase of service and the other a second phase of service. In this model, our main purpose is to estimate the parameters of the model, traffic intensity, and mean system size, in the steady state, via maximum likelihood and Bayesian methods. Furthermore, we find asymptotic confidence intervals for mean system size. Finally, by a simulation study, we compute the confidence levels and mean length for asymptotic confidence intervals of mean system size with a nominal level 0.95.     

Inference for Weibull distribution based on progressively Type-II hybrid censored data

Progressive Type-II hybrid censoring is a mixture of progressive Type-II and hybrid censoring schemes. In this paper, we discuss the statistical inference on Weibull parameters when the observed data are progressively Type-II hybrid censored. We derive the maximum likelihood estimators (MLEs) and the approximate maximum likelihood estimators (AMLEs) of the Weibull parameters. We then use the asymptotic distributions of the maximum likelihood estimators to construct approximate confidence intervals. Bayes estimates and the corresponding highest posterior density credible intervals of the unknown parameters are obtained under suitable priors on the unknown parameters and also by using the Gibbs sampling procedure. Monte Carlo simulations are then performed for comparing the confidence intervals based on all those different methods. Finally, one data set is analyzed for illustrative purposes.