Journal of Data Science

In this paper a new two-parameter distribution is proposed. This new model provides more flexibility to modeling data with increasing and bathtub hazard rate function. Several statistical and reliability properties of the proposed model are also presented in this paper, such as moments, moment generating function, order statistics and stress-strength reliability. The maximum likelihood estimators for the parameters are discussed as well as a bias corrective approach based on bootstrap techniques. A numerical simulation is carried out to examine the bias and the mean square error of the proposed estimators. Finally, an application using a real data set is presented to illustrate our model.

Analyzing time to event data arises in a number of fields such as Biology and Engineering. A common feature of this data is that, the exact failure time for all units may not be observable. Accordingly, several types of censoring were presented. Progressive censoring allows units to be randomly removed before the terminal point of the experiment. Marshall-Olkin bivariate lifetime distribution was first introduced in 1967 using the exponential distribution. Recently, bivariate Marshall-Olkin Kumaraswamy lifetime distribution was derived. This paper derives the likelihood function under progressive type-I censoring for the bivariate Marshall-Olkin family in general and applies it on the bivariate Kumaraswamy lifetime distribution. Maximum likelihood estimators of model parameters were derived. Simulation study and a real data set are presented to illustrate the proposed procedure. Absolute bias, mean square error, asymptotic confidence intervals, confidence width and coverage probability are obtained. Simulation results indicate that the mean square error is smaller and confidence width is narrower and more precise when number of removals gets smaller. Also, increasing the terminal point of the experiment results in reducing the mean square error and confidence width.

Abstract: In the area of survival analysis the most popular regression model is the Cox proportional hazards (PH) model. Unfortunately, in practice not all data sets satisfy the PH condition and thus the PH model cannot be used. To overcome the problem, the proportional odds (PO) model ( Pettitt 1982 and Bennett 1983a) and the generalized proportional odds (GPO) model ( Dabrowska and Doksum, 1988) were proposed, which can be considered in some sense generalizations of the PH model. However, there are examples indicating that the use of the PO or GPO model is not appropriate. As a consequence, a more general model must be considered. In this paper, a new model, called the proportional generalized odds (PGO) model, is introduced, which covers PO and GPO models as special cases. Estimation of the regression parameters as well as the underlying survival function of the GPO model is discussed. An application of the model to a data set is presented.

In this article, the maximum likelihood estimators of the k independent exponential populations parameters are obtained based on joint progressive type- I censored (JPC-I) scheme. The Bayes estimators are also obtained by considering three different loss functions. The approximate confidence, two Bootstrap confidence and the Bayes credible intervals for the unknown parameters are discussed. A simulated and real data sets are analyzed to illustrate the theoretical results.

In this paper, a new four parameter zero truncated Poisson Frechet distribution is defined and studied. Various structural mathematical properties of the proposed model including ordinary moments, incomplete moments, generating functions, order statistics, residual and reversed residual life functions are investigated. The maximum likelihood method is used to estimate the model parameters. We assess the performance of the maximum likelihood method by means of a numerical simulation study. The new distribution is applied for modeling two real data sets to illustrate empirically its flexibility.