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: Suppose that an order restriction is imposed among several means in time series. We are interested in testing the homogeneity of these unknown means under this restriction. In the present paper, a test based on the isotonic regression is done for monotonic ordered means in time series with stationary process and short range dependent sequences errors. A test statistic is proposed using the penalized likelihood ratio (PLR) approach. Since the asymptotic null distribution of test statistic is complicated, its critical values are computed by using Monte Carlo simulation method for some values of sample sizes at different significance levels. The power study of our test statistic is provided which is more powerful than that of the test proposed by Brillinger (1989). Finally, to show the application of the proposed test, it is applied to real dataset contains monthly Iran rainfall records.

Abstract: The association between bivariate binary responses has been studied using Pearson’s correlation coefficient, odds ratio, and tetrachoric correlation coefficient. This paper introduces a copula to model the association. Numerical comparisons between the proposed method and the existing methods are presented. Results show that these methods are comparative. However, the copula method has a clearer interpretation and is easier to extend to bivariate responses with three or more ordinal categories. In addition, a goodness-of-fit test for the selection of a model is performed. Applications of the method on two real data sets are also presented.

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.