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: A new distribution, called Odds Generalized Exponential-Exponential distribution (OGEED) is proposed for modeling lifetime data. A comprehensive account of the mathematical properties of the new distribution including estimation and simulation issues is presented. A data set has been analyzed to illustrate its applicability.

Analysing seasonality in count time series is an essential application of statistics to predict phenomena in different fields like economics, agriculture, healthcare, environment, and climatic change. However, the information in the existing literature is scarce regarding the performances of relevant statistical models. This study provides the Yule-Walker (Y-W), Conditional Least Squares (CLS), and Maximum Likelihood Estimation (MLE) for First-order Non-negative Integer-valued Autoregressive, INAR(1), process with Poisson innovations with different monthly means. The performance of Y-W, CLS, and MLE are assessed by the Monte Carlo simulation method. The performance of this model is compared with another seasonal INAR(1) model by reproducing the monthly number of rainy days in the Blackwater River watershed located in coastal Virginia. Two forecast-coherent methods in terms of mode and probability function are applied to make predictions. The models’ performances are assessed using the Root Mean Square Error and Index of Agreement criteria. The results reveal the similar performance of Y-W, CLS, and MLE for estimating the parameters of data sets with larger sample size and values of α close to unite root. Moreover, the results indicate that INAR(1) with different monthly Poisson innovations is more appropriate for modelling and predicting seasonal count time series.

In this paper, we introduce the alternative methods to estimation for the new weibull-pareto distribution parameters. We discussed of point estimation and interval estimation for parameters of the new weibull-pareto distribution. We have also discussed the method of Maximum Likelihood estimation, the method of Least Squares estimation, the method of Weighted Least Squares estimation and the method of Maximum Product Spacing estimation. In addition, we discussed the raw moment of random variable X and the reliability functions (survival and hazard functions). Further, we compared between the results of the methods that have been discussed using Monte Carlo Simulation method and application study.

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 paper, we introduce a new lifetime model, called the Gen- eralized Weibull-Burr XII distribution. We discuss some of its mathematical properties such as density, hazard rate functions, quantile function and mo- ments. Maximum likelihood method is used to estimate model parameters. A simulation study is performed to assess the performance of maximum like- lihood estimators by means of biases, mean squared errors. Finally, we prove that the proposed distribution is a very competitive model to other classical models by means of application on real data set.

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.

Although the two-parameter Beta distribution is the standard distribution for

Providing a new distribution is always precious for statisticians. A new three parameter distribution called the gamma normal distribution is defined and studied. Various structural properties of the new distribution are derived, including some explicit expressions for the moments, quantile and generating functions, mean deviations, probability weighted moments and two types of entropy. We also investigate the order statistics and their moments. Maximum likelihood techniques are used to fit the new model and to show its potentiality by means of two examples of real data. Based on three criteria, the proposed distribution provides a better fit then the skew-normal distribution.