Journal of Data Science

Survival analysis is the widely used statistical tool for new intervention comparison in presence of hazards of follow up studies. However, it is difficult to obtain suitable survival rate in presence of high level of hazard within few days of surgery. The group of patients can be directly stratified into cured and non-cured strata. The mixture models are natural choice for estimation of cure and non-cure rate estimation. The estimation of cure rate is an important parameter of success of any new intervention. The cure rate model is illustrated to compare the surgery of liver cirrhosis patients with consenting for participation HFLPC (Human Fatal Liver Progenitor Cells) Infusion vs. consenting for participation alone group in South Indian popula-tion. The surgery is best available technique for liver cirrhosis treatment. The success of the surgery is observed through follow up study. In this study, MELD (Model for End-Stage Liver Disease) score is considered as response of interest for cured and non-cured group. The primary efficacy of surgery is considered as covariates of interest. Distributional assumptions of the cure rate are solved with Markov Chain Monte Carlo (MCMC) techniques. It is found that cured model with parametric approach allows more consistent estimates in comparison to standard procedures. The risk of death due to liver transplantation in liver cirrhosis patients including time dependent effect terms has also been explored. The approach assists to model with different age and sex in both the treatment groups.

In this paper, we consider functional varying coefficient model in present of a time invariant covariate for sparse longitudinal data contaminated with some measurement errors. We propose a regularization method to estimate the slope function based on a reproducing kernel Hilbert space approach. As we will see, our procedure is easy to implement. Our simulation results show that the procedure performs well, especially when either sampling frequency or sample size increases. Applications of our method are illustrated in an analysis of a longitudinal CD4+ count dataset from an HIV study.

This paper examines the performance of different kind of GARCH models with Gaussian, Student-t and generalized error distribution for Colombo Stock Exchange (CSE), in Sri Lanka. Analyzing the daily closing price index of CSE from January 02, 2007 to March 10, 2013. It was found that the Asymmetric GARCH models give better result than symmetric GARCH model. According to distributional assumption these models under Student-t as well as generalized error provided better fit than normal distributional assumption. The Non-Parametric Specification test suggest that the GARCH, EGARCH, TARCH and APARCH models with Student-t distributional assumption are the most successful model for CSE.

This paper empirically investigates the impact of the government bailout on analysts’ forecast optimism regardingfirms in the automotive industry. We compare the results from M- and MM-robust methodologies to the results from OLS regression in an event study context and find that inferences change. When M- and MM-robust estimation methods are used to estimate the same model, the results for key control variables fall directly in line with those of similar previous studies. Furthermore, an analysis of residuals indicates that the application of M- and MM estimation methods pulls the main prediction equation towards the main sample data, suggesting a more rigorous fit. Based on robust methods, we observe changes in analyst optimism during the announcement period of the bailout, as evidenced by the significantly positive variable of interest. We support our empirical results with simulations and confirm significant improvements in estimation accuracy when robust regression methods are applied to the samples contaminated by outliers.

Social phenomena that are related to human beings cannot be performed under controlled conditions, making it difficult for policy planners to have an idea about the expected future conditions in the society under varying situations and forming policies. However, modelling can be really helpful to planners in these situations. The present paper attempts to find the distributions of age at last conception of women with the help of stochastic modelling for human fertility taking into consideration different parity progression behaviours among couples. This may be helpful to planners for having at least a rough idea of estimated proportion of women of different age groups who will be completing their childbearing and willing to go for sterilization after marriage under different stopping rules regarding desired family size and sex composition of children. Accordingly, these estimates will help planners to optimize the cost and service provision for sterilization programs for women.

The normal distribution is the most popular model in applications to real data. We propose a new extension of this distribution, called the Kummer beta normal distribution, which presents greater flexibility to model scenarios involving skewed data. The new probability density function can be represented as a linear combination of exponentiated normal pdfs. We also propose analytical expressions for some mathematical quantities: Ordinary and incomplete moments, mean deviations and order statistics. The estimation of parameters is approached by the method of maximum likelihood and Bayesian analysis. Likelihood ratio statistics and formal goodnessof-fit tests are used to compare the proposed distribution with some of its sub-models and non-nested models. A real data set is used to illustrate the importance of the proposed model.

The statistical modeling of natural disasters is an indispensable tool for extracting information for prevention and risk reduction casualties. The Poisson distribution can reveal the characteristics of 1 a natural disaster. However, this distribution is insufficient for the clustering of natural events and related casualties. The best approach is to use a Neyman type A (NTA) distribution which has the feature that two or more events occur in a short time. We obtain some properties of the NTA distribution and suggest that it could provide a suitable description to analyze the natural disaster distribution and casualties. We support this argument using disaster events, including earthquakes, floods, landslides, forest fires, avalanches, and rock falls in Turkey between 1900 and 2013. The data strongly supports that the NTA distribution represents the main tool for handling disaster data. The findings indicate that approximately three earthquakes, fifteen landslides, five floods, six rock falls, six avalanches, and twenty nine forest fires are expected in a year. The results from this model suggest that the probability of the total number of casualties is the highest for the earthquakes and the lowest for the rock falls. This study also finds that the expected number of natural disasters approximately equals to 64 per year and inter-event time between two successive earthquakes is approximately four months. The inter-event time for the natural disasters is approximately six days in Turkey.

In this paper, we proposed the Bayesian estimation for the parameter and reliability function of exponentiated gamma distribution under progressive type-II censored samples. The Bayes estimate of the parameter and reliability function are derived under the assumption of independent gamma prior by three different approximation methods namely Lindley’s approximation, Tierney-Kadane and Markov Chain Monte Carlo methods. Further, the comparison of Bayes estimators with corresponding maximum likelihood estimators have been carried out through simulation study. Finally, a real data set has been used to illustrate the above study in realistic phenomenon.

The unknown or unobservable risk factors in the survival analysis cause heterogeneity between individuals. Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyze the bivariate data on related survival times, the shared frailty models were suggested. The most common shared frailty model is a model in which frailty act multiplicatively on the hazard function. In this paper, we introduce the shared inverse Gaussian frailty model with the reversed hazard rate and the generalized inverted exponential distribution and the generalized exponential distribution as baseline distributions. We introduce the Bayesian estimation procedure using Markov Chain Monte Carlo(MCMC) technique to estimate the parameters involved in the models. We present a simulation study to compare the true values of the parameters with the estimated values. Also we apply the proposed models to the Australian twin data set and a better model is suggested.

The Lindley distribution has been generalized by many authors in recent years. However, all of the known generalizations so far have restricted tail behaviors. Here, we introduce the most flexible generalization of the Lindley distribution with its tails controlled by two independent parameters. Various mathematical properties of the generalization are derived. Maximum likelihood estimators of its parameters are derived. Fisher’s information matrix and asymptotic confidence intervals for the parameters are given. Finally, a real data application shows that the proposed generalization performs better than all known ones