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Crime is an unavoidable social phenomenon prevailing more or less in every social structure. The incidences of crime either can be minimized or controlled, however, it is difficult to eradicate it completely. To observe crime pattern of a particular place, trend analysis plays vital role in examining shape and structure of the data. In crime study, it provides help in solving issues like crime mapping, policy-prescription, prediction, etc. Trend analysis in crime data provides comprehensive as well as extensive observations of the statistics, because of which behavioral study of the same becomes trouble-free. In this paper, an attempt has been made to analyze crime data of India for last two decades. To study the trend, Dynamic Time Warping (DTW) technique has been exercised. Hierarchical clustering of all the states and UTs has been performed as well based on crime rates to figure out places with similar pattern. Moreover, simple statistical analysis has also been carried out for better understanding of the scenario. [ABSTRACT FROM AUTHOR]

Frailty model in survival analysis is a special kind of random effect model, which can also deal with heterogeneity, caused by unmeasured covariates, where the random effect (the frailty) has a multiplicative effect on the baseline hazard function. With recent advances in computing technology, Bayesian approaches to frailty models are now computationally feasible and several researchers have been developing Bayesian methodologies to analyse survival data with different frailty models. In this paper, an attempt has been made to develop two new multivariate Accelerated Failure Time Frailty models under Bayesian approach with different baseline hazard functions. For making a comparative analysis, we consider the same two Accelerated Failure Time (AFT) models without the frailty term. To illustrate the models a real life survival data set of Diabetic Retinopathy Study is used and posterior inferences are drawn using Markov Chain Monte Carlo (MCMC) simulation methods and model comparison tools like deviance information criteria (DIC) and the log pseudo marginal likelihood (LPML) are also calculated and to check the fit of the model Cox-Snell residual plot is employed. [ABSTRACT FROM AUTHOR]

Regression models form the core of the discipline of econometrics. One of the basic assumptions of classical linear regression model is that the values of the explanatory variables are fixed in repeated sampling. However, in most of the real life cases, particularly in economics the assumption of fixed regressors is not always tenable. Under a non-experimental or uncontrolled environment, the dependent variable is often under the influence of explanatory variables that are stochastic in nature. There is a huge literature related to stochastic regressors in various aspects. In this paper, a historical perspective on some of the works related to stochastic regressor is being tried to pen down based on literature search. [ABSTRACT FROM AUTHOR]