Rohan J. Dalpatadu

Adaptive Bayes estimators for parameters of the Gompertz survival model

The two-parameter Gompertz model is a commonly used survival time distribution in actuarial science and reliability and life testing. The estimation of the parameters of this model is numerically involved. We consider the estimation problem in a Bayesian framework and give the Bayesian estimators of parameters in terms of single numerical integrations. We propose an adaptive Bayesian estimation procedure by putting a prior only on one parameter and finding the other parameter by minimizing the distance between empirical and parametric cumulative distribution functions. This easily computable (even for large samples) adaptive Bayesian procedure is compatible with the exact Bayesian procedure. In particular, numerical integration for computing the exact Bayesian procedure is difficult for large samples. Furthermore, for the no prior information situation, a noninformative adaptive Bayes procedure is given. Some examples of the proposed adaptive method along with a comparison with other existing methods are given. Monte Carlo simulation has been used to compare the existing procedures with the proposed procedures.

LINEAR FUNCTIONS OF UNIFORM ORDER STATISTICS AND B-SPLINES

ABSTRACT The purpose of the present paper is to give a simplified method of finding the density function and the moments of linear function of order statistics from uniform distribution. This is done by using a relationship between a B-spline and the linear function of uniform order statistics. Two examples are presented to illustrate this method. Some applications of the results are also considered.

Selection of Transformations of Continuous Predictors in Logistic Regression

The binary logistic regression is a machine learning tool for classification and discrimination that is widely used in business analytics and medical research. Transforming continuous predictors to improve model performance of logistic regression is a common practice, but no systematic method for finding optimal transformations exists in the statistical or data mining literature. In this paper, the problem of selecting transformations of continuous predictors to improve the performance of logistic regression models is considered. The proposed method is based upon the point-biserial correlation coefficient between the binary response and a continuous predictor. Several examples are presented to illustrate the proposed method.