International Journal of Statistics and Probability
In this note, stochastic comparisons and results for weighted and Lindley models are presented. Approximation of weighted distributions via Lindley distribution in the class of increasing failure rate (IFR) and decreasing failure rate (DFR) weighted distributions with monotone weight functions are obtained including approximations via the length-biased Lindley distribution. Some useful bounds and moment-type inequality for weighted life distributions and applications are presented. Incorporation of covariates into Lindley model is considered and an application to illustrate the usefulness and applicability of the proposed Lindley-Cox model is given.
Oluyede, Broderick O., Macaulay Okwuokenye, Karl E. Peace.
"Inequalities and Approximations of Weighted Distributions by Lindley Reliability Measures, and the Lindley-Cox Model with Applications."
International Journal of Statistics and Probability, 4 (2).