Non-Parametric Test for Decreasing Uncertainty of Residual Life Distribution (DURL)

In this paper, we propose a new statistic to test the monotonicity of uncertainty based on derivative criteria and the histogram method. We test the null hypothesis that residual entropy is constant against the fact that it decreases over time. Hence, by the fact that the exponential distribution is the distribution with a constant uncertainty, we establish the test exponential distribution against the decreasing uncertainty of residual life distribution. Consistency and asymptotic normality are proved. The critical values of the statistics are given by means of the Monte Carlo simulation method to decide on the test. Then, the power estimates of the new test are compared to those of the test based on the criteria of monotonicity of residual entropy. Finally, we show, with real survival data, that the distributions belong to a decreasing uncertainty residual life class. Moreover, by applying a test of goodness of fit, we confirm that the data follow parametric distributions belonging to a decreasing uncertainty of residual life class.