Uniform Strong Consistent Estimation of an Ifra Distribution Function

Let 1n be an estimator of an IFRA survival function 1 and let A be such that 0 < 1(A) < 1. The main result constructs an IFRA estimator by splicing the smallest increasing failure rate on the average majorant and greatest increasing failure rate on the average minorant of the restrictions of 1n to the intervals [0, A] and [A, [infinity]), respectively. The resulting etimator 1n has the property that supx 1n - 1 <= k supx 1n - 1 where k >= 2, and k = 2 if and only if A is the median of F. As a consequence, if 1n represents the empirical survival function, or the Kaplan-Meier estimator, the estimator 1n inherits the strong and uniform convergence properties, as well as the optimal rates of convergence of the empirical survival function and Kaplan-Meier estimator respectively. Simulations show a substantial improvement in mean-squared error when comparing 1n to those IFRA estimators available in the literature. Under suitable conditions, asymptotic confidence intervals for 1(t0) are also provided.