Optimal kernel density estimation by statistical modeling with random censoring of observations
Abstract
The problems of nonparametric estimation of the probability of failure-free operation and the density distribution function of the operating time of some physical device are considered. Randomly right-censored observations are used. Estimates of a complex structure are constructed: multiplying, exponential, as well as power estimates and an estimate with modification. New estimates for the distribution density using the kernel method are proposed. Tables of the optimal choice of smoothing parameters obtained using statistical modeling are presented.