Long-Tailed Duration Distributions for Disability in Aged People

Long tails of the duration distributions for disabilities in the aged are analyzed. Log–normal distribution shows excellent fit with various data on the durations of disabilities, irrespective of their severity. Persisting long tails suggest the fractal nature of disability distributions. For approximately 60% of the patients, the duration distributions are also mimicked by the first passage time distribution (FPTD) of one-dimensional Brownian motion. The finding that the data fit the log–normal distribution very well and FPTD fairly well reveals disability for the aged to be a stochastic process of suffering successively from various endogenous diseases, i.e., multiple pathology.