Rayleigh-half normal distribution for modeling tooth movement data

Clear aligners provide a recent technique to induce orthodontic tooth movement. In this paper, a new one-parameter model, called, Rayleigh-Half Normal distribution (RHN) is proposed for modeling tooth movement data. Various statistical and reliability properties including moments and its associated measures, mean residual life, survival and hazard functions are derived and studied. Moreover, the model parameter is estimated via the method of moments and maximum likelihood. A simulation study was performed to examine the bias and mean square error of the estimated parameter. Finally, the flexibility of the proposed model is illustrated by utilizing a real dental data. The results showed that it could give a better fit than other well-known models.