We are interested in the problem of nonparametric prediction ; therefore , we will study the relationship between a current observation and past observations , where the conditional cumulative distribution function and the conditional quantiles plays an important role . Note that the conditional cumulative distribution function is used unreliability or in survival analysis since it is involved in many applications . Conditional quantiles can also be deduced from F * ( y ) by ( pseudo ) -inversion given x of the function F ( y ) , and the same procedure may be applied to the estimator of F to find conditional quantile estimators . The conditional cumulative distribution function conditioned to a explanatory random variable X is defined as follows :