Cumulative Density Functions
Cumulative density functions are used in describing the distribution of random variables. The best thing about the cumulative density functions is that they are defined in any random variable. In cumulative density functions, the F(x) accumulates all the probabilities less or equal to x. In any case, the CMF for continuous random variables is a straightforward extension of the discrete case, and the summation needs to be replaced with an integral.
Nonlinear Mixed Models
Nonlinear mixed models are made up of statistical models that generalize linear mixed-effects models. The nonlinear mixed models are useful in areas where several similar statistical units are dependent on the related statistical units. The nonlinear mixed models are popularly used in pharmacology, ecology, health, and medicine. In nonlinear mixed models, when the random effects are Gaussian, the likelihood estimation is done using nonlinear least squares.
Incorporating covariates is a good way of building flexible nonstationary covariate models. In statistics, covariate and response data are often involved in misaligned data in space. To avoid a bias parameter estimation and prediction, a common strategy is applied to interpolate the covariate in the locations with response data. Both response and covariate processes are represented in a basic system, and the covariate effect is introduced through a linear model between the coefficients of the basis vectors.
Right-Censored Data Analysis
In right-censored data analysis, the event of interest never has enough time to occur. This is also the most common form of censoring. The most common forms of right-censored data analysis are the survival models and the reliability tests. The right-censored data analysis is used in any epidemiological cohort and disease screening applications.