Noncompartmental analyses leverage statistical moment theory to examine time-related changes in macroscopic events, encapsulating the collective outcomes stemming from the constituent elements in play. Statistical moment theory is a mathematical approach used to describe the time course of drug concentration in the body without assuming a specific compartmental model. SMT provides insights into drug absorption, distribution, metabolism, and elimination by treating drug concentration versus time data as a statistical distribution of molecules in time.

Mean residence time (MRT) is a pivotal parameter that describes the movement of drug molecules in and out of the system. It considers the individual movement of molecules within a system based on residence-time considerations. Residence-time considerations refer to analyzing how long individual drug molecules remain within the body or a specific compartment before being eliminated. The residence-time analysis uses statistical approaches to study the behavior of individual molecules as a distribution of times they reside in the body.

Calculating a drug's MRT within the body uses the moment curve obtained by integrating a probability density function of the drug multiplied by time. This yields insights into the distribution's characteristics, facilitating a deeper understanding of the drug's behavior within the biological system.

Substituting the m^th moment into the moment curve yields various moment curves, each with distinct implications. For instance, the zero moment corresponds to the area under the curve, while the first moment defines the mean of the distribution via the area under the first moment curve. The second moment characterizes the variance of the distribution, and higher moments represent skewness and kurtosis.

Noncompartmental analysis, underpinned by statistical moment theory, offers a comprehensive framework for unraveling drug molecules' temporal dynamics and distribution characteristics within biological systems.