determine a plurality of types of attribute values used to measure a plurality of age dependent products belonging to different product types;

translate all of the plurality of types of attribute values into ranges on a universal developmental scale such that each age dependent product is associated with one or more development stages each corresponding to a range on the universal developmental scale, wherein the plurality of types of attribute values include at least: age range, product size, and product stage, each related to a different product type;

receive, from a computing device, a search query submitted by the customer;

determine, from the plurality of age dependent products, a subset of age dependent products based on prior engagements by the customer's household;

retrieve, from the database, the respective development stages associated with each of the age dependent products in the subset;

determine a probability the customer's household containing a child at one or more of the retrieved development stages by performing Gaussian mixture modeling upon the retrieved developmental stages;

determine a developmental stage associated with the customer's household based on the probability;

determine a number of children in the customer's household by performing multivariate kernel density estimation upon the retrieved developmental stages;

recommend selective ones of the plurality of age dependent products to the customer's household based upon the determined developmental stage associated with the customer's household, the determined number of children in the customer's household, and the search query;

transmit, in response to the search query, the selective age dependent products to the computing device as search results; and

validate performance of the Gaussian mixture model using an evaluation metric based on statistical reasoning.