Computer-implemented systems and methods for response curve estimation

A non-transitory computer-readable storage medium containing instructions that, when executed by at least one electronic processor of an estimation system, causes the at least one electronic processor to perform operations for an improved display of electronic content, the operations comprising:

• determining, by the estimation system, an input-output point comprising a first request value and a corresponding first volume value, wherein the estimation system is in communication with a web server and a user device by an electronic network, the estimation system and/or web server being in communication with a request-volume data store;
• generating, by the estimation system, a first transformed request value by modifying the first request value using a stabilizing factor;
• generating, by the estimation system, a twice-transformed request value by modifying the first transformed request value based on a control range of request values, the control range comprising a lower boundary and an upper boundary;
• determining, by the estimation system, values along a spline function to obtain a curve weight factor by recursively calculating a matrix comprising the twice-transformed request value;
• generating, by the estimation system, a second transformed request value by modifying a second request value using the stabilizing factor, the second request value being different from the first request value;
• determining, by the estimation system, based on the second transformed request value, values along the spline function and the first derivative of the spline function, to obtain an estimated volume value and estimated volume rate associated with the second request value;
• determining, by the estimation system, electronic content to display on a web page based on the estimated volume value and the estimated volume rate;
• and
• communicating, from the estimation system to the web server, instructions to display the electronic content on the user device.

A system for an improved online display of electronic content, comprising:

• at least one electronic processor of an estimation system, wherein the estimation system is in communication with a web server and a user device by an electronic network, the estimation system and/or web server being in communication with a request-volume data store;
• and
• a storage device that stores instructions that, when executed by the at least one electronic processor, causes the at least one electronic processor to:
• determine, by the estimation system, an input-output point comprising a first request value and a corresponding first volume value;
• generate, by the estimation system, a first transformed request value by modifying the first request value using a stabilizing factor;
• generate, by the estimation system, a twice-transformed request value by modifying the first transformed request value based on a control range of request values, the control range comprising a lower boundary and an upper boundary;
• determine, by the estimation system, values along a spline function to obtain a curve weight factor by recursively calculating a matrix comprising the twice-transformed request value;
• generate, by the estimation system, a second transformed request value by modifying a second request value using the stabilizing factor, the second request value being different from the first request value;
• determine, by the estimation system, based on the second transformed request value, values along the spline function and the first derivative of the spline function, to obtain an estimated volume value and estimated volume rate associated with the second request value;
• determining, by the estimation system, electronic content to display on a web page based on the estimated volume value and the estimated volume rate, and
• communicate, from the estimation system to the web server, instructions to display the electronic content on the user device.