Methods and apparatus for estimating total unique audiences
Methods and apparatus for determining a unique audience exposed to media while reducing memory resources of a computing device are disclosed herein. An example method includes receiving impression requests at a server from a plurality of client devices via a network; based on the impression requests, logging, with the server, a plurality of impressions corresponding to the media accessed at the client devices; obtaining a number of demographic impressions logged by a database proprietor; obtaining a number of registered users of the database proprietor exposed to the media; multiplying, by executing an instruction with a processor, a number of the plurality of impressions by a square of the number of the registered users to generate a product; dividing, by executing an instruction with the processor, the product by a number of the demographic impressions to generate a quotient; and determining, by executing an instruction with the processor, the unique audience based on a square root of the quotient.
1. A method of determining a unique audience exposed to media, the method comprising:
receiving impression requests at a server from a plurality of client devices via a network;
based on the impression requests, logging, with the server, a plurality of impressions corresponding to the media accessed at the client devices;
obtaining a number of demographic impressions logged by a database proprietor;
obtaining a number of registered users of the database proprietor exposed to the media;
selecting a first process to determine the unique audience instead of a second process to determine the unique audience, the first process to cause more resource-efficient operation of a computer than the second process by utilizing less processor resources and memory resources than the second process;
executing, with a processor of the computer, the first process by:
multiplying, by executing an instruction with the processor, a number of the plurality of impressions by a square of the number of the registered users to generate a product;
dividing, by executing an instruction with the processor, the product by the number of the demographic impressions to generate a quotient; and
determining, by executing an instruction with the processor, the unique audience based on a square root of the quotient.
2. The method of claim 1 , wherein the registered users of the database proprietor exposed to the media correspond to the demographic impressions and to at least some of the plurality of impressions.
3. The method of claim 1 , further including generating a report indicating the unique audience.
4. The method of claim 1 , further including crediting the media associated with the plurality of impressions based on the unique audience.
5. The method of claim 1 , further including determining a frequency distribution for the plurality of impressions based on the unique audience by:
dividing the unique audience by the number of the plurality of impressions to determine a second quotient; and
calculating a geometric distribution based on the second quotient.
6. A method of determining a unique audience exposed to media, the method comprising:
receiving impression requests at a server from a plurality of client devices via a network;
based on the impression requests, logging, with the server, a plurality of impressions corresponding to the media accessed at the client devices;
obtaining a first number of first demographic impressions corresponding to the media accessed via a first website and logged by a first database proprietor, the first demographic impressions corresponding to first registered users of the first database proprietor;
obtaining a second number of second demographic impressions corresponding to the media accessed via a second website and identified by a second database proprietor, the second demographic impressions corresponding to second registered users of the second database proprietor;
obtaining a first number of the first registered users exposed to the media;
obtaining a second number of the second registered users exposed to the media;
generating, by executing an instruction with a processor, a constraint matrix and a constraint vector based on the first number of the first demographic impressions and the second number of the second demographic impressions, the constraint vector representative of a plurality of ratios of constraints to a number of the plurality of impressions; and
determining, by executing an instruction with the processor, a first unique audience exposed to the media via the first website, a second unique audience exposed to the media via the second website, and a total unique audience exposed to the media via the first and second websites based on the constraint matrix and the constraint vector.
7. The method of claim 6 , wherein the total unique audience is a count of unique audience members across the first unique audience and the second unique audience.
8. The method of claim 6 , wherein the constraint matrix is a first constraint matrix and the constraint vector is a first constraint vector, and further including determining the first unique audience, the second unique audience, and the total unique audience by:
generating the first constraint matrix and the first constraint vector based on the first number of the first demographic impressions, the first number of the first registered users, the second number of the second demographic impressions, and the second number of the second registered users;
determining impression characteristics associated with the first constraint matrix and the first constraint vector, the impression characteristics including maximized values based on the first constraint matrix and the first constraint vector; and
generating a second constraint matrix and a second constraint vector based on the impression characteristics, the first and second constraint matrices and the first and second constraint vectors corresponding to audience characteristics, the audience characteristics including maximized values based on the second constraint matrix and the second constraint vector, the first unique audience, the second unique audience, and the total unique audience being based on the audience characteristics.
9. The method of claim 8 , further including determining a frequency distribution based on the impression characteristics.
10. The method of claim 8 , wherein the impression characteristics include probabilities representing likelihoods of different numbers of people exposed to the media via at least one of the first website or the second website.
11. The method of claim 8 , wherein the audience characteristics include probabilities representing likelihoods of different sizes of unique audiences corresponding to at least one of the first website or the second website.
12. The method of claim 6 , wherein the first database proprietor is the second database proprietor.
13. The method of claim 6 , further including generating a report indicating at least one of the first unique audience, the second unique audience, or the total unique audience.
14. The method of claim 6 , further including crediting the media associated with the plurality of impressions based on at least one of the first unique audience, the second unique audience, or the total unique audience.
15. The method of claim 6 , wherein the constraint matrix includes constraints represented in sub-matrices, the constraints including at least one of a first size of a first audience exposed to the media via the first website, a second size of a second audience exposed to the media via the second website, a third size of a total audience exposed to the media via the first and second websites, a fourth size of a universe audience via any website, a first count of first impressions corresponding to the media accessed via the first website, and a second count of second impressions corresponding to the media accessed via the second website.
16. A method of determining a unique audience exposed to media, the method comprising:
receiving impression requests at a server from a plurality of client devices via a network;
based on the impression requests, logging, with the server, a plurality of impressions corresponding to the media accessed at the client devices;
obtaining a first number of first demographic impressions corresponding to the media accessed via a first website and logged by a first database proprietor, the first demographic impressions corresponding to first registered users of the first database proprietor;
obtaining a second number of second demographic impressions corresponding to the media accessed via a second website and logged by a second database proprietor, the second demographic impressions corresponding to second registered users of the second database proprietor;
obtaining a first number of the first registered users exposed to the media;
obtaining a second number of the second registered users exposed to the media;
determining, by executing an instruction with a processor, a first enumeration table, the first enumeration table including first values based on a system of non-linear equations associated with the first number of the first demographic impressions, the first number of the first registered users, the second number of the second demographic impressions and the second number of the second registered users;
determining, by executing an instruction with the processor, a second enumeration table including second values based on a second system of non-linear equations associated with the first values calculated in the first enumeration table and the plurality of impressions; and
determining, by executing an instruction with the processor, a first unique audience of the media accessed via the first website, a second unique audience of the media accessed via the second website, and a total unique audience of the media accessed via the first and second websites using second expressions solved based on the second values in the second enumeration table.
17. The method of claim 16 , wherein the first enumeration table is an estimated distribution of the plurality of impressions across the first registered users and the second registered users.
18. The method of claim 16 , wherein the second enumeration table is an estimated distribution of the plurality of impressions across the total unique audience.
19. The method of claim 18 , further including determining a frequency distribution of impressions for the total unique audience based on the second enumeration table.
20. The method of claim 16 , wherein the second enumeration table is based on population constraints, the population constraints representative of:
a third number of the first demographic impressions corresponding to the media accessed via the first website, the third number of the first demographic impressions including the first number of the first demographic impressions; and
a fourth number of the second demographic impressions corresponding to the media accessed via the second website, the fourth number of the second demographic impressions including the second number of the second demographic impressions.
21. The method of claim 16 , wherein the first database proprietor is the second database proprietor.
22. The method of claim 16 , further including generating a report indicating at least one of the first unique audience, the second unique audience, or the total unique audience.
23. The method of claim 16 , further including crediting the media associated with the plurality of impressions based on at least one of the first unique audience, the second unique audience, or the total unique audience.