Methods and apparatus to improve reach calculation efficiency

Abstract

Methods, apparatus, systems and articles of manufacture are disclosed to improve reach calculation efficiency. An example method includes estimating, with a processor, a sample distribution of marketing data to generate a maximum entropy distribution, generating, with the processor, a geometric distribution based on estimating a minimum cross entropy of (a) the maximum entropy distribution and (b) the sample distribution of marketing data, and improving calculation efficiency of the public reach of the sample distribution of marketing data by generating, with the processor, conserved quantity expressions of the geometric distribution.

1 . (canceled) 
     
     
         2 . An apparatus to improve an efficiency of determining a published reach value, the apparatus comprising:
 a market data evaluator to identify a negative binomial distribution (NBD) feasibility region corresponding to a published gross rating point (GRP) value, the published GRP value corresponding to a quantity change associated with an advertising campaign; and   a conserved quantity engine to, after the market data evaluator has identified the NBD feasibility region is associated with a number of samples below a threshold:
 generate a model of the published GRP value; and 
 reduce a computational burden associated with determining the published reach value of a sample distribution of marketing data by generating closed-loop conserved quantity expressions based on the model of the published GRP value. 
   
     
     
         3 . The apparatus as defined in  claim 2 , further including a maximum entropy engine to, in response to the market data evaluator identifying the NBD feasibility region is associated with the number of samples below the threshold, generate a maximum entropy distribution based on estimating the sample distribution of the marketing data. 
     
     
         4 . The apparatus as defined in  claim 3 , wherein the maximum entropy engine is to constrain the maximum entropy distribution by a first GRP value and a first reach value, the first GRP value (a) empirically measured and (b) corresponding to the sample distribution of the marketing data, the first reach value based on the first GRP value. 
     
     
         5 . The apparatus as defined in  claim 4 , wherein the maximum entropy engine is to constrain the first GRP value and the first reach value for a probability of zero advertising impressions associated with the sample distribution of the marketing data. 
     
     
         6 . The apparatus as defined in  claim 2 , further including a maximum entropy constraint manager to generate a geometric distribution based on estimating a minimum cross entropy corresponding to (a) a maximum entropy distribution and (b) the sample distribution of the marketing data, the maximum entropy distribution based on the sample distribution of the marketing data. 
     
     
         7 . The apparatus as defined in  claim 6 , further including a minimum cross entropy constraint manager to constrain the minimum cross entropy with the published GRP value of the sample distribution of the marketing data. 
     
     
         8 . The apparatus as defined in  claim 2 , wherein the conserved quantity engine is to associate at least one of a combination of (a) one or more additional GRP values and one or more additional reach values, (b) one or more additional GRP values and one or more frequencies, or (c) one or more additional reach values and one or more frequencies, via the closed-loop conserved quantity expressions. 
     
     
         9 . The apparatus as defined in  claim 2 , wherein the quantity change associated with the advertising campaign includes an increase of product sales. 
     
     
         10 . A tangible computer readable storage medium comprising instructions to improve an efficiency of determining a published reach value that, when executed, cause a processor to, at least:
 identify a negative binomial distribution (NBD) feasibility region corresponding to a published gross rating point (GRP) value, the published GRP value corresponding to a quantity change associated with an advertising campaign;   after having identified that the NBD feasibility region is associated with a number of samples below a threshold, generate a model of the published GRP value; and   reduce a computational burden associated with determining the published reach value of a sample distribution of marketing data by generating closed-loop conserved quantity expressions based on the model of the published GRP value.   
     
     
         11 . The tangible computer readable storage medium as defined in  claim 10 , wherein the instructions, when executed, cause the processor to, in response to having identified that the NBD feasibility region is associated with the number of samples below the threshold, estimate the sample distribution of the marketing data to generate a maximum entropy distribution. 
     
     
         12 . The tangible computer readable storage medium as defined in  claim 11 , wherein the instructions, when executed, cause the processor to constrain the maximum entropy distribution by a first GRP value and a first reach value, the first GRP value (a) empirically measured and (b) corresponding to the sample distribution of the marketing data, the first reach value based on the first GRP value. 
     
     
         13 . The tangible computer readable storage medium as defined in  claim 12 , wherein the instructions, when executed, cause the processor to constrain the first GRP value and the first reach value for a probability of zero advertising impressions associated with the sample distribution of the marketing data. 
     
     
         14 . The tangible computer readable storage medium as defined in  claim 10 , wherein the instructions, when executed, cause the processor to generate a geometric distribution based on estimating a minimum cross entropy corresponding to (a) a maximum entropy distribution and (b) the sample distribution of the marketing data, the maximum entropy distribution based on the sample distribution of the marketing data. 
     
     
         15 . The tangible computer readable storage medium as defined in  claim 14 , wherein the instructions, when executed, cause the processor to constrain the minimum cross entropy with the published GRP value of the sample distribution of the marketing data. 
     
     
         16 . The tangible computer readable storage medium as defined in  claim 10 , wherein the instructions, when executed, cause the processor to associate at least one of a combination of (a) one or more additional GRP values and one or more additional reach values, (b) one or more additional GRP values and one or more frequencies, or (c) one or more additional reach values and one or more frequencies, via the closed-loop conserved quantity expressions. 
     
     
         17 . The tangible computer readable storage medium as defined in  claim 10 , wherein the quantity change associated with the advertising campaign includes an increase of product sales. 
     
     
         18 . An apparatus to improve an efficiency of determining a published reach value, the apparatus comprising:
 market data evaluation means to identify a negative binomial distribution (NBD) feasibility region corresponding to a published gross rating point (GRP) value, the published GRP value corresponding to a quantity change associated with an advertising campaign; and   conserved quantity generation means to, after the market data evaluation means has identified the NBD feasibility region is associated with a number of samples below a threshold:
 generate a model of the published GRP value; and 
 reduce a computational burden associated with determining the published reach value of a sample distribution of marketing data by generating closed-loop conserved quantity expressions based on the model of the published GRP value. 
   
     
     
         19 . The apparatus as defined in  claim 18 , further including maximum entropy distribution generation means to, in response to the market data evaluation means identifying the NBD feasibility region is associated with the number of samples below the threshold, generate a maximum entropy distribution based on estimating the sample distribution of the marketing data. 
     
     
         20 . The apparatus as defined in  claim 19 , wherein the maximum entropy distribution generation means is to constrain the maximum entropy distribution by a first GRP value and a first reach value, the first GRP value (a) empirically measured and (b) corresponding to the sample distribution of the marketing data, the first reach value based on the first GRP value. 
     
     
         21 . The apparatus as defined in  claim 20 , wherein the maximum entropy distribution generation means is to constrain the first GRP value and the first reach value for a probability of zero advertising impressions associated with the sample distribution of the marketing data.