Methods and apparatus to improve reach calculation efficiency
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. A computer-implemented method to improve an efficiency of determining a published reach, comprising:
identifying, by executing an instruction with at least one processor, a negative binomial distribution feasibility region corresponding to a candidate gross rating point (GRP) value;
in response to identifying the negative binomial distribution feasibility region is associated with a number of samples below a threshold, estimating, by executing an instruction with the at least one processor, a sample distribution of marketing data to generate a maximum entropy distribution, the maximum entropy distribution being constrained by a first GRP value and a first reach value, the first GRP value empirically measured, the first GRP value corresponding to the sample distribution of marketing data, the first reach value based on the first GRP value;
generating, by executing an instruction with the at least one 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, the minimum cross entropy being constrained by the candidate GRP value of the sample distribution of marketing data, the candidate GRP value based on an advertising campaign increase quantity;
determining, by executing an instruction with the at least one processor, a model of the candidate GRP value, the model based on an assistance value corresponding to the candidate GRP value; and
reducing a computational burden associated with determining the published reach of the sample distribution of marketing data by generating, by executing an instruction with the at least one processor, closed-loop conserved quantity expressions of the geometric distribution based on the model of the candidate GRP value.
2. The computer-implemented method as defined in claim 1 , wherein the first GRP value and the first reach value are constrained for a probability of zero advertising impressions associated with the sample distribution.
3. The computer-implemented method as defined in claim 1 , wherein estimating the minimum cross entropy includes applying a Kullback-Leibler divergence probability.
4. The computer-implemented method as defined in claim 1 , wherein the conserved quantity expressions associate at least one of (a) GRP and reach, (b) GRP and frequency, or (c) reach and frequency.
5. An apparatus to improve an efficiency of determining a published reach, comprising:
a market data evaluator to identify a negative binomial distribution feasibility region corresponding to a candidate gross rating point (GRP) value;
a maximum entropy engine to:
in response to the market data evaluator identifying the negative binomial distribution feasibility region is associated with a number of samples below a threshold:
generate a maximum entropy distribution, based on estimating a sample distribution of marketing data, the maximum entropy distribution constrained by a first GRP value and a first reach value, the first GRP value corresponding to the sample distribution of marketing data, the first reach value based on the first GRP value;
a maximum entropy constraint manager to generate a geometric distribution based on estimating a minimum cross entropy of (a) the maximum entropy distribution and (b) the sample distribution of marketing data;
a minimum cross entropy constraint manager to constrain the minimum cross entropy with the candidate GRP value of the sample distribution of marketing data, the candidate GRP value based on an advertising campaign increase quantity; and
a conserved quantity engine to:
determine a model of the candidate GRP value, the model based on an assistance value corresponding to the candidate GRP value; and
reduce a computational burden associated with determining the published reach of the sample distribution of marketing data by generating closed-loop conserved quantity expressions of the geometric distribution based on the model of the candidate GRP value.
6. The apparatus as defined in claim 5 , 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.
7. The apparatus as defined in claim 5 , further including a minimum cross-entropy engine to estimate the minimum cross entropy with a Kullback-Leibler divergence probability.
8. The apparatus as defined in claim 5 , wherein the conserved quantity expressions associate at least one of (a) GRP and reach, (b) GRP and frequency, or (c) reach and frequency.
9. A tangible computer readable storage medium comprising instructions to improve an efficiency of determining a published reach that, when executed, causes a processor to, at least:
identify a negative binomial distribution feasibility region corresponding to a candidate gross rating point (GRP) value;
in response to identifying the negative binomial distribution feasibility region is associated with a number of samples below a threshold, estimate a sample distribution of marketing data to generate a maximum entropy distribution, the maximum entropy distribution being constrained by a first GRP value and a first reach value, the first GRP value empirically measured, the first GRP value corresponding to the sample distribution of marketing data, the first reach value based on the first GRP value;
generate a geometric distribution based on estimating a minimum cross entropy of (a) the maximum entropy distribution and (b) the sample distribution of marketing data, the minimum cross entropy being constrained by the candidate GRP value of the sample distribution of marketing data, the candidate GRP value based on an advertising campaign increase quantity;
determine a model of the candidate GRP value, the model based on an assistance value corresponding to the candidate GRP value; and
reduce a computational burden associated with determining the published reach of the sample distribution of marketing data by generating closed-loop conserved quantity expressions of the geometric distribution based on the model of the candidate GRP value.
10. The tangible computer readable storage medium of claim 9 , wherein the instructions, when executed, further 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.