Methods, systems and apparatus to improve the efficiency of calculating a customer retention rate
Methods, systems and apparatus to improve the efficiency of calculating a customer retention rate are disclosed herein. An example apparatus described herein that may be implemented to calculate a customer retention rate includes a retention rate model generator to generate a baseline retention rate model based on survivability data associated with an observed duration of interest, a shifted-beta-geometric distribution generator to generate a shifted-beta-geometric distribution model based on the survivability data, a model modifier to modify the baseline retention rate model based on the shifted-beta-geometric distribution model to create a modified retention rate model, and a model comparator to reduce a computational burden of calculating the customer retention rate by merging the modified retention rate model with the baseline retention rate model to generate a merged shifted-beta-geometric model, the merged shifted-beta-geometric model including first and second shifted-beta-geometric model parameters to determine the customer retention rate.
1. An apparatus to determine a customer retention rate, the apparatus comprising:
memory;
retention rate model generator instructions;
shifted-beta-geometric distribution generator instructions;
model modifier instructions;
model comparator instructions;
variable definer instructions;
linear relationship definer instructions;
retention rate estimator instructions; and
processor circuitry to:
execute the retention rate model generator instructions to generate a baseline retention rate model based on a first set of survivability data associated with a first observed duration of interest, the baseline retention rate model including a first survivor function and a second survivor function indicative of survivability;
execute the shifted-beta-geometric distribution generator instructions to generate a shifted-beta-geometric distribution model based on the first set of survivability data;
execute the model modifier instructions to modify the first survivor function and the second survivor function of the baseline retention rate model based on first and second shifted-beta-geometric model parameters of the shifted-beta-geometric distribution model to create a modified retention rate model;
execute the model comparator instructions to, in response to the creation of the modified retention rate model, combine the modified retention rate model and the baseline retention rate model to generate a merged shifted-beta-geometric model, the merged shifted-beta-geometric model including the first and second shifted-beta-geometric model parameters to determine the customer retention rate;
execute the variable definer instructions to define a survivability variable of the first set of survivability data, the survivability variable corresponding to a predicted customer retention rate based on the merged shifted-beta-geometric model and a number of active customers;
execute the linear relationship definer instructions to:
facilitate linear least squares solving of the first and second shifted-beta-geometric model parameters by establishing a linear relationship therebetween;
define a matrix for multiple time periods of interest based on the linear relationship; and
derive a closed-form solution for the first and second shifted-beta-geometric model parameters based on the matrix; and
execute the retention rate estimator instructions to:
output the customer retention rate for a first forecast period based on the first and second shifted-beta-geometric model parameters, the first and second shifted-beta-geometric model parameters fitted to the modified retention rate model; and
update the customer retention rate for a second forecast period based on a second set of survivability data, the second set of survivability data associated with a second observed duration of interest.
2. The apparatus as defined in claim 1 , further including a customer data storage to store customer data, including the first set of survivability data and the second set survivability data.
3. The apparatus as defined in claim 2 , further including survivability data retriever instructions, the processor circuitry to execute the survivability data retriever instructions to retrieve the first set of survivability data and the second set survivability data from the customer data storage.
4. The apparatus as defined in claim 1 , further including parameter estimator instructions, the processor circuitry to execute the parameter estimator instructions to estimate the first shifted-beta-geometric model parameter based on the merged shifted-beta-geometric model.
5. The apparatus as defined in claim 1 , wherein the processor circuitry is to execute the retention rate estimator instructions to determine the customer retention rate based on the first and second shifted-beta-geometric model parameters and the merged shifted-beta-geometric model.
6. The apparatus as defined in claim 1 , wherein the processor circuitry is to execute the model comparator instructions to:
solve the shifted-beta-geometric model for one of the first or second shifted-beta-geometric model parameters;
substitute the survivability variable into the shifted-beta-geometric model to simplify the shifted-beta-geometric model;
define the matrix based on the linear relationship between the first and second shifted-beta-geometric model parameters; and
generate a system of equations based on the matrix to be implemented to determine the customer retention rate.
7. The apparatus as defined in claim 6 , wherein the system of equations is derived from the matrix.
8. A computer-implemented method to determine a customer retention rate, the method comprising:
generating, by executing an instruction with a processor, a baseline retention rate model based on a first set of survivability data associated with a first observed duration of interest, the baseline retention rate model including a first survivor function and a second survivor function indicative of survivability;
generating, by executing an instruction with the processor, a shifted-beta-geometric distribution model based on the first set of survivability data;
modifying, by executing an instruction with the processor, the first survivor function and the second survivor function of the baseline retention rate model based on first and second shifted-beta-geometric model parameters of the shifted-beta-geometric distribution model to create a modified retention rate model;
in response to the creation of the modified retention rate model, combining, by executing an instruction with the processor, the modified retention rate model and the baseline retention rate model to generate a merged shifted-beta-geometric model, the merged shifted-beta-geometric model including the first and second shifted-beta-geometric model parameters to determine the customer retention rate;
defining, by executing an instruction with the processor, a survivability variable of the first set of survivability data, the survivability variable corresponding to a predicted customer retention rate based on the merged shifted-beta-geometric model and a number of active customers; facilitating, by executing an instruction with the processor, linear least squares solving of the first and second shifted-beta-geometric model parameters by establishing a linear relationship therebetween;
defining, by executing an instruction with the processor, a matrix for multiple time periods of interest based on the linear relationship;
deriving, by executing an instruction with the processor, a closed-form solution for the first and second shifted-beta-geometric model parameters based on the matrix;
outputting, by executing an instruction with the processor, the customer retention rate for a first forecast period based on the first and second shifted-beta-geometric model parameters, the first and second shifted-beta-geometric model parameters fitted to the modified retention rate model; and
updating, by executing an instruction with the processor, the customer retention rate for a second forecast period based on a second set of survivability data, the second set of survivability data associated with a second observed duration of interest.
9. The method as defined in claim 8 , further including retrieving the first set of survivability data and the second set of survivability data from a customer data storage.
10. The method as defined in claim 9 , further including estimating the first shifted-beta-geometric model parameter based on the merged shifted-beta-geometric model.
11. The method as defined in claim 8 , further including calculating the customer retention rate based on the first and second shifted-beta-geometric model parameters and the merged shifted-beta-geometric model.
12. The method as defined in claim 8 , further including establishing a linear relationship between the first shifted-beta-geometric model parameter and the second shifted-beta-geometric model parameter.
13. The method as defined in claim 12 , further including defining the matrix based on the linear relationship between the first and second shifted-beta-geometric model parameters.
14. The method as defined in claim 13 , further including generating a system of equations to be implemented to determine the customer retention rate.
15. A non-transitory tangible machine readable storage medium comprising instructions that, when executed, cause a machine to at least:
generate a baseline retention rate model based on a first set of survivability data associated with a first observed duration of interest, the baseline retention rate model including a first survivor function and a second survivor function indicative of survivability;
generate a shifted-beta-geometric distribution model based on the first set of survivability data;
modify the first survivor function and the second survivor function of the baseline retention rate model based on first and second shifted-beta-geometric parameters of the shifted-beta-geometric distribution model to create a modified retention rate model;
in response to the creation of the modified retention rate model, combine the modified retention rate model and the baseline retention rate model to generate a merged shifted-beta-geometric model, the merged shifted-beta-geometric model including the first and second shifted-beta-geometric model parameters to determine a customer retention rate;
define a survivability variable of the first set of survivability data, the survivability variable corresponding to a predicted customer retention rate based on the merged shifted-beta-geometric model and a number of active customers;
facilitate linear least squares solving of the first and second shifted-beta-geometric model parameters by establishing a linear relationship therebetween;
define a matrix for multiple time periods of interest based on the linear relationship;
derive a closed-form solution for the first and second shifted-beta-geometric model parameters based on the matrix;
output the customer retention rate for a first forecast period based on the first and second shifted-beta-geometric model parameters, the first and second shifted-beta-geometric model parameters fitted to the modified retention rate model; and
update the customer retention rate for a second forecast period based on a second set of survivability data, the second set of survivability data associated with a second observed duration of interest.
16. The non-transitory tangible machine readable storage medium of claim 15 , wherein the instructions, when executed, cause the machine to retrieve the first set of survivability data and the second set of survivability data from a customer data storage.
17. The non-transitory tangible machine readable storage medium of claim 16 , wherein the instructions, when executed, cause the machine to estimate the first shifted-beta-geometric model parameter based on the merged shifted-beta-geometric model.
18. The non-transitory tangible machine readable storage medium of claim 15 , wherein the instructions, when executed, cause the machine to determine the customer retention rate based on the first and second shifted-beta-geometric model parameters and the merged shifted-beta-geometric model.
19. The non-transitory tangible machine readable storage medium of claim 15 , wherein the instructions, when executed, cause the machine to generate a system of equations to be implemented to determine the customer retention rate.
20. An apparatus to determine a customer retention rate, the apparatus comprising:
at least one memory;
instructions; and
processor circuitry to execute the instructions to:
generate a baseline retention rate model based on a first set of survivability data associated with a first observed duration of interest, the baseline retention rate model including a first survivor function and a second survivor function indicative of survivability;
generate a shifted-beta-geometric distribution model based on the first set of survivability data;
modify the first survivor function and the second survivor function of the baseline retention rate model based on first and second shifted-beta-geometric model parameters of the shifted-beta-geometric distribution model to create a modified retention rate model;
in response to the creation of the modified retention rate model, combine the modified retention rate model and the baseline retention rate model to generate a merged shifted-beta-geometric model, the merged shifted-beta-geometric model including the first and second shifted-beta-geometric model parameters to determine the customer retention rate;
define a survivability variable of the first set of survivability data, the survivability variable corresponding to a predicted customer retention rate based on the merged shifted-beta-geometric model and a number of active customers;
facilitate linear least squares solving of the first and second shifted-beta-geometric model parameters by establishing a linear relationship therebetween;
define a matrix for multiple time periods of interest based on the linear relationship;
derive a closed-form solution for the first and second shifted-beta-geometric model parameters based on the matrix;
output the customer retention rate for a first forecast period based on the first and second shifted-beta-geometric model parameters, the first and second shifted-beta-geometric model parameters fitted to the modified retention rate model; and
update the customer retention rate for a second forecast period based on a second set of survivability data, the second set of survivability data associated with a second observed duration of interest.
21. The apparatus as defined in claim 20 , wherein the processor circuitry is to store customer data, including the first set of survivability data and the second set of survivability data, in a customer data storage.
22. The apparatus as defined in claim 21 , wherein the processor circuitry is to retrieve the first set of survivability data and the second set of survivability data from the customer data storage.
23. The apparatus as defined in claim 20 , wherein the processor circuitry is to estimate the first shifted-beta-geometric model parameter based on the merged shifted-beta-geometric model.
24. The apparatus as defined in claim 20 , wherein the processor circuitry is to determine the customer retention rate based on the first and second shifted-beta-geometric model parameters and the merged shifted-beta-geometric model.
25. The apparatus as defined in claim 20 , wherein the processor circuitry is to:
solve the shifted-beta-geometric model for one of the first or second shifted-beta-geometric model parameters;
substitute the survivability variable into the shifted-beta-geometric model to simplify the shifted-beta-geometric model;
define the matrix based on the linear relationship between the first and second shifted-beta-geometric model parameters; and
generate a system of equations based on the matrix to be implemented to determine the customer retention rate.
26. The apparatus as defined in claim 25 , wherein the system of equations is derived from the matrix.