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**A stochastic comparison of customer classifiers with an application to customer attrition in commercial banking.**
*(English)*
Zbl 1402.91267

Summary: The classification of clients is an essential matter in commercial banking, insurance companies, electrical corporations, communication business, etc. Those companies frequently classify their customers by means of the information provided by the so-called classifier. Motivated by the need to compare systems of classification, we introduce a new stochastic order which permits the comparison of classifiers. The stochastic order is analysed in detail, providing characterizations and properties as well as connections with other stochastic orders and other classification systems. Such an order is applied to compare some classifiers used by a Spanish commercial banking to analyse the key problem of customer churn, obtaining conclusive results by means of real databases. Namely, the optimal classifier among them in the new stochastic order is obtained.

### MSC:

91B42 | Consumer behavior, demand theory |

60E15 | Inequalities; stochastic orderings |

06A06 | Partial orders, general |

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\textit{M. C. López-Díaz} et al., Scand. Actuar. J. 2017, No. 7, 606--627 (2017; Zbl 1402.91267)

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