Abstract
One of the key elements related to calculating Customer Lifetime Value is to estimate the duration of a client’s relationship with a bank in the future. This can be done using survival analysis. The aim of the article is to examine which of the known distributions used in survival analysis (Weibull, Exponential, Gamma, Log‑normal) best describes the churn phenomenon of a bank’s clients. If the aim is to estimate the distribution according to which certain units (bank customers) survive and the factors that cause this are not so important, then parametric models can be used. Estimation of survival function parameters is faster than estimating a full Cox model with a properly selected set of explanatory variables. The authors used censored data from a retail bank for the study. The article also draws attention to the most common problems related to preparing data for survival analysis.
Highlights
Nowadays, there is an increasing need to measure the effectiveness of marketing activities
By reviewing the literature about modelling survival data, it can be seen that the Exponential, Gamma, Log‐normal, and Weibull probability distribution functions are commonly used in survival analysis
The estimation of the parameters and the calculation of statistics, such as AIC and logLik, have shown that the Log‐normal and Weibull distributions are best for this particular sample of clients
Summary
There is an increasing need to measure the effectiveness of marketing activities. Survival time data measure the time to a certain event, such as failure, death, response, relapse, parole, divorce, or the development of a disease These times are subject to random variations, and like any random variables, they form a distribution (Balicki, 2006: 17). The hazard function (t) of survival time T gives the conditional failure rate. This is defined as the probability of failure during a very small time interval, assuming that the individual has survived to the beginning of the interval, or as the limit of the probability that an individual will fail within a very short interval, t + ∆t, given that the individual has survived till time T:. By reviewing the literature about modelling survival data, it can be seen that the Exponential, Gamma, Log‐normal, and Weibull probability distribution functions are commonly used in survival analysis. The first criterion is the Akaike Information Criterion (Akaike, 1974: 716–723), and the other is the logLik or Maximised Log‐likelihood (Jackson, 2016: 1–33)
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