A New Customer Lifetime Duration Distribution: The Kumaraswamy Lindley Distribution

Abstract

Companies are viewing customers in terms of their lifetime duration. Customer lifetime duration is a powerful and straightforward measure that synthesizes churn (attrition) risk at individual customer level. For existing customers, customer lifetime duration can help companies develop customer loyalty and treatment strategies to maximize customer value. In this study, based on the Kumaraswamy distribution, the Kumaraswamy Lindley distribution is studied. Some mathematical properties of Kumaraswamy Lindley distribution such as moments, hazard function, quantile function, skewness, kurtosis are derived. The method of maximum likelihood is used to estimate the model parameters and the observed information matrix is derived. An application of our results is provided to show the applicability of this distribution, especially for customer lifetime duration. Therefore, the proposed distribution can be a useful tool to analyze customer lifetime duration in marketing research.