Statistics Papers

Document Type

Journal Article

Date of this Version


Publication Source

Applied Stochastic Models in Business and Industry





Start Page


Last Page





Call centres are becoming increasingly important in our modern commerce. We are interested in modelling the time-varying pattern of average customer service times at a bank call centre. Understanding such a pattern is essential for efficient operation of a call centre. The call service times are shown to be lognormally distributed. Motivated by this observation and the important application, we propose a new method for inference about non-parametric regression curves when the errors are lognormally distributed. Estimates and pointwise confidence bands are developed. The method builds upon the special relationship between the lognormal distribution and the normal distribution, and improves upon a naive estimation procedure that ignores this distributional structure. Our approach includes local non-parametric estimation for both the mean function and the heteroscedastic variance function of the logged data, and uses local polynomial regression as a fitting tool. A simulation study is performed to illustrate the method. We then apply the method to model the time-varying patterns of mean service times for different types of customer calls. Several operationally interesting findings are obtained and discussed.

Copyright/Permission Statement

This is the peer reviewed version of the following article: Shen, H. and D. Brown, L. (2006), Non-parametric modelling of time-varying customer service times at a bank call centre. Appl. Stochastic Models Bus. Ind., 22: 297–311., which has been published in final form at This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving [link to].


service engineering, queueing theory, local polynomial regression, variance estimation, heteroscedasticity, bandwidth selection



Date Posted: 27 November 2017

This document has been peer reviewed.