Exact Non-parametric Confidence Intervals for Quantiles with Progressive Type-II Censoring

It is shown how various exact non-parametric inferences based on order statistics in one or two random samples can be generalized to situations with progressive type-II censoring, which is a kind of evolutionary right censoring. Ordinary type-II right censoring is a special case of such progressive censoring. These inferences include confidence intervals for a given parent quantile, prediction intervals for a given order statistic of a future sample, and related two-sample inferences based on exceedance probabilities. The proposed inferences are valid for any parent distribution with continuous distribution function. The key result is that each observable uncensored order statistic that becomes available with progressive type-II censoring can be represented as a mixture with known weights of underlying ordinary order statistics. The importance of this mixture representation lies in that various properties of such observable order statistics can be deduced immediately from well-known properties of ordinary order statistics.     

Loyalty-based segmentation and the customer development process

As process management fast becomes recognised as the means by which customer value can be created, it is now equally well understood that the mechanism of value delivery is among the core processes. Without managing Customer Development as a core process, the implementation of strategic plans will lack clear focus. The author argues that the function of the Customer Development process is to build relationships with preferred customers. Working on the premise that all customers are not created equal, the priority for customer development in mature markets is to build these preferred relationships among existing customers. It is now accepted wisdom that these customer relationships deliver superior profits. How customer development management select these customers, or groups of customers, and build specific relationships is directed by the Principles of Loyalty Management.These principles acknowledge that customer loyalty is relative which means that customers as well as product and service brands need to be differentiated. The Diamond of Loyalty© provides a new management tool for this purpose by categorising customer purchasing styles according to their level of involvement (i.e. brand or company relationship) and their purchasing portfolio across suppliers.Finally, it is argued that customer development should discriminate in favour of supporting `high share' customers over `low share' customers in building preferred relationship among existing customers.