Best upper and lower bounds on Spearman’s rho for zero-inflated continuous variables and their application to insurance

In this note, we establish the best lower and upper bounds on Spearman’s rho for zero-inflated continuous random variables studied by Pimentel (Kendall’s Tau and Spearman’s Rho for Zero Inflated Data (Ph.D. dissertation). Western Michigan University, Kalamazoo, 2009). The proposed bounds are explicitly expressed in terms of the respective probability masses at the origin. As illustrated in an example based on insurance data, these bounds are useful in practice when interpreting the values of Spearman’s rho.