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 Rho Zero Inflated Data (Ph.D. dissertation). Western Michigan University, Kalamazoo, 2009). The proposed are explicitly expressed in terms of respective probability masses at origin. As illustrated an example based insurance data, these useful practice when interpreting values rho.