ABSTRACT Weighted distributions can be used to fit various forms of resource selection probability functions (RSPF) under the use-versus-available study design (Lele and Keim 2006). Although valid, the numerical maximization procedure used by Lele and Keim (2006) is unstable because of the inherent roughness of the Monte Carlo likelihood function. We used a combination of the methods of partial likelihood and data cloning to obtain maximum likelihood estimators of the RSPF in a numerically stable fashion. We demonstrated the methodology using simulated data sets generated under the log—log RSPF model and a reanalysis of telemetry data presented in Lele and Keim (2006) using the logistic RSPF model. The new method for estimation of RSPF can be used to understand differential selection of resources by animals, an essential component of studies in conservation biology, wildlife management, and applied ecology.