Euclidean distance-based spatial interpolation methods that are conceptually simple are commonly used for the imputation of missing precipitation and other hydroclimatic variable datasets. Improved variants of these methods are essential as Euclidean distance will not always serve as an appropriate surrogate that can quantify the inter-gauge relationships in all hydroclimatic and topographical settings. Probability space-based error measure (linear error in probability space (LEPS)) and three distribution similarity hypothesis test statistic values are proposed as surrogates for distances in weighting methods to address this limitation. A k-fold cross-validation exercise of the imputation of precipitation data at 22 rain gauges in a temperate climatic region is used for the evaluation of methods. Improved imputation of missing data was noted from proposed methods compared to that from a distance-based method and is confirmed with statistical inference testing of multiple error and performance measures. Also, the LEPS-based method provided performance measures that are as good as those from a nonlinear optimization method. A local spatial interpolation approach that uses LEPS and two-sample Kolmogorov-Smirnov hypothesis test results quantified as binary outcomes for objective selection of rain gauges are also evaluated. Better estimates of missing data are obtained using this approach compared to those from a Euclidean distance-based global interpolation method. The proposed new probability space-based distances are conceptually superior alternatives to Euclidean distances when used in weighting methods for spatial interpolation.