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There have long been some experiment findings that the behavior of a power amplifier (PA) to digitally modulated stimuli depends on its input statistics. Correspondingly, there have been efforts in characterizing PA behaviors and, more recently, in designing amplifier linearization devices by including the information of envelope statistics or using statistical methods. Superior performance have been reported for resultant linearizer designs compared with similar designs based on conventional approaches. In this brief, an adaptation procedure on envelope statistics will be introduced that can further improve the performance of any predistorter design derived from a statistical amplifier model, or more generally, derived from the sample data sets of the input and the output of the PA.