Basedonthemaximumentropyprincipleanewprobabilitydensityfunction(PDF)f(x)forthesurfaceelevationofnonlinearseawaves,X,isderivedthroughperformingacoordinatetransformofXandsolvingavariationproblemsubjecttothreeconstraintconditionsoff(x).ComparedwiththemaximumentropyPDFspresentedpreviously,thenewPDFhasthefollowingmerits:(1)ithasfourparameterstobedeterminedandhencecangivemorerefinedfittoobserveddataandhaswidersuitabilityfornonlinearwavesindifferentconditions;(2)theseparametersareexpressedintermsofdistributionmomentsofXinarelativelysimpleformandhenceareeasytobedeterminedfromobserveddata;(3)thePDFisfreeoftherestrictionofweaknonlinearityandpossibletobeusedforseawavesincomplicatedconditions,suchasthoseinshallowwaterswithcomplicatedtopography;and(4)thePDFissimpleinformandhenceconvenientfortheoreticalandpracticaluses.Laboratorywind-waveexperimentshavebeenconductedtotestthecompetenceofthenewPDFforthesurfaceelevationofnonlinearwaves.TheexperimentalresultsmanifestthatthenewPDFgivessomewhatbetterfittothelaboratorywind-wavedatathanthewell-knownGram-CharlierPDFandbetaPDF.
