program define pdf_f
    version 4.0

    local x   = "`1'"
    local fx  =  "`2'"
    local df1 = `3'
    local df2 = `4'

    quietly {
        local v1half=`df1'/2
        local v2half=`df2'/2
        local vsum=`v1half'+`v2half'
        local vrat=`v1half'/`v2half'
        local c1=`v1half'*log(`vrat')+lngamma(`vsum')-lngamma(`v1half')-lngamma(`v2half')
        replace `fx' =exp(`c1'+(`v1half'-1)*log(`x')-`vsum'*log(1+`vrat'*`x'))}

end