Transition Functions¶
Full Mathematical Format¶
Non-Linear Gaussian Cumulative Functions¶
2073 z=0.25a(1+erf((x-b)/(sqrt(2)*c)))*(1+erf((y-d)/(sqrt(2)*e)))
2074 z=a+0.25b(1+erf((x-c)/(sqrt(2)*d)))*(1+erf((y-e)/(sqrt(2)*f)))
2075 z=0.25a(1+erf((x-b)/(sqrt(2)*c)))*(1+erf((y-d)/(sqrt(2)*c)))
2076 z=a+0.25b(1+erf((x-c)/(sqrt(2)*d)))*(1+erf((y-e)/(sqrt(2)*d)))
2077 z=0.5a(1+erf((x-b)/(sqrt(2)*c)))+0.5d(1+erf((y-e)/(sqrt(2)*f)))
2078 z=a+0.5b(1+erf((x-c)/(sqrt(2)*d)))+0.5e(1+erf((y-f)/(sqrt(2)*g)))
2079 z=a+by+0.5c(1+erf((x-d)/(sqrt(2)*e)))
2080 z=a+bx+0.5c(1+erf((y-d)/(sqrt(2)*e)))
2081 z=a+by+cy2+0.5d(1+erf((x-e)/(sqrt(2)*f)))
2082 z=a+bx+cx2+0.5d(1+erf((y-e)/(sqrt(2)*f)))
2083 z=0.5a(1+erf((x-b)/(sqrt(2)*c)))+0.5d(1+erf((y-e)/(sqrt(2)*f)))+0.25g(1+erf((x-b)/(sqrt(2)*c)))*(1+erf((y-e)/(sqrt(2)*f)))
2084 z=a+0.5b(1+erf((x-c)/(sqrt(2)*d)))+0.5e(1+erf((y-f)/(sqrt(2)*g)))+0.25h(1+erf((x-c)/(sqrt(2)*d)))*(1+erf((y-f)/(sqrt(2)*g)))
Non-Linear Lorentzian Cumulative Functions¶
2085 z=a(0.5+atan((x-b)/c)/p)*(0.5+atan((y-d)/e)/p)
2086 z=a+b(0.5+atan((x-c)/d)/p)*(0.5+atan((y-e)/f)/p)
2087 z=a(0.5+atan((x-b)/c)/p)*(0.5+atan((y-d)/c)/p)
2088 z=a+b(0.5+atan((x-c)/d)/p)*(0.5+atan((y-e)/d)/p)
2089 z=a(0.5+atan((x-b)/c)/p)+d(0.5+atan((y-e)/f)/p)
2090 z=a+b(0.5+atan((x-c)/d)/p)+e(0.5+atan((y-f)/g)/p)
2091 z=a+by+c(0.5+atan((x-d)/e)/p)
2092 z=a+bx+c(0.5+atan((y-d)/e)/p)
2093 z=a+by+cy2+d(0.5+atan((x-e)/f)/p)
2094 z=a+bx+cx2+d(0.5+atan((y-e)/f)/p)
2095 z=a(0.5+atan((x-b)/c)/p)+d(0.5+atan((y-e)/f)/p)+g(0.5+atan((x-b)/c)/p)*(0.5+atan((y-e)/f)/p)
2096 z=a+b(0.5+atan((x-c)/d)/p)+e(0.5+atan((y-f)/g)/p)+h(0.5+atan((x-c)/d)/p)*(0.5+atan((y-f)/g)/p)
Non-Linear Log-Normal Cumulative Functions¶
2097 z=0.25aerfc(c/sqrt(2)-ln(x/b)/(csqrt(2)))*erfc(e/sqrt(2)-ln(y/d)/(esqrt(2)))
2098 z=a+0.25berfc(d/sqrt(2)-ln(x/c)/(dsqrt(2)))*erfc(f/sqrt(2)-ln(y/e)/(fsqrt(2)))
2099 z=0.25aerfc(c/sqrt(2)-ln(x/b)/(csqrt(2)))*erfc(c/sqrt(2)-ln(y/d)/(csqrt(2)))
2100 z=a+0.25berfc(d/sqrt(2)-ln(x/c)/(dsqrt(2)))*erfc(d/sqrt(2)-ln(y/e)/(dsqrt(2)))
2101 z=0.5aerfc(c/sqrt(2)-ln(x/b)/(csqrt(2)))+0.5derfc(f/sqrt(2)-ln(y/e)/(fsqrt(2)))
2102 z=a+0.5berfc(d/sqrt(2)-ln(x/c)/(dsqrt(2)))+0.5eerfc(g/sqrt(2)-ln(y/f)/(gsqrt(2)))
2103 z=a+by+0.5cerfc(e/sqrt(2)-ln(x/d)/(esqrt(2)))
2104 z=a+bx+0.5cerfc(e/sqrt(2)-ln(y/d)/(esqrt(2)))
2105 z=a+by+cy2+0.5derfc(f/sqrt(2)-ln(x/e)/(fsqrt(2)))
2106 z=a+bx+cx2+0.5derfc(f/sqrt(2)-ln(y/e)/(fsqrt(2)))
2107 z=0.5aerfc(c/sqrt(2)-ln(x/b)/(csqrt(2)))+0.5derfc(f/sqrt(2)-ln(y/e)/(fsqrt(2)))+0.25gerfc(c/sqrt(2)-ln(x/b)/(csqrt(2)))*erfc(f/sqrt(2)-ln(y/e)/(fsqrt(2)))
2108 z=a+0.5berfc(d/sqrt(2)-ln(x/c)/(dsqrt(2)))+0.5eerfc(g/sqrt(2)-ln(y/f)/(gsqrt(2)))+0.25herfc(d/sqrt(2)-ln(x/c)/(dsqrt(2)))*erfc(g/sqrt(2)-ln(y/f)/(gsqrt(2)))
Non-Linear Sigmoid (Logistic Cumulative) Functions¶
2109 z=a(1/(1+exp(-((x-b)/c))))*(1/(1+exp(-((y-d)/e))))
2110 z=a+b(1/(1+exp(-((x-c)/d))))*(1/(1+exp(-((y-e)/f))))
2111 z=a(1/(1+exp(-((x-b)/c))))*(1/(1+exp(-((y-d)/c))))
2112 z=a+b(1/(1+exp(-((x-c)/d))))*(1/(1+exp(-((y-e)/d))))
2113 z=a(1/(1+exp(-((x-b)/c))))+d(1/(1+exp(-((y-e)/f))))
2114 z=a+b(1/(1+exp(-((x-c)/d))))+e(1/(1+exp(-((y-f)/g))))
2115 z=a+by+c(1/(1+exp(-((x-d)/e))))
2116 z=a+bx+c(1/(1+exp(-((y-d)/e))))
2117 z=a+by+cy2+d(1/(1+exp(-((x-e)/f))))
2118 z=a+bx+cx2+d(1/(1+exp(-((y-e)/f))))
2119 z=a(1/(1+exp(-((x-b)/c))))+d(1/(1+exp(-((y-e)/f))))+g(1/(1+exp(-((x-b)/c))))*(1/(1+exp(-((y-e)/f))))
2120 z=a+b(1/(1+exp(-((x-c)/d))))+e(1/(1+exp(-((y-f)/g))))+h(1/(1+exp(-((x-c)/d))))*(1/(1+exp(-((y-f)/g))))
Non-Linear Extreme Value Cumulative Functions¶
2121 z=aexp(-exp(-(x-b)/c))*exp(-exp(-(y-d)/e))
2122 z=a+bexp(-exp(-(x-c)/d))*exp(-exp(-(y-e)/f))
2123 z=aexp(-exp(-(x-b)/c))*exp(-exp(-(y-d)/c))
2124 z=a+bexp(-exp(-(x-c)/d))*exp(-exp(-(y-e)/d))
2125 z=aexp(-exp(-(x-b)/c))+dexp(-(y-e)/f))
2126 z=a+bexp(-exp(-(x-c)/d))+eexp(-(y-f)/g))
2127 z=a+by+cexp(-exp(-(x-d)/e))
2128 z=a+bx+cexp(-exp(-(y-d)/e))
2129 z=a+by+cy2+dexp(-exp(-(x-e)/f))
2130 z=a+bx+cx2+dexp(-exp(-(y-e)/f))
2131 z=aexp(-exp(-(x-b)/c))+dexp(-(y-e)/f))+gexp(-exp(-(x-b)/c))*exp(-exp(-(y-e)/f))
2132 z=a+bexp(-exp(-(x-c)/d))+eexp(-(y-f)/g))+hexp(-exp(-(x-c)/d))*exp(-exp(-(y-f)/g))
Non-Linear Logistic Dose Response Functions¶
2133 z=a(1/(1+(x/b)-c))*(1/(1+(y/d)-e))
2134 z=a+b(1/(1+(x/c)-d))*(1/(1+(y/e)-f))
2135 z=a(1/(1+(x/b)-c))*(1/(1+(y/d)-c))
2136 z=a+b(1/(1+(x/c)-d))*(1/(1+(y/e)-d))
2137 z=a(1/(1+(x/b)-c))+d(1/(1+(y/e)-f))
2138 z=a+b(1/(1+(x/c)-d))+e(1/(1+(y/f)-g))
2139 z=a+by+c(1/(1+(x/d)-e))
2140 z=a+bx+c(1/(1+(y/d)-e))
2141 z=a+by+cy2+d(1/(1+(x/e)-f))
2142 z=a+bx+cx2+d(1/(1+(y/e)-f))
2143 z=a(1/(1+(x/b)-c))+d(1/(1+(y/e)-f))+g(1/(1+(x/b)-c))*(1/(1+(y/e)-f))
2144 z=a+b(1/(1+(x/c)-d))+e(1/(1+(y/f)-g))+h(1/(1+(x/c)-d))*(1/(1+(y/f)-g))
Notational Format¶
Non-Linear Gaussian Cumulative Functions¶
2073 z=GCUMX(a,b,c)*GCUMY(1,d,e)
2074 z=a+GCUMX(b,c,d)*GCUMY(1,e,f)
2075 z=GCUMX(a,b,c)*GCUMY(1,d,c)
2076 z=a+GCUMX(b,c,d)*GCUMY(1,e,d)
2077 z=GCUMX(a,b,c)+GCUMY(d,e,f)
2078 z=a+GCUMX(b,c,d)+GCUMY(e,f,g)
2079 z=a+by+GCUMX(c,d,e)
2080 z=a+bx+GCUMY(c,d,e)
2081 z=a+by+cy2+GCUMX(d,e,f)
2082 z=a+bx+cx2+GCUMY(d,e,f)
2083 z=GCUMX(a,b,c)+GCUMY(d,e,f)+GCUMX(g,b,c)*GCUMY(1,e,f)
2084 z=a+GCUMX(b,c,d)+GCUMY(e,f,g)+GCUMX(h,c,d)*GCUMY(1,f,g)
Non-Linear Lorentzian Cumulative Functions¶
2085 z=LORCUMX(a,b,c)*LORCUMY(1,d,e)
2086 z=a+LORCUMX(b,c,d)*LORCUMY(1,e,f)
2087 z=LORCUMX(a,b,c)*LORCUMY(1,d,c)
2088 z=a+LORCUMX(b,c,d)*LORCUMY(1,e,d)
2089 z=LORCUMX(a,b,c)+LORCUMY(d,e,f)
2090 z=a+LORCUMX(b,c,d)+LORCUMY(e,f,g)
2091 z=a+by+LORCUMX(c,d,e)
2092 z=a+bx+LORCUMY(c,d,e)
2093 z=a+by+cy2+LORCUMX(d,e,f)
2094 z=a+bx+cx2+LORCUMY(d,e,f)
2095 z=LORCUMX(a,b,c)+LORCUMY(d,e,f)+LORCUMX(g,b,c)*LORCUMY(1,e,f)
2096 z=a+LORCUMX(b,c,d)+LORCUMY(e,f,g)+LORCUMX(h,c,d)*LORCUMY(1,f,g)
Non-Linear Log-Normal Cumulative Functions¶
2097 z=LNCUMX(a,b,c)*LNCUMY(1,d,e)
2098 z=a+LNCUMX(b,c,d)*LNCUMY(1,e,f)
2099 z=LNCUMX(a,b,c)*LNCUMY(1,d,c)
2100 z=a+LNCUMX(b,c,d)*LNCUMY(1,e,d)
2101 z=LNCUMX(a,b,c)+LNCUMY(d,e,f)
2102 z=a+LNCUMX(b,c,d)+LNCUMY(e,f,g)
2103 z=a+by+LNCUMX(c,d,e)
2104 z=a+bx+LNCUMY(c,d,e)
2105 z=a+by+cy2+LNCUMX(d,e,f)
2106 z=a+bx+cx2+LNCUMY(d,e,f)
2107 z=LNCUMX(a,b,c)+LNCUMY(d,e,f)+LNCUMX(g,b,c)*LNCUMY(1,e,f)
2108 z=a+LNCUMX(b,c,d)+LNCUMY(e,f,g)+LNCUMX(h,c,d)*LNCUMY(1,f,g)
Non-Linear Sigmoid (Logistic Cumulative) Functions¶
2109 z=SIGX(a,b,c)*SIGY(1,d,e)
2110 z=a+SIGX(b,c,d)*SIGY(1,e,f)
2111 z=SIGX(a,b,c)*SIGY(1,d,c)
2112 z=a+SIGX(b,c,d)*SIGY(1,e,d)
2113 z=SIGX(a,b,c)+SIGY(d,e,f)
2114 z=a+SIGX(b,c,d)+SIGY(e,f,g)
2115 z=a+by+SIGX(c,d,e)
2116 z=a+bx+SIGY(c,d,e)
2117 z=a+by+cy2+SIGX(d,e,f)
2118 z=a+bx+cx2+SIGY(d,e,f)
2119 z=SIGX(a,b,c)+SIGY(d,e,f)+SIGX(g,b,c)*SIGY(1,e,f)
2120 z=a+SIGX(b,c,d)+SIGY(e,f,g)+SIGX(h,c,d)*SIGY(1,f,g)
Non-Linear Extreme Value Cumulative Functions¶
2121 z=EXVCUMX(a,b,c)*EXVCUMY(1,d,e)
2122 z=a+EXVCUMX(b,c,d)*EXVCUMY(1,e,f)
2123 z=EXVCUMX(a,b,c)*EXVCUMY(1,d,c)
2124 z=a+EXVCUMX(b,c,d)*EXVCUMY(1,e,d)
2125 z=EXVCUMX(a,b,c)+EXVCUMY(d,e,f)
2126 z=a+EXVCUMX(b,c,d)+EXVCUMY(e,f,g)
2127 z=a+by+EXVCUMX(c,d,e)
2128 z=a+bx+EXVCUMY(c,d,e)
2129 z=a+by+cy2+EXVCUMX(d,e,f)
2130 z=a+bx+cx2+EXVCUMY(d,e,f)
2131 z=EXVCUMX(a,b,c)+EXVCUMY(d,e,f)+EXVCUMX(g,b,c)*EXVCUMY(1,e,f)
2132 z=a+EXVCUMX(b,c,d)+EXVCUMY(e,f,g)+EXVCUMX(h,c,d)*EXVCUMY(1,f,g)
Non-Linear Logistic Dose Response Functions¶
2133 z=LDRX(a,b,c)*LDRY(1,d,e)
2134 z=a+LDRX(b,c,d)*LDRY(1,e,f)
2135 z=LDRX(a,b,c)*LDRY(1,d,c)
2136 z=a+LDRX(b,c,d)*LDRY(1,e,d)
2137 z=LDRX(a,b,c)+LDRY(d,e,f)
2138 z=a+LDRX(b,c,d)+LDRY(e,f,g)
2139 z=a+by+LDRX(c,d,e)
2140 z=a+bx+LDRY(c,d,e)
2141 z=a+by+cy2+LDRX(d,e,f)
2142 z=a+bx+cx2+LDRY(d,e,f)
2143 z=LDRX(a,b,c)+LDRY(d,e,f)+LDRX(g,b,c)*LDRY(1,e,f)
2144 z=a+LDRX(b,c,d)+LDRY(e,f,g)+LDRX(h,c,d)*LDRY(1,f,g)