# How to plot Extreme-Value functions that have parameters with finite intervals?

I would like to plot \$min\$ and \$max\$ values of a function whose parameters have finite intervals but I am receiving error messages as follows:

````h=0.7; cspeed = 299792.458; OmegaΛ0 = 0.7; Omegam0 = 0.3; Omega0 = 1.0002; Yp = Interval[0.2534 + 0.0083 {-1, 1}]; alpha = Interval[0.17 + 0.03 {-1, 1}]; logvc0 =  Interval[1.58 + 0.05 {-1, 1}]; logvc1 = Interval[3.14 + 0.38 {-1, 1}]; beta = Interval[-0.50 + 0.18 {-1, 1}];  var1 = Interval[10.79 + 0.01 {-1, 1}]; phi1 = Interval[-3.31 + 0.20 {-1, 1}]; phi2 = Interval[-2.01 + 0.28 {-1, 1}]; alpha1 = Interval[-1.69 + 0.10 {-1, 1}]; alpha2 = Interval[-0.79 + 0.04 {-1, 1}];  α0 = Interval[-1.412 + {-0.105, 0.020}]; αa = Interval[0.731 + {-0.296, 0.344}];  δ0 = Interval[3.508 + {-0.369, 0.087}]; δa = Interval[2.608 + {-1.261, 2.446}]; δz = Interval[-0.043 + {-0.071, 0.958}];  γ0 = Interval[0.316 + {-0.012, 0.076}]; γa =  Interval[1.319 + {-1.261, 0.584}]; γz = Interval[0.279 + {-0.081, 0.256}];  ϵ0 = Interval[-1.777 + {-0.146, 0.133}]; ϵa = Interval[-0.006 + {-0.361, 0.113}]; ϵz = Interval[0.0 + {-0.104, 0.003}]; ϵa2 = Interval[-0.119 + {-0.012, 0.061}];  M10 = Interval[11.514 + {-0.009, 0.053}]; M1a = Interval[-1.793 + {-0.330, 0.315}]; M1z = Interval[-0.251 + {-0.125, 0.012}];  α[z_?NumericQ] := α[z] = 1./(1. + z); distance[z_?NumericQ] := distance[z] = NIntegrate[(Omegam0*(1 + u)^3 + OmegaΛ0 + (Omega0 - Omegam0 - OmegaΛ0)*(1 + u)^2)^(-1/2), {u, 0, z}]; F[z_?NumericQ] := F[z] = (Sin[distance[z]*(Omega0 - 1.)^(1/2)]/(distance[z]*(Omega0 - 1.)^(1/2))); ComovingVolume[z_?NumericQ] := ComovingVolume[z] = (4*π)/3*(cspeed/100)^3*(distance[z])^3*((3*(1 - (Sin[2*distance[z]*(Omega0 - 1.)^(1/2)]/(2*distance[z]*(Omega0 - 1.)^(1/2)))))/(2*(Omega0 - 1)*(distance[z])^2)); dComovingVolumedz[z_?NumericQ] := dComovingVolumedz[z] = Derivative[1][ComovingVolume][z] // N; νfunc[z_?NumericQ] := νfunc[z] = Exp[-4 *(α[z] )^2];  αfunc[z_?NumericQ, α0_, αa_] := αfunc[z, α0, αa] = α0 + (αa *(α[z] - 1))*νfunc[z];   δfunc[z_?NumericQ, δ0_, δa_, δz_] := δfunc[z, δ0, δa, δz] = δ0 + (δa *(\ α[z] - 1) + δz* z) *νfunc[z];  γfunc[z_?NumericQ, γ0_, γa_, γz_] := γfunc[z, γ0, γa, γz] = γ0 + (γa (\ α[z] - 1) + γz *z) *νfunc[z];  log10ϵ[z_?NumericQ, ϵ0_, ϵa_, ϵz_, \ ϵa2_] := log10ϵ[z, ϵ0, ϵa, ϵz, ϵa2] = ϵ0 + (ϵa*(α[z] - 1) + ϵz*z)*νfunc[z] + ϵa2*(α[z] - 1); log10M1[z_?NumericQ, M10_, M1a_, M1z_] := log10M1[z, M10, M1a, M1z] =     Log10[h] + M10 + (M1a*(α[z] - 1) + M1z*z)*νfunc[z]; fun[y_?NumericQ, z_?NumericQ, α0_, αa_, δ0_, δa_, δz_, γ0_, γa_, γz_] :=    fun[y, z, α0, αa, δ0, δa, δz, γ0, γa, γz] = -Log10[10^( (αfunc[z, α0, αa])*y) + 1] + δfunc[z, δ0, δa, δz] *(Log10[1 + Exp[y]])^ γfunc[z, γ0, γa, γz]/(1 + Exp[10^-y]); MStar[z_?NumericQ, M_?NumericQ, ϵ0_, ϵa_, ϵz_, ϵa2_, M10_, M1a_, M1z_, α0_, αa_, δ0_, δa_, δz_, γ0_, γa_, γz_] :=    MStar[z, M, ϵ0, ϵa, ϵz, ϵa2, M10, M1a, M1z, α0, αa, δ0, δa, δz, γ0, γa, γz] = log10ϵ[z, ϵ0, ϵa, ϵz, ϵa2] + log10M1[z, M10, M1a, M1z] + fun[M - log10M1[z, M10, M1a, M1z], z, α0, αa, δ0, δa, δz, γ0, γa, γz] - fun[0, z, α0, αa, δ0, δa, δz, γ0, γa, γz]; dLogMStardLogM[z_?NumericQ, M_?NumericQ, ϵ0_, ϵa_, ϵz_, ϵa2_, M10_, M1a_, M1z_, α0_, αa_, δ0_, δa_, δz_, γ0_, γa_, γz_] := dLogMStardLogM[z, M, ϵ0, ϵa, ϵz, ϵa2, M10, M1a, M1z, α0, αa, δ0, δa, δz, γ0, γa, γz] = Derivative[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0][MStar][z, M, ϵ0, ϵa, ϵz, ϵa2, M10, M1a, M1z, α0, αa, δ0, δa, δz, γ0, γa, γz]; LocalSMFAllGalaxiesWSB[MS_?NumericQ, var1_, phi1_, phi2_, alpha1_, alpha2_] := LocalSMFAllGalaxiesWSB[MS, var1, phi1, phi2, alpha1, alpha2] =     Log[10.]*Exp[-(10.^(MS - var1 - Log10[h]))]*(10.^phi1*(10.^(MS - var1 - Log10[h]))^(alpha1 + 1.) + 10.^phi2*(10.^(MS - var1 - Log10[h]))^(alpha2 + 1.)); LocalSMF[z_?NumericQ, M_?NumericQ, var1_, phi1_, phi2_, alpha1_, alpha2_, ϵ0_, ϵa_, ϵz_, ϵa2_, M10_, M1a_, M1z_, α0_, αa_, δ0_, δa_, δz_, γ0_, γa_, γz_] := LocalSMF[z, M, var1, phi1, phi2, alpha1, alpha2, ϵ0, ϵa, ϵz, ϵa2, M10, M1a, M1z, α0, αa, δ0, δa, δz, γ0, γa, γz] = LocalSMFAllGalaxiesWSB[MStar[z, M, ϵ0, ϵa, ϵz, ϵa2, M10, M1a, M1z, α0, αa, δ0, δa, δz, γ0, γa, γz], var1, phi1, phi2, alpha1, alpha2]; dNgalaxiesdzWSB[z_, M_, var1_, phi1_, phi2_, alpha1_, alpha2_, ϵ0_, ϵa_, ϵz_, ϵa2_, M10_, M1a_, M1z_, α0_, αa_, δ0_, δa_, δz_, γ0_, γa_, γz_] := dNgalaxiesdzWSB[z, M, var1, phi1, phi2, alpha1, alpha2, ϵ0, ϵa, ϵz, ϵa2, M10, M1a, M1z, α0, αa, δ0, δa, δz, γ0, γa, γz] = 7748./(4.*π)*(π/180.)^2.*dComovingVolumedz[z]*Integrate[LocalSMF[z, p, var1, phi1, phi2, alpha1, alpha2, ϵ0, ϵa, ϵz, ϵa2, M10, M1a, M1z, α0, αa, δ0, δa, δz, γ0, γa, γz], {p, M, 15.}];  LogPlot[{ Min[dNgalaxiesdzWSB[0.03, M, var1, phi1, phi2, alpha1, alpha2, ϵ0, ϵa, ϵz, ϵa2, M10, M1a, M1z, α0, αa, δ0, δa, δz, γ0, γa, γz]],  Max[dNgalaxiesdzWSB[0.03, M, var1, phi1, phi2, alpha1, alpha2, ϵ0, ϵa, ϵz, ϵa2, M10, M1a, M1z, α0, αa, δ0, δa, δz, γ0, γa, γz]]},  {M, 10.25, 12.95},  PlotRange -> {10^-3, 10^7.4},   Filling -> {1 -> {{2}, LightGreen}},   PlotStyle -> {{Green, Thickness[0.005]}, {Green, Thickness[0.005]}},  Frame -> True, FrameLabel -> {Style["X", FontSize -> 26], Style["Y", FontSize -> 26]},   FrameTicksStyle -> Directive[FontSize -> 26]] `
```

NIntegrate::inumr: The integrand LocalSMF[0.03,p,Interval[{10.78,10.8}],Interval[{-3.51,-3.11}],Interval[{-2.29,-1.73}],Interval[{-1.79,-1.59}],Interval[{-0.83,-0.75}],Interval[{-1.923,-1.644}],<<7>>,Interval[{0.435,1.075}],Interval[{3.139,3.595}],Interval[{1.347,5.054}],Interval[{-0.114,0.915}],Interval[{0.304,0.392}],Interval[{0.058,1.903}],Interval[{0.198,0.535}]] has evaluated to non-numerical values for all sampling points in the region with boundaries {{10.2501,15.}}. >>

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Category: plotting Time: 2016-07-29 Views: 0