updates arithmetic documentation

Author: Ander Gray

docs/src/arithmetic.md

@@ -97,17 +97,34 @@ julia> convOpposite(a, b, op = *)
 Binary operations with a specified correlation coefficient may also be performed:
 
 ```julia
-julia> a = normal(0,1);
-julia> b = normal(1,1);
-julia> conv(a,b, op = +, corr = 0.5)
- Pbox: 	  ~  ( range=[-5.18046,7.18046], mean=1.0, var=[2.57835,3.96457])
+julia> conv(a, b, op = *, corr = -0.5)
+ Pbox: 	  ~  ( range=[6.9098, 26.18], mean=15.0, var=[5.5032, 7.9116])
+
+julia> conv(a, b, op = *, corr = 0.5)
+ Pbox: 	  ~  ( range=[6.9098, 26.18], mean=15.0, var=[12.985, 16.804])
+```
+```@raw html
+<img src="./plots/prodCor1.png" width="49.5%"/>
+<img src="./plots/prodCor2.png" width="49.5%"/>
 ```
+
 This assumes that a and b follow a Gaussian Copula. You may however perform the operation with any copula by using the function
 ```julia
-julia> convCorr(a, b, C = C, op = +)
+julia> C1 = clayton(5)
+julia> convCorr(a, b, op = *, C = C1)
+ Pbox: 	  ~  ( range=[6.9098, 26.18], mean=[15.024, 15.473], var=[15.738, 19.714])
+
+julia> C2 = Frank(-2)
+julia> convCorr(a, b, op = *, C = C2)
+ Pbox: 	  ~  ( range=[6.9098, 26.18], mean=15.0, var=[6.78, 9.5713])
 ```
 where C is a copula (see section on dependence modelling).
 
+```@raw html
+<img src="./plots/prodCop1.png" width="49.5%"/>
+<img src="./plots/prodCop2.png" width="49.5%"/>
+```
+
 Note that:
 
 ```julia

docs/src/plots/make_arithmetic_plots.jl

@@ -41,3 +41,23 @@ savefig("sumOpposite.png")
 plot(convOpposite(a, b, op = *), fontsize = 22)
 PyPlot.xlabel("a * b (opposite)", fontsize = 26)
 savefig("prodOpposite.png")
+
+
+plot(conv(a, b, op = *, corr = -0.5), fontsize = 22)
+PyPlot.xlabel("a * b (r = -0.5)", fontsize = 26)
+savefig("prodCor1.png")
+
+plot(conv(a, b, op = *, corr = 0.5), fontsize = 22)
+PyPlot.xlabel("a * b (r = 0.5)", fontsize = 26)
+savefig("prodCor2.png")
+
+C1 = Clayton(5)
+C2 = Frank(-2)
+
+plot(convCorr(a, b, op = *, C = C1), fontsize = 22)
+PyPlot.xlabel("a * b (C = Clayton(5))", fontsize = 26)
+savefig("prodCop1.png")
+
+plot(convCorr(a, b, op = *, C = C2), fontsize = 22)
+PyPlot.xlabel("a * b (C = Frank(-2))", fontsize = 26)
+savefig("prodCop2.png")

docs/src/plots/prodCop1.png

@@ -171,5 +171,7 @@ julia> plot(a, name = "ab", col = "red", fontsize = 22)
 julia> plot(b, name = "ab", col = "blue", fontsize = 22)
 julia> plot(c, fontsize = 22)
 ```
-!["envelope of an interval and a gaussian"](./plots/intersection1.png) 
-!["envelope of an interval and a gaussian"](./plots/intersection2.png)
+```@raw html
+<img src="./plots/intersection1.png" width="49.5%"/>
+<img src="./plots/intersection2.png" width="49.5%"/>
+```