## 3158 Reputation

16 years, 122 days

## Thanx alec !! You are the...

Thanx alec !! You are the man !  It looks like it will do the trick ! I love this Maple forum ha ha

## I think the biggest problem...

I think the biggest problem I have is to write the if function for the sequence elements.

restart:
randomize():
coin:=rand(0..1):
coin_1:=proc(n) seq(coin(),i=1..n) end:
x_1:=seq([coin_1(10)],i=1..1);

[1, 1, 0, 1, 0, 0, 1, 1, 0, 0]

randomize():
coin:=rand(1..10):
coin_1:=proc(n) seq(coin(),i=1..n) end:
x_2:=seq([coin_1(10)],i=1..1);

[2, 3, 5, 2, 5, 1, 7, 8, 8, 10]

I want to create a third sequence x_3 that have the same value as x_1 in the previous period if x_2 in this period is larger than 6 and is random ( 0 or 1) if x_2 in this period is smaller  than 6.

I can then change the threshold (in this case 6) to control the amount of serial correlation

Any suggestions?

## thanx Doug....I will have a...

thanx Doug....I will have a try.... it looks like it might do the trick. Again thanx

## my reasoning is as...

my reasoning is as follows: Either I do all my mathematical derivations + ploting with Maple which means that I need more flexibility to do algebraically manipulation or I just do all my derivations with a pen and paper and only use Maple as a tool to plot differential equations.... humm...

## ok, thanx for your input. I...

ok, thanx for your input. I still find it a little bit strange that I can not manipulate the expression more with such a high-end mathematical software such as Maple... humm

## ok, thanx for your input. I...

ok, thanx for your input. I still find it a little bit strange that I can not manipulate the expression more with such a high-end mathematical software such as Maple... humm

## again, thanx doug, very...

again, thanx doug, very informative !

## as I said you are the man...

as I said you are the man doug ! Could not have done it without your help thanx.. Varphi is the consumption per capital ratio but the important thing is the plot. So I think we can treat varphi as an independent variable as you correctly assumed. I can derive the model for you if you are interested but it is going to take 20 A4 pages (I know since I have done it, he he). I am quite satisfied with your current solution without the bifurcation diagram but for your information varphi is given by: diff(varphi(t),t)=((1/theta)*(a*z-dep-p)*(z-dep-varphi))*varphi where theta is the risk aversion parameter that determind the curvature of the utility function, z is the average product of physical capital, dep is depreciation, a=0.3. The model acctual consits of three diff equations that are visualized on three panes. Again thanx for your help... // Alex

## you are the man doug! Ok, in...

you are the man doug! Ok, in economics you have a model called the Uzawa-Lucas Model. You have one differential equation of the form. x_:=diff(u(t),t)=(B/a-B+B*u-varphi)*u; The isocline (diff(u(t),t)/u=u(dot)/u=0) for such a diff equation is given by: varphi_:=B/a-B+B*u; If we assume that B:=1: a:=0.3: we get: x_=diff(u(t),t)=(2.33+u-varphi)*u; # diff equation varphi_=2.33+u; # Isocline What I want to do is to plot the diff equation plus the isocline plus the arrows (stability) in a plot with varphi on the y-axis and u on the x-axis. The arrows below the 45 degree isocline should be pointing to the right and the arrows above the isocline to the left. I know how to plot the isocline restart; varphi_1:=B/a-B+B*u; B:=1: a:=0.3: varphi_1; plot(varphi_1,u=0..6,color=black,thickness=2, labels=["u", "varphi"]); but what code do I use so I get the arrows in the above plot ??

## again thanx for your...

again thanx for your input... maybe I have to revaluate my position.... It is just that sometimes in economics you just have one single diff and one single isocline. In such a case it would be useful to be able to plot the corresponding arrows on each side of the isocline.......anyway... thanx

## ok, thanx for your input.....

ok, thanx for your input.. It works (if you remove labels in display) but it is not perfect.. however I doubt it will get any better than this. I still thinks it is strange that I can’t plot a simple phase plane(one diff) in Maple

## thanks for your input but...

thanks for your input but can you be more specific ! Could you please give me some code that I can try. I have tried all kinds of combinations with deplots but I still cant get the result that I want which is a phase plot with k(dot) on the y-axis and k on the x-axis as I explained previously.. for example the code restart; dif1:= diff(k(t),t) = 0.7*k^0.3-0.13*k : with(DEtools): DEplot(dif1,[k(t)],t=-4..4, k=0..15,scene=[k(t),t] ); Does not give me the result I want.. I tried to change t in scene to k(dot) but that does not work

## I think I have solve it...

I think I have solve it myself ! I post the code so it can be useful for someone else... restart: randomize(): coin:=rand(0..1): coin_1:=proc(n) seq(coin(),i=1..n) end: x_1:=seq([coin_1(10)],i=1..5): x_2:=[seq(numboccur(1,x_1[i]),i=1..5)]: with(Statistics): Histogram(x_2,frequencyscale=relative,discrete = true ); Change the number 5 in the above code to 1000 and you will see the convergence from a binomial and random coin toss to a normal distribution

## again thanx for your...

again thanx for your imput.. The code that I use right now is: restart: coin:=rand(0..1): coin_1:=proc(n) seq(coin(),i=1..n) end: L:=[coin_1(1000)]: x_1:=remove(Testzero, map(nops, [ListTools:-Split(`=`,L, 1)])): # Sequence 0 x_2:=remove(Testzero, map(nops, [ListTools:-Split(`=`,L, 0)])): # sequence 1 x_11:=x_1*(-1): # Transform to a -1 and 1 coin toss y:=[op(x_11),op(x_2)]:# with(stats[statplots]): histogram(y,area = count, numbars = 12 ); Its not beautiful but... I will try your version to see if its better. I also found another code that can be used to illustrate the law of large numbers by changing 2500: restart; with(Statistics): data := Sample(RandomVariable(Normal(0, 1)),2500): n_1:=Histogram(data,frequencyscale=relative): with(stats):with(plots): with(stats[statplots]):n_2:=plot(statevalf[pdf,normald[0,1]],-4..4): display( {n_1,n_2} );

## thanx... I have no idea what...

thanx... I have no idea what the code mean but is seem to fulfil its purpose... I just have to figure out how I am going to plot it in a histogram.. humm
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