Méthode de simulation

> lambda:= 3; mu:=4;

lambda := 3

mu := 4

densité

> plot(a(t), t=0..4); pl1:= %:

[Maple Plot]

Pr(t <= T)

> Int('a(t)', t=0..T); tmp:= value(%); plot(%, T=0..3);

Int(a(t),t = 0 .. T)

tmp := -exp(-3*T)+1

[Maple Plot]

On a distrib uniforme
et on veut une distrib exponentielle

> 'ra()'$10;

.3856872716, .5729886111, .7942317252, .3337767812,...
.3856872716, .5729886111, .7942317252, .3337767812,...

> z= tmp; solve(%, T); subs(z=1-y, %);
g:= unapply(%,y);

z = -exp(-3*T)+1

-1/3*ln(-z+1)

-1/3*ln(y)

g := proc (y) options operator, arrow; -1/3*ln(y) e...

> 'g(ra())'$10;

.5510416787, .4480123730, .5876481830e-2, .13419096...
.5510416787, .4480123730, .5876481830e-2, .13419096...

> ga:= eval(g)@ra;

ga := `@`(proc (y) options operator, arrow; -1/3*ln...

> subs(-1/lambda=-1/mu, eval(g)): gb:= % @ra;

gb := `@`(proc (y) options operator, arrow; -1/4*ln...