;--------------------------------------------------
;STATISTICAL METHODS IN ASTRONOMY
; EXERCISES I
; 21.02.2008 Heikki Salo
; exercise1_bino1.pro
;--------------------------------------------------

 program='exercise1_poisson1'
 ps=0
 psdirect,program,ps

;-------------------------------------------------
;Poisson distribution
;
;              mu^V 
; prob(V) =    -----  exp(-mu)   V=0,1,2,3,...
;               V! 
;-------------------------------------------------

;Draw with in the case mu=1.69 and mu=11.48
;(corresponds to plots in page 31, except that the curves
;should be multiplied by the number of samples (100 and 60)

;make also a 10 finer grid


!p.multi=[0,2,1]

;----------------------------------------------------------
mu=1.69
vtab=findgen(10)
ptab=vtab
for v=0,n_elements(vtab)-1 do begin
ptab(v)=mu^v/exp(lngamma(v+1))*exp(-mu)
endfor
nwin
plot,vtab,ptab,title='Poisson with mu='+string(mu),psym=6,syms=0.5


vtab=findgen(100)*.1
ptab=vtab
for i=0,n_elements(vtab)-1 do begin
v=vtab(i)
ptab(i)=mu^v/exp(lngamma(v+1))*exp(-mu)
endfor
oplot,vtab,ptab


;----------------------------------------------------------
mu=11.48
vtab=findgen(23)
ptab=vtab
for v=0,n_elements(vtab)-1 do begin
ptab(v)=mu^v/exp(lngamma(v+1))*exp(-mu)
endfor

plot,vtab,ptab,title='Poisson with mu='+string(mu),psym=6,syms=0.5


vtab=findgen(230)*.1
ptab=vtab
for i=0,n_elements(vtab)-1 do begin
v=vtab(i)
ptab(i)=mu^v/exp(lngamma(v+1))*exp(-mu)
endfor

oplot,vtab,ptab
 psdirect,program,ps,/stop
end