/*************basic Poisson calculations****************/

/*******Calculate p(x) for x=0,1,...,10 when lambda=2********/

data poi_cal;
do x=0 to 10 by 1;
pihat=PDF("poisson",x,2);   *PDF("poisson",,)is the Poisson probability function or "density" ;
keep x pihat;
output;
end;
run;

proc print;run;


/************plot Poisson distribution with lambda=2**************/



proc sgplot data=poi_cal;
needle x=x y=pihat / baseline=0;
title "Poisson Distribution (lambda=2)";
run;

title;



/*********Calculate the cumulative probability of Poisson distribution********/

data poi_cal_c;
a=CDF("poisson",6,2);   *CDF("poisson",,)is the cumulative distribution function, P(X <= x);
aa=SUM(PDF("poisson",0,2),PDF("poisson",1,2),PDF("poisson",2,2),PDF("poisson",3,2),
           PDF("poisson",4,2),PDF("poisson",5,2),PDF("poisson",6,2));
            *Instead of using CDF(), you could have added the probabilities;

aaa=1-CDF("poisson",6,2);  *Find P(Y>6) when lambda=2;
run;

proc print;run;

/******** Make a table of the first 11 Poisson probabilities and cumulative probabilities when lambda=2***********/

data poi_cal_all;
do x=0 to 10 by 1;
pihat=round(PDF("poisson",x,2),0.001);
cumlp=round(CDF("poisson",x,2),0.001);
keep x pihat cumlp;
output;
end;
run;

proc print;run;