Solving a summation for unknown limits of integration

How can I sum the Poisson CDF of x/15 and solve for the limits of summation:

solve(symsum(poisscdf(x,90/52)/15,x,r,r+14)>.98) I want to solve the sum and find the level r that makes that inequality true.

[Walter Roberson]

Although you can convert the summation to a definite formula,

((1/15)*GAMMA(1+r, 45/26)*(8+r)*(7+r)*(6+r)*(5+r)*(4+r)*(3+r)*(2+r)*(1+r)+(1/15)*GAMMA(2+r, 45/26)*(8+r)*(7+r)*(6+r)*(5+r)*(4+r)*(3+r)*(2+r)+(1/15)*GAMMA(3+r, 45/26)*(8+r)*(7+r)*(6+r)*(5+r)*(4+r)*(3+r)+(1/15)*GAMMA(4+r, 45/26)*(8+r)*(7+r)*(6+r)*(5+r)*(4+r)+(1/15)*GAMMA(5+r, 45/26)*(8+r)*(7+r)*(6+r)*(5+r)+(1/15)*GAMMA(6+r, 45/26)*(8+r)*(7+r)*(6+r)+(1/15)*GAMMA(7+r, 45/26)*(8+r)*(7+r)+(8/15+(1/15)*r)*GAMMA(8+r, 45/26)+(1/15)*GAMMA(9+r, 45/26)+(1/15)*GAMMA(10+r, 45/26)/(9+r)+(1/15)*GAMMA(11+r, 45/26)/((9+r)*(10+r))+(1/15)*GAMMA(12+r, 45/26)/((9+r)*(10+r)*(11+r))+(1/15)*GAMMA(13+r, 45/26)/((9+r)*(10+r)*(11+r)*(12+r))+(1/15)*GAMMA(r+14, 45/26)/((9+r)*(10+r)*(11+r)*(12+r)*(13+r))+(1/15)*GAMMA(15+r, 45/26)/((9+r)*(10+r)*(11+r)*(12+r)*(13+r)*(r+14)))/GAMMA(9+r)

solving this for any particular value will have to be done numerically.

Answer 1

[Roger Stafford]

There will be infinitely many levels r that make your inequality true. I believe you really want to find the first such level.

   r = 0;
   while true
     if sum(poisscdf(r:r+14,90/52)/15) > .98, break, end
     r = r+1;
   end

The value of r will be the first to satisfy the inequality.

[Shane Kosir]

I think this is correct. However when I tried it no result came back

[Walter Roberson]

disp(r)