Cumulative Poisson Distribution Table
A cumulative poisson distribution is used to calculate the probability of getting atleast n successes in a poisson experiment. The below given table shows cumulative probability functions of Poisson Distribution with various α values. Each columns corresponds to various values for the mean (λ) of a Poisson variable. The table below gives the probability of a Poisson random variable X with mean = λ which is less than or equal to x. For example, a Poisson variable of mean 0.7 is 1 or less with probability 0.844.
x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 0.905 0.819 0.741 0.670 0.607 0.549 0.497 0.449 0.407 0.368 1 0.995 0.982 0.963 0.938 0.910 0.878 0.844 0.809 0.772 0.736 2 1.000 0.999 0.996 0.992 0.986 0.977 0.966 0.953 0.937 0.920 3 1.000 1.000 1.000 0.999 0.998 0.997 0.994 0.991 0.987 0.981 4 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.999 0.998 0.996 5 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 6 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
x 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 0 0.333 0.301 0.273 0.247 0.223 0.202 0.183 0.165 0.150 0.135 1 0.699 0.663 0.627 0.592 0.558 0.525 0.493 0.463 0.434 0.406 2 0.900 0.879 0.857 0.833 0.809 0.783 0.757 0.731 0.704 0.677 3 0.974 0.966 0.957 0.946 0.934 0.921 0.907 0.891 0.875 0.857 4 0.995 0.992 0.989 0.986 0.981 0.976 0.970 0.964 0.956 0.947 5 0.999 0.998 0.998 0.997 0.996 0.994 0.992 0.990 0.987 0.983 6 1.000 1.000 1.000 0.999 0.999 0.999 0.998 0.997 0.997 0.995 7 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.999 0.999 8 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
x 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 0 0.111 0.091 0.074 0.061 0.050 0.041 0.033 0.027 0.022 0.018 1 0.355 0.308 0.267 0.231 0.199 0.171 0.147 0.126 0.107 0.092 2 0.623 0.570 0.518 0.469 0.423 0.380 0.340 0.303 0.269 0.238 3 0.819 0.779 0.736 0.692 0.647 0.603 0.558 0.515 0.473 0.433 4 0.928 0.904 0.877 0.848 0.815 0.781 0.744 0.706 0.668 0.629 5 0.975 0.964 0.951 0.935 0.916 0.895 0.871 0.844 0.816 0.785 6 0.993 0.988 0.983 0.976 0.966 0.955 0.942 0.927 0.909 0.889 7 0.998 0.997 0.995 0.992 0.988 0.983 0.977 0.969 0.960 0.949 8 1.000 0.999 0.999 0.998 0.996 0.994 0.992 0.988 0.984 0.979 9 1.000 1.000 1.000 0.999 0.999 0.998 0.997 0.996 0.994 0.992 10 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.999 0.998 0.997 11 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.999 12 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
x 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0 0 0.015 0.012 0.010 0.008 0.007 0.006 0.005 0.004 0.003 0.002 1 0.078 0.066 0.056 0.048 0.040 0.034 0.029 0.024 0.021 0.017 2 0.210 0.185 0.163 0.143 0.125 0.109 0.095 0.082 0.072 0.062 3 0.395 0.359 0.326 0.294 0.265 0.238 0.213 0.191 0.170 0.151 4 0.590 0.551 0.513 0.476 0.440 0.406 0.373 0.342 0.313 0.285 5 0.753 0.720 0.686 0.651 0.616 0.581 0.546 0.512 0.478 0.446 6 0.867 0.844 0.818 0.791 0.762 0.732 0.702 0.670 0.638 0.606 7 0.936 0.921 0.905 0.887 0.867 0.845 0.822 0.797 0.771 0.744 8 0.972 0.964 0.955 0.944 0.932 0.918 0.903 0.886 0.867 0.847 9 0.989 0.985 0.980 0.975 0.968 0.960 0.951 0.941 0.929 0.916 10 0.996 0.994 0.992 0.990 0.986 0.982 0.977 0.972 0.965 0.957 11 0.999 0.998 0.997 0.996 0.995 0.993 0.990 0.988 0.984 0.980 12 1.000 0.999 0.999 0.999 0.998 0.997 0.996 0.995 0.993 0.991 13 1.000 1.000 1.000 1.000 0.999 0.999 0.999 0.998 0.997 0.996 14 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.999 0.999 15 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 16 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
x 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 0 0.002 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1 0.011 0.007 0.005 0.003 0.002 0.001 0.001 0.000 0.000 0.000 2 0.043 0.030 0.020 0.014 0.009 0.006 0.004 0.003 0.002 0.001 3 0.112 0.082 0.059 0.042 0.030 0.021 0.015 0.010 0.007 0.005 4 0.224 0.173 0.132 0.100 0.074 0.055 0.040 0.029 0.021 0.015 5 0.369 0.301 0.241 0.191 0.150 0.116 0.089 0.067 0.050 0.038 6 0.527 0.450 0.378 0.313 0.256 0.207 0.165 0.130 0.102 0.079 7 0.673 0.599 0.525 0.453 0.386 0.324 0.269 0.220 0.179 0.143 8 0.792 0.729 0.662 0.593 0.523 0.456 0.392 0.333 0.279 0.232 9 0.877 0.830 0.776 0.717 0.653 0.587 0.522 0.458 0.397 0.341 10 0.933 0.901 0.862 0.816 0.763 0.706 0.645 0.583 0.521 0.460 11 0.966 0.947 0.921 0.888 0.849 0.803 0.752 0.697 0.639 0.579 12 0.984 0.973 0.957 0.936 0.909 0.876 0.836 0.792 0.742 0.689 13 0.993 0.987 0.978 0.966 0.949 0.926 0.898 0.864 0.825 0.781 14 0.997 0.994 0.990 0.983 0.973 0.959 0.940 0.917 0.888 0.854 15 0.999 0.998 0.995 0.992 0.986 0.978 0.967 0.951 0.932 0.907 16 1.000 0.999 0.998 0.996 0.993 0.989 0.982 0.973 0.960 0.944 17 1.000 1.000 0.999 0.998 0.997 0.995 0.991 0.986 0.978 0.968 18 1.000 1.000 1.000 0.999 0.999 0.998 0.996 0.993 0.988 0.982 19 1.000 1.000 1.000 1.000 0.999 0.999 0.998 0.997 0.994 0.991 20 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.998 0.997 0.995 21 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.999 0.998 22 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.999 23 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
