Fitting the Poisson to frequency data

Obs y obsfreq yexp yobs
1 0 24 -0.1 0.1
2 1 16 0.9 1.1
3 2 16 1.9 2.1
4 3 18 2.9 3.1
5 4 15 3.9 4.1
6 5 9 4.9 5.1
7 6 6 5.9 6.1
8 7 5 6.9 7.1
9 8 3 7.9 8.1
10 9 4 8.9 9.1
11 10 3 9.9 10.1
12 11 0 10.9 11.1
13 12 1 11.9 12.1

Fitting the Poisson to frequency data

The UNIVARIATE Procedure

Variable: y

 

Freq: obsfreq

Moments
N 120 Sum Weights 120
Mean 3.16666667 Sum Observations 380
Std Deviation 2.78752724 Variance 7.77030812
Skewness 0.91183392 Kurtosis 0.32893349
Uncorrected SS 2128 Corrected SS 924.666667
Coeff Variation 88.0271761 Std Error Mean 0.25446526
Basic Statistical Measures
Location Variability
Mean 3.166667 Std Deviation 2.78753
Median 3.000000 Variance 7.77031
Mode 0.000000 Range 12.00000
    Interquartile Range 4.00000
Tests for Location: Mu0=0
Test Statistic p Value
Student's t t 12.4444 Pr > |t| <.0001
Sign M 48 Pr >= |M| <.0001
Signed Rank S 2328 Pr >= |S| <.0001
Quantiles (Definition 5)
Level Quantile
100% Max 12
99% 10
95% 9
90% 7
75% Q3 5
50% Median 3
25% Q1 1
10% 0
5% 0
1% 0
0% Min 0
Extreme Observations
Lowest Highest
Value Freq Obs Value Freq Obs
0 24 1 7 5 8
1 16 2 8 3 9
2 16 3 9 4 10
3 18 4 10 3 11
4 15 5 12 1 13

Fitting the Poisson to frequency data

The UNIVARIATE Procedure

Fitting the Poisson to frequency data; Histogram for y 0.0 1.5 3.0 4.5 6.0 7.5 9.0 10.5 12.0 y 0 10 20 30 40 Count Distribution of y

Fitting the Poisson to frequency data

Obs n ybar var
1 120 3.16667 7.77031

Fitting the Poisson to frequency data

Obs n ybar var y obsfreq yexp yobs poisprob expfreq
1 120 3.16667 7.77031 0 24 -0.1 0.1 0.04214 5.0573
2 120 3.16667 7.77031 1 16 0.9 1.1 0.13346 16.0147
3 120 3.16667 7.77031 2 16 1.9 2.1 0.21130 25.3565
4 120 3.16667 7.77031 3 18 2.9 3.1 0.22304 26.7652
5 120 3.16667 7.77031 4 15 3.9 4.1 0.17658 21.1892
6 120 3.16667 7.77031 5 9 4.9 5.1 0.11183 13.4198
7 120 3.16667 7.77031 6 6 5.9 6.1 0.05902 7.0827
8 120 3.16667 7.77031 7 5 6.9 7.1 0.02670 3.2041
9 120 3.16667 7.77031 8 3 7.9 8.1 0.01057 1.2683
10 120 3.16667 7.77031 9 4 8.9 9.1 0.00372 0.4462
11 120 3.16667 7.77031 10 3 9.9 10.1 0.00118 0.1413
12 120 3.16667 7.77031 11 0 10.9 11.1 0.00034 0.0407
13 120 3.16667 7.77031 12 1 11.9 12.1 0.00009 0.0107
Fitting the Poisson to frequency data; Plot of expfreq by yexp expfreq 0 10 20 30 yexp -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Fitting the Poisson to frequency data PLOT expfreq obsfreq