Fitting the Poisson to frequency data

Obs y obsfreq yexp yobs
1 0 6 -0.1 0.1
2 1 15 0.9 1.1
3 2 17 1.9 2.1
4 3 29 2.9 3.1
5 4 20 3.9 4.1
6 5 6 4.9 5.1
7 6 5 5.9 6.1
8 7 1 6.9 7.1
9 8 1 7.9 8.1
10 9 0 8.9 9.1
11 10 0 9.9 10.1

Fitting the Poisson to frequency data

The UNIVARIATE Procedure

Variable: y

 

Freq: obsfreq

Moments
N 100 Sum Weights 100
Mean 2.91 Sum Observations 291
Std Deviation 1.62116681 Variance 2.62818182
Skewness 0.39509921 Kurtosis 0.31136421
Uncorrected SS 1107 Corrected SS 260.19
Coeff Variation 55.7101996 Std Error Mean 0.16211668
Basic Statistical Measures
Location Variability
Mean 2.910000 Std Deviation 1.62117
Median 3.000000 Variance 2.62818
Mode 3.000000 Range 8.00000
    Interquartile Range 2.00000
Tests for Location: Mu0=0
Test Statistic p Value
Student's t t 17.95003 Pr > |t| <.0001
Sign M 47 Pr >= |M| <.0001
Signed Rank S 2232.5 Pr >= |S| <.0001
Quantiles (Definition 5)
Level Quantile
100% Max 8.0
99% 7.5
95% 6.0
90% 5.0
75% Q3 4.0
50% Median 3.0
25% Q1 2.0
10% 1.0
5% 0.0
1% 0.0
0% Min 0.0
Extreme Observations
Lowest Highest
Value Freq Obs Value Freq Obs
0 6 1 4 20 5
1 15 2 5 6 6
2 17 3 6 5 7
3 29 4 7 1 8
4 20 5 8 1 9

Fitting the Poisson to frequency data

The UNIVARIATE Procedure

Fitting the Poisson to frequency data; Histogram for y 0.6 1.8 3.0 4.2 5.4 6.6 7.8 y 0 5 10 15 20 25 30 Count Distribution of y

Fitting the Poisson to frequency data

Obs n ybar var
1 100 2.91 2.62818

Fitting the Poisson to frequency data

Obs n ybar var y obsfreq yexp yobs poisprob expfreq
1 100 2.91 2.62818 0 6 -0.1 0.1 0.05448 5.4476
2 100 2.91 2.62818 1 15 0.9 1.1 0.15852 15.8524
3 100 2.91 2.62818 2 17 1.9 2.1 0.23065 23.0653
4 100 2.91 2.62818 3 29 2.9 3.1 0.22373 22.3733
5 100 2.91 2.62818 4 20 3.9 4.1 0.16277 16.2766
6 100 2.91 2.62818 5 6 4.9 5.1 0.09473 9.4730
7 100 2.91 2.62818 6 5 5.9 6.1 0.04594 4.5944
8 100 2.91 2.62818 7 1 6.9 7.1 0.01910 1.9100
9 100 2.91 2.62818 8 1 7.9 8.1 0.00695 0.6947
10 100 2.91 2.62818 9 0 8.9 9.1 0.00225 0.2246
11 100 2.91 2.62818 10 0 9.9 10.1 0.00065 0.0654

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 Fitting the Poisson to frequency data PLOT expfreq obsfreq