International Journal of Mathematics and Mathematical Sciences / 2009 / Article / Tab 2

Research Article

Generalizing Benford's Law Using Power Laws: Application to Integer Sequences

Table 2

Minimum chi-square estimators.

Name of sequence Sample size TSPB PB

ParameterParameters
calphabetam

Square1000.7983715.559571.74552100
Cube5002.465195.558491.69860100
Cube10002.2679820.565061.47082100
Cube100002.2705420.535771.475760100
Square root991.40176894917231.34334100
Prime < 100252.6858123.139522.14449100
Prime < 10001682.9521622.997542.28436100
Prime < 1000012293.0354229.767292.30760100
Princeton number252.761706.945952.36119100
Mixing sequence6182.539584.786411.83119100
Pentagonal number1002.948472.067973.31268100
Keith number712.733382.161072.637201000
Bell number 1001.0819110.148201.24828100
Catalan number 1001.135220.670951.153775000
Lucky number453.157217.569620.94576100
Ulam number443.553759.994450.81215100
Numeri ideoni 651.124101297612.160.98591100
Fibonacci number 1002.05365257000.421.00560100
Partition number 941.232680.656511.714091000