### Sakai, H (1991)

#### Frequency distribution of first digit among population

Jinko mondai kenkyu. [Journal of population problems] 47(3), 74-78.

**ISSN/ISBN:** Not available at this time.
**DOI:** Not available at this time.

Note - this is a foreign language paper: JPN

**Abstract:** The law of gradual decrease in frequency distribution of 1st digit in population is applicable for checking accuracy of area-specific population distribution, age-specific population distribution and the like in developing nations. The law of gradual decrease in frequency distribution of 1st digit exists because the ratio of frequency expectancy of 1st digit is a ratio of time required for population change, provided its increase rate is constant, i.e., a certain population of 1000 will take time t with a constant annual increase rate of r to reach 2000. That means t = log (2000/1000)/log (l+r) Likewise, increases from 2000 to 3000 etc are calculated. Table 4 shows, from left to right, 1st digit numeral, population change, time required for the population change, and ratio of time required. If another population with a different increase rate which is constant grows, similar distribution of 1st digit numerals is expected. If demographic changes in the 2 populations are independent of each other, distribution expectancy of frequency of 1st digit numerals is the same for the combined populations also.log(2/1) = log(10/9)/(9/8)/(8/7)/(7/6)/(6/5) = log(10/9)+log(9/8)+log(8/7)+log(7/6)+log(6/5) All the following tables confirm the above theory. Table 1 shows frequency distribution of 1st, 2nd, and 3rd digit numerals for the world population in 1950, 1960 and 1970 as well as 1988. Table 3 shows frequency distribution of 1st digit for populations of Japan, prefectures and metropolitan Tokyo. Table 5 shows frequency distribution of 1st digit 100 years later in the population groups (1-1000) with a constant annual increase of 0% to 10%. Table 6 shows frequency distribution of 1st digit in the population (1-100,000) with a random annual increase of -50%-100%.

**Bibtex:**

```
@article{,
title={Frequency distribution of first digit among population},
author={Sakai, H},
journal={Jinko Mondai Kenkyu. Journal of Population Problems},
volume={47},
number={3},
pages={74--8},
year={1991}
}
```

**Reference Type:** Journal Article

**Subject Area(s):** Statistics