You are here: Home :: Area CULI :: Linguistics and literature

Hussien, Osama A.

The Lerchianness plot

Hoaglin (1980) introduced the Poissonness plot to detect departures of data from a hypothesized Poisson model. Hoaglin and Tukey (1985) extended the use of the Poissonness plot to other one parameter discrete distributions include geometric and logarithmic distributions. On the other hand, in many applications the Zipf plot is used to verify that the data obeys the Zipf's law. We present a unified presentation of these plots and extend its use for 3-parameter families. In particular, the Lerch family of discrete distributions, which includes as special cases the Zipf, Zipf-Mandelbrot, the logarithmic and the polylogarithmic distributions. A comparison with other types of plots for discrete distributions shows the resistance and power of this plot, the Lerchianness plot. We apply this plot to some of the Hoaglin and Tukey data sets and show it gives better fits. In addition, an application to subject and letter frequencies and to Egyptian city sizes has been presented.

Glottometrics, RAM-Verlag

Volume: 7, 03/2004
Pages: 50-64

Show full article (external site)

Show all available items of this journal

 

Area CULI