Plotting positions are an essential tool in statistical analysis, allowing us to visualize the distribution of a dataset. One such formula is Filliben's (1975), which provides an estimate of the medians of U(k). In this article, we will delve into the history and application of Filliben's plotting position.

History

Filliben's formula was first introduced by John J. Filliben in his 1975 paper "The Probability Plot Correlation Coefficient Test for Normality" (Filliben, 1975). This expression is an alternative to other popular plotting positions, such as Blom's (1958) and Irving I. Gringorten's (1963).

Formula

The formula for Filliben's plotting position is given by:

U(k) = k / (n+1)

where k is the rank of the observation, n is the sample size, and U(k) is the plotting position.

Applications

Filliben's plotting position has been widely used in various fields, including statistics, engineering, and quality control. For instance, it was employed by Irving I. Gringorten (1963) to plot points in tests for the Gumbel distribution. Additionally, it was used by Filliben himself (1975) as a test for normality.

Comparison with Other Plotting Positions

Filliben's plotting position is not the only formula used in probability plotting. Other popular formulas include Blom's (1958) and Irving I. Gringorten's (1963). While these formulas have their own strengths and weaknesses, Filliben's formula has been shown to be particularly effective in certain situations.

##, Filliben's plotting position is a valuable tool for statistical analysis, providing an estimate of the medians of U(k). Its history dates back to 1975, when it was first introduced by John J. Filliben. The formula has been widely used in various fields and has been shown to be particularly effective in certain situations.

References

Benard, A.; Bos-Levenbach, E. C. (September 1953). "The plotting of observations on probability paper". Statistica Neerlandica (in Dutch). 7: 163–173. doi:10.1111/j.1467-9574.1953.tb00821.x.

Blom, G. (1958), Statistical estimates and transformed beta variables, New York: John Wiley and Sons

Cleveland, W.S. (1994) The Elements of Graphing Data, Hobart Press ISBN 0-9634884-1-4

Filliben, J. J. (February 1975), "The Probability Plot Correlation Coefficient Test for Normality", Technometrics, 17 (1), American Society for Quality: 111–117, doi:10.2307/1268008, JSTOR 1268008.

Gibbons, Jean Dickinson; Chakraborti, Subhabrata (2003), Nonparametric statistical inference (4th ed.), CRC Press, ISBN 978-0-8247-4052-8

Gnanadesikan, R. (1977). Methods for Statistical Analysis of Multivariate Observations. Wiley. ISBN 0-471-30845-5.

Gringorten, Irving I. (1963). "A plotting rule for extreme probability paper". Journal of Geophysical Research. 68 (3): 813–814. Bibcode:1963JGR….68..813G. doi:10.1029/JZ068i003p00813. ISSN 2156-2202.

Hazen, Allen (1914), "Storage to be provided in the impounding reservoirs for municipal water supply", Transactions of the American Society of Civil Engineers (77): 1547–1550

Madsen, H.O.; et al. (1986), Methods of Structural Safety

Makkonen, L. (2008), "Bringing closure to the plotting position controversy", Communications in Statistics – Theory and Methods, 37 (3): 460–467, doi:10.1080/03610920701653094, S2CID 122822135

Thode, Henry C. (2002), Testing for normality, New York: Marcel Dekker, ISBN 0-8247-9613-6