Bringing Closure to the Plotting Position Controversy

  title={Bringing Closure to the Plotting Position Controversy},
  author={Lasse Makkonen},
  journal={Communications in Statistics - Theory and Methods},
  pages={460 - 467}
  • L. Makkonen
  • Published 30 January 2008
  • Business
  • Communications in Statistics - Theory and Methods
In this article, it is explicitly demonstrated that the probability of non exceedance of the mth value in n order ranked events equals m/(n + 1). Consequently, the plotting position in the extreme value analysis should be considered not as an estimate, but to be equal to m/(n + 1), regardless of the parent distribution and the application. The many other suggested plotting formulas and numerical methods to determine them should thus be abandoned. The article is intended to mark the end of the… 

A Note on the Plotting Position Controversy and a New Distribution-free Formula

The recent work “Bringing closure to the plotting position controversy” (Makkonen, 2008a) states the impossibility of a different solution from the classical plotting position proposed by Weibull

An objective look at obtaining the plotting positions for QQ-plots

ABSTRACT Choosing the plotting positions for the QQ-plot has been a subject of much debate in the statistical and engineering literature. This paper looks at this problem objectively by considering

Discussion on “Plotting positions for fitting distributions and extreme value analysis”

Plotting positions are used in the extreme value analysis for many engineering applications. The authors of the discussed paper concluded based on their simulations that distribution dependent

Plotting positions close to the exact unbiased solution: application to the Pozzuoli's bradeysism earthquake data

Graphical techniques are recommended for critical applications in order to share information with non-statisticians, since they allow for a visual analysis and helpful understanding of the results.

New Distribution-Free Plotting Position Through an Approximation to the Beta Median

Even in the modern software, graphical techniques are often utilized to visualize the data and to determine the actual underlying distribution. In this chapter, a new and better distribution-free

Plotting positions for fitting distributions and extreme value analysis

Random data are often examined on plotting paper to determine appropriate probability distributions and distribution parameters for extreme-value analyses and other applications. Engineers are not

Flood frequency analysis – Part 2: Development of a modified plotting position

The original plotting position concept was suggested more than a century ago. Since then, many alternative plotting position approaches have been developed. Despite a general lack of agreement around

An improved method of extreme value analysis




On the Choice of Plotting Positions on Probability Paper

Abstract This article is an attempt to throw more light on the problem of choosing plotting positions for the frequencies related to ordered sample values. The problem is particularly pertinent where

Plotting positions via maximum-likelihood for a non-standard situation

Abstract. A new approach is developed for the specification of the plotting positions used in the frequency analysis of extreme flows, rainfalls or similar data. The approach is based on the concept

A plotting rule for extreme probability paper

A primary purpose in plotting a set of ordered observations on probability paper is to simplify the inspection of their distribution. With this limited objective a plotting rule for the ith of n

A new unbiased plotting position formula for Gumbel distribution

Abstract. The probability plots (graphical approach) are used to fit the probability distribution to given series, to identify the outliers and to assess goodness of fit. The graphical approach

The plotting of observations on probability-paper

The plotting of observations on probability paper. The mathematical foundation of probability paper for a variate with a cumulative distribution function F (α x + β) is explained as well as its

Another look at plotting positions

Probability paper was used as early as 1896, and was mentioned in the literature more than 30 times before 1950, mainly by hydrologists, most of whom used the plotting position (i-0.5)/n proposed by

Probability Plotting Methods and Order Statistics

SUMMARY Graphical methods of assessing the validity of a probability model, and of estimating location and scale parameters, have been widely applied over many years. A variety of different

A Geometric Determination of the Median Value of a System of Normal Variants, from two of its Centiles

A SHORT account appeared in NATURE, October 12, p. 584, of a paper read by me at the British Association, entitled the “Median Estimate,” which will appear in the forthcoming Journal of the