Data-adaptive Probability Plot and its Applications

In the statistical data analysis process, data investigation plays a most basic and important role. Its importance is emphasized and illustrated as the initial examination (Cox & Snell, 1981; Chatfield, 1985, 1991; Goto, 1986). In each step of data investigation, graphics is highlighted as one of the leading tools. However, in general, data investigation not only includes statistical graphics, but also formal analytical techniques. In the paper, we tried to conduct the data investigation based solely on the statistical graphical techniques. Then, as an elementary tool of graphical diagnosis, we proposed the data-adaptive probability plot. Moreover, we constructed a guardrail on the data-adaptive probability plot for inferential interpretation of the result of the plot. Furthermore, some useful aspects of the data-adaptive probability plot were assessed in several practical examples. As a consequence, we can say that the data-adaptive probability plot is a more flexible and interpretable tool than ordinary probability plots.

[1]  C. Daniel.  Use of Half-Normal Plots in Interpreting Factorial Two-Level Experiments , 1959 .

[2]  Chris Chatfield,et al.  The Initial Examination of Data , 1985 .

[3]  R. Gnanadesikan,et al.  A Probability Plotting Procedure for General Analysis of Variance , 1970 .

[4]  P. Bickel,et al.  An Analysis of Transformations Revisited , 1981 .

[5]  R. Gnanadesikan,et al.  Probability plotting methods for the analysis of data. , 1968, Biometrika.

[6]  W. Meredith,et al.  Statistics and Data Analysis , 1974 .

[7]  J. R. Michael.  The stabilized probability plot , 1983 .

[8]  Jeffrey S. Simonoff,et al.  A Casebook for a First Course in Statistics and Data Analysis. , 1995 .

[9]  V. Barnett.  Probability Plotting Methods and Order Statistics , 1975 .

[10]  R. Prentice,et al.  A generalization of the probit and logit methods for dose response curves. , 1976, Biometrics.

[11]  W. D. Stirling,et al.  Understanding data : principles and practice of statistics , 1998 .

[12]  Kjell A. Doksum,et al.  Empirical Probability Plots and Statistical Inference for Nonlinear Models in the Two-Sample Case , 1974 .

[13]  E. Aly,et al.  Quantile-Quantile plots under random censorship , 1986 .

[14]  Masashi Goto,et al.  SOME PROPERTIES OF POWER NORMAL DISTRIBUTION , 1980 .

[15]  R. Gnanadesikan,et al.  Estimation of parameters of the gamma distribution using order statistics , 1962 .

[16]  Masashi Goto,et al.  Graphical comparisons of multivariate data , 1987 .

[17]  M. Goto.  Power-normal distribution and its applications , 1983 .

[18]  Brian Everitt,et al.  Graphical Techniques for Multivariate Data. , 1979 .

[19]  Jiajuan Liang,et al.  A t -distribution plot to detect non-multinormality , 1999 .

[20]  R. Prentice.  A LOG GAMMA MODEL AND ITS MAXIMUM LIKELIHOOD ESTIMATION , 1974 .

[21]  Masashi Goto,et al.  STATISTICAL GRAPHICS: A CLASSIFIED AND SELECTED BIBLIOGRAPHY , 1991 .

[22]  David R. Cox,et al.  Some Remarks on the Role in Statistics of Graphical Methods , 1978 .

[23]  E. Holmgren,et al.  The P-P Plot as a Method for Comparing Treatment Effects , 1995 .

[24]  David R. Cox.  A note on the graphical analysis of survival data , 1979 .

[25]  A. C. Atkinson,et al.  Two graphical displays for outlying and influential observations in regression , 1981 .

[26]  Jan Beirlant,et al.  Goodness-of-fit analysis for multivariate normality based on generalized quantiles , 1999 .

[27]  R. McCulloch,et al.  A Multivariate Generalization of Quantile-Quantile Plots , 1990 .

[28]  M. Gerson.  The Techniques and Uses of Probability Plotting , 1975 .

[29]  Chris Chatfield,et al.  Avoiding Statistical Pitfalls , 1991 .