qq.lnorm(pl, mu, sigma, aveple = TRUE,...)TRUE, calculate plotting positions by averagingx mu, sigma, and Rsq The PLE is used to determine the plotting positions on the horizontal
axis for the censored data version of a theoretical q-q plot for the lognormal distribution. Waller and Turnbull (1992)
provide a good overview of q-q plots and other graphical methods for
censored data. The lognormal q-q plot is obtained by plotting
detected values $a[j]$(on log scale) versus $H[p(j)]$ where $H(p)$ is the
inverse of the distribution function of the standard normal
distribution. If the largest data value is not censored then the PLE
is 1 and H(1) is off scale. The "plotting positions" $p[j]$ are
determined from the PLE of F(x) by multiplying each estimate by
$n /(n+1)$, or by averaging adjacent values--see Meeker and Escobar
(1998, Chap 6)]. In complete data case without ties the first approach
is equivalent to replacing the sample CDF $j / n$ with $j / (n+1)$, and for
the second approach the plotting positions are equal to $(j - .5) / n$. If
the lognormal distribution is a close approximation to the empirical
distribution, the points on the plot will fall near a straight line.
An objective evaluation of this is obtained by calculating Rsq the
square of the correlation coefficient associated with the plot.
A line is added to the plot based on the values of mu and sigma.
If either of these is missing mu and sigma are estimated by
linear regression of $log(y)$ on $H[p(j)]$.
Fay, M. P. (1999), "Comparing Several Score Tests for Interval Censored Data," Statistics in Medicine, 1999; 18:273-85. (Corr: 1999, Vol 19, p.2681).
Frome, E. L. and Wambach, P. F. (2005), "Statistical Methods and Software for the Analysis of Occupational Exposure Data with Non-Detectable Values," ORNL/TM-2005/52,Oak Ridge National Laboratory, Oak Ridge, TN 37830. Available at: http://www.csm.ornl.gov/esh/aoed/ORNLTM2005-52.pdf
Hesel, D. R. and T. A. Cohn (1988), "Estimation of Descriptive Statistics for Multiply Censored Water Quality Data," Water Resources Research, 24, 1997-2004. Meeker, W. Q. and L. A. Escobar (1998), Statistical Methods for Reliability Data, John Wiley and Sons, New York.
Ny, M. P. (2002), "A Modification of Peto's Nonparametric Estimation of Survival Curves for Interval-Censored Data," Biometrics, 58, 439-442.
Waller, L. A. and B. W. Turnbull (1992), "Probability Plotting with Censored Data," The American Statistician, 46(1), 5-12.
plekm, plend, pleicf data(SESdata) # use SESdata data set Example 1 from ORNLTM-2005/52
pnd<- plend(SESdata)
qq.lnorm(pnd) # lognormal q-q plot based on PLE
Ia <- "Q-Q plot For SESdata "
qqout <- qq.lnorm(pnd,main=Ia) # lognormal q-q plot based on PLE
qqout
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