Compute Product Limit Estimate (PLE) of F(x) and Confidence Limits for data with non-detects (left censored data).

1 | ```
plekm(dd,gam)
``` |

`dd` |
An n by 2 matrix or data frame with |

`gam` |
one-sided confidence level |

R function `survreg`

is used to calculate Kaplan-Meier estimate
of S(z), where z = k - x and k is greater than the largest x value.
This technique of "reversing the data" to convert left censored data
to right censored data was first suggested by Nelson (1972). conf.type
= "plain" is required in survreg for correct CLs. The value of S(z)
is then used to calculate F(x). Note that if *γ* = 0.95 the 90%
two-sided CLs are calculated.

Data frame with columns

`a` |
is the value of j |

`ple` |
is PLE of F(x) at |

`stder` |
standard error of F(x) at |

`lower` |
lower CL for PLE at |

`upper` |
upper CL for PLE at |

`n` |
number of detects or non-detects |

`d` |
number of detects equal to |

In survival analysis S(x) = 1 - F(x) is the survival function i.e., S(x) = P [X > x]. In environmental and occupational situations S(x) is the "exceedance" function, i.e., S(x) = is the proportion of X values that exceed x. The PLE is the sample estimate of F(x), i.e., the proportion of values in the sample that are less than x.

E. L. Frome

Nelson, W.(1972), "Theory and Application of Hazard Plotting for
Censored Failure Data", *Technometrics*, 14, 945-66

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

Schmoyer, R. L., J. J. Beauchamp, C. C. Brandt and F. O. Hoffman, Jr.
(1996), "Difficulties with the Lognormal Model in Mean Estimation and
Testing," *Environmental and Ecological Statistics*, 3, 81-97.

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