Description Usage Arguments Details Value Note Author(s) References See Also Examples

Kaplan- Meier Estimate of Mean and Standard Error of the Mean for Left Censored Data

1 | ```
kmms(dd, gam = 0.95)
``` |

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

`gam` |
one-sided confidence level |

The product limit estimate (PLE) of the cumulative distribution function
was first proposed by Kaplan and Meier (1958) for right censored data.
Turnbull (1976) provides a more general treatment of nonparametric
estimation of the distribution function for arbitrary censoring. For
randomly left censored data, the PLE is defined by Schmoyer et al.
(1996)–see `plend`

.

The mean of the PLE is a censoring-adjusted
point estimate of E(X) the mean of X. An approximate standard error
of the PLE mean can be obtained using the method of Kaplan and Meier
(1958), and the *100γ\%* UCL is *KM.mean + t(γ -1,
m-1) sp*, where `sp`

is the Kaplan-Meier standard error of the mean
adjusted by the factor *m/(m-1)*, where `m`

is the number of detects in the
sample. When there is no censoring this reduces to the second
approximate method described by Land (1972).

A LIST with components:

`KM.mean` |
Kaplan- Meier(KM) estimate of mean E(X) |

`KM.LCL ` |
KM estimate of lower confidence limit |

`KM.UCL ` |
KM estimate of upper confidence limit |

`KM.se ` |
estimate of standard error of KM-mean |

`gamma` |
one-sided confidence level |

Error in KM.se corrected on 12 June 2007. KM standard error is adjusted by multiplying by sqrt(m/(m-1)) where m is number of detected values. Error occurred if there were ties in detected values by calculating the number of unique detected values. For example, for beTWA sqrt(m/(m-1)) is 1.004796 . Due to error 1.008032 was used. The sqrt(m/(m-1)) will always be smaller after correction, depending on value of m and the number of ties. See the example.

E. L. Frome

Kaplan, E. L. and Meier, P. (1958), "Nonparametric Estimation from Incomplete Observations,"
*Journal of the American Statistical Association*, 457-481.

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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