# Gives the Integrated Empirical Distribution Function

### Description

Like `intECDF`

, except returns a function
*\bar I* instead of a value. The function *\bar I(l,r)* is given
by

*\bar{I}(l,r) = \int_{l}^{r} \bar{F}(u) du*

where *\bar F* is the empirical distribution function of
*x_1,…,x_m*. Note that *l* and *r* must lie in
*[x_1,x_m]*.

For an exact formula related to *\bar{I}*, see `intECDF`

.

### Usage

1 | ```
intECDFfn(x)
``` |

### Arguments

`x` |
Vector |

### Value

The function *\bar I*.

### References

Duembgen, L, Huesler, A. and Rufibach, K. (2010) Active set and EM algorithms for log-concave densities based on complete and censored data. Technical report 61, IMSV, Univ. of Bern, available at http://arxiv.org/abs/0707.4643.

Duembgen, L. and Rufibach, K. (2009) Maximum likelihood estimation
of a log-concave density and its distribution function: basic
properties and uniform consistency. *Bernoulli*,
**15(1)**, 40–68.

Duembgen, L. and Rufibach, K. (2011) logcondens: Computations
Related to Univariate Log-Concave Density Estimation.
*Journal of Statistical Software*, **39(6)**,
1–28. http://www.jstatsoft.org/v39/i06

Doss, C. R. (2013). Shape-Constrained Inference for Concave-Transformed Densities and their Modes. PhD thesis, Department of Statistics, University of Washington, in preparation.

Doss, C. R. and Wellner, J. A. (2013). Inference for the mode of a log-concave density. Technical Report, University of Washington, in preparation.

### See Also

See `intECDF`

which returns values instead of a function.

### Examples

1 2 3 4 5 6 7 8 |