# TutzPritscher: Discrete non parametric kernel hazard rate estimator In NPHazardRate: Nonparametric Hazard Rate Estimation

## Description

Implementation of the kernel discrete hazard rate estimator of Tutz and Pritscher (1996) based on the discrete `Habbema` kernel. The estimate is used for comparison with the semiparametric estimate deveoped in Tutz and Pritscher (1996).

## Usage

 `1` ``` TutzPritscher(xin, cens, xout) ```

## Arguments

 `xin` A vector of data points. Missing values not allowed. `cens` Censoring indicators as a vector of 1s and zeros, 1's indicate uncensored observations, 0's correspond to censored obs. `xout` The grid points where the estimates will be calculated.

## Details

The discrete kernel estimate of Tutz and Pritscher (1996) is defined by

λ(t_m|v) =

where w_m is the discrete Habbema kernel.

## Value

Returns a vector with the values of the hazard rate estimates at x=xout.

## References

```SemiparamEst ```
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```options(echo=FALSE) xin<-c(7,34,42,63,64, 74, 83, 84, 91, 108, 112,129, 133,133,139,140,140,146, 149,154,157,160,160,165,173,176,185, 218,225,241, 248,273,277,279,297, 319,405,417,420,440, 523,523,583, 594, 1101, 1116, 1146, 1226, 1349, 1412, 1417) cens<-c(1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1, 0,1,0,1,1,1,1,1,0,1,1,1,0,1) xin<-xin/30.438 #Adjust the data storage.mode(xin)<-"integer" # turn the data to integers xout<-seq(1,47, by=1) # define the grid points to evaluate the estimate arg<-TutzPritscher(xin,cens,xout) #Discrete kernel estimate plot(xout, arg, type="l", ylim=c(0, .35), lty=2, col=6) # plot the estimate argSM<-lambdahat(xin, cens, xout) #crude nonparametric estimate lines(xout, argSM, lty=3, col=5) # plot the crude estimate ```