# DiscHazRateAuxFunctions: Auxiliary functions for discrete hazard rate estimators In NPHazardRate: Nonparametric Hazard Rate Estimation

## Description

Auxiliary functions for discrete semiparametric and kernel smooth hazard rate estimation

## Usage

 1 2 3 4 5 6  nsf(xin, cens, xout) Tm(tk, xout, distribution, par1, par2) CparamCalculation(gamparam, VehHazard) power.matrix(M, n) base(m, b) SmoothedEstimate(NonParEst, VehHazard, gammapar, SCproduct, Cpar) 

## Arguments

 xin A vector of data points. Missing values not allowed. cens A vector of 1s and zeros, 1's indicate uncensored observations, 0's correspond to censored obs. xout The points where the estimate should be calculated. tk desing points for the NPMLE estimate. distribution which distribution to use? par1 distribution parameter 1 par2 distribution parameter 2 gamparam gamma parameter M a matrix to be raised to a power n the power the matrix will be raised at m express m as a power of b b express m as a power of b NonParEst The crude nonparametric hazard rate estimate. VehHazard Vehicle hazard rate gammapar gamma parameter SCproduct SC product, the result of DetermineSCprod Cpar C parameter, the result of CparamCalculation.

## Details

Auxiliary functions for discrete hazard rate estimators. The function nsf is used for the kernel smooth estimate TutzPritscher.

• Tm used to calculate \max(t_k; 1-∑_{l=0}^k η_l > ε), ε>0 in the implementation of the semiparametric estimate

• CparamCalculationreturns the C smoothing parameter calculated as C= γ/\max_{k ≥q 0} ( λ(t_{k-1}) + λ(t_k) + λ(t_{k+1}) )

• DetermineSCprodthis finds SC = γ((n+1) \hat B_1)^{-1} \hat V_1 n = number of obs, gammapar = sum of vehicle haz at xout (computed elsewhere)

## Value

A vector with the values of the hazard rate estimates.

## References

NPHazardRate documentation built on May 2, 2019, 10:24 a.m.