double.truncation (version 1.8)

PMLE.loglogistic: Parametric Inference for the log-logistic model

Description

Maximum likelihood estimates (MLEs) and their standard errors (SEs) are computed for the log-logistic model based on doubly-truncated data (Dorre et al. 2021). Also computed are the likelihood value, AIC, and other qnantities.

Usage

PMLE.loglogistic(u.trunc, y.trunc, v.trunc,epsilon = 1e-5,D1=2,D2=2,d1=2,d2=2)

Value

eta

estimates

SE

standard errors

convergence

Log-likelihood, degree of freedom, AIC, the number of iterations

Score

score vector at the converged value

Hessian

Hessian matrix at the converged value

Arguments

u.trunc

a vector of lower truncation limits

y.trunc

a vector of variables of interest

v.trunc

a vector of upper truncation limits

epsilon

a small positive number for the error tolerance for Newton-Raphson iterations

D1

a positive number: Randomize the intial value for a divergent iteration (the updated amount for mu is greater than D1)

D2

a positive number: Randomize the intial value for a divergent iteration (the updated amount for sigma is greater than D2)

d1

a positive number: For a divergent iteration, U(-d1,d1) is added to the intial value of mu

d2

a positive number: For a divergent iteration, U(-d2,d2) is added to the intial value of log(sigma)

Author

Takeshi Emura

Details

A randomized Newton–Raphson algorithm (Section 3.2 of Dorre et al.(2021)) was employed to compute the MLE.

References

Dorre A, Huang CY, Tseng YK, Emura T (2021) Likelihood-based analysis of doubly-truncated data under the location-scale and AFT model, Computation Stat 36(1): 375-408

Examples

## A data example from Efron and Petrosian (1999) ## 
y.trunc=c(0.75, 1.25, 1.50, 1.05, 2.40, 2.50, 2.25)
u.trunc=c(0.4, 0.8, 0.0, 0.3, 1.1, 2.3, 1.3)
v.trunc=c(2.0, 1.8, 2.3, 1.4, 3.0, 3.4, 2.6)
PMLE.loglogistic(u.trunc,y.trunc,v.trunc)