PMLE.lognormal: Parametric Inference for the lognormal model

In double.truncation: Analysis of Doubly-Truncated Data

Parametric Inference for the lognormal model

Description

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

Usage

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

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)

Details

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

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

Author(s)

Takeshi Emura

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.lognormal(u.trunc,y.trunc,v.trunc)

double.truncation documentation built on April 4, 2025, 3:31 a.m.