PMLE.SEF3.positive: Parametric Inference for the three-parameter SEF model...
In double.truncation: Analysis of Doubly-Truncated Data

Description Usage Arguments Details Value Author(s) References Examples

Maximum likelihood estimates and their standard errors (SEs) are computed. Also computed are the likelihood value, AIC, and other qnantities.

1 2	PMLE.SEF3.positive(u.trunc, y.trunc, v.trunc, tau2 = max(y.trunc), epsilon = 1e-04, D1=20, D2=10, D3=1, d1=6, d2=0.5)

`u.trunc`	lower truncation limit
`y.trunc`	variable of interest
`v.trunc`	upper truncation limit
`tau2`	upper support
`epsilon`	error tolerance for Newton-Raphson
`D1`	Divergence condition for eta_1
`D2`	Divergence condition of eta_2
`D3`	Divergence condition of eta_3
`d1`	Range of randomization for eta_1
`d2`	Range of randomization for eta_2

Details are seen from the references.

`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

Takeshi Emura, Ya-Hsuan Hu

Hu YH, Emura T (2015) Maximum likelihood estimation for a special exponential family under random double-truncation, Computation Stat 30 (4): 1199-229

Emura T, Hu YH, Konno Y (2017) Asymptotic inference for maximum likelihood estimators under the special exponential family with double-truncation, Stat Pap 58 (3): 877-909

Dorre A, Emura T (2019) Analysis of Doubly Truncated Data, An Introduction, JSS Research Series in Statistics, Springer

## The first 10 samples of the childhood cancer data ##
y.trunc=c(6,7,15,43,85,92,96,104,108,123)
u.trunc=c(-1643,-24,-532,-1508,-691,-1235,-786,-261,-108,-120)
v.trunc=u.trunc+1825
PMLE.SEF3.positive(u.trunc,y.trunc,v.trunc)