PMLE.Clayton.Weibull: Parametric Inference for Models with Dependent Truncation...

Description Usage Arguments Details Value Author(s) References Examples

Description

Maximum likelihood estimation (MLE) for dependent truncation data under the Clayton copula with Weibull margins for a bivariate lifetimes (L, X). The truncated data (L_j, X_j), subject to L_j<=X_j for all j=1, ..., n, are used to obtain the MLE for the population parameters of (L, X).

Usage

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PMLE.Clayton.Weibull(l.trunc, x.trunc, GOF = TRUE)

Arguments

l.trunc

vector of truncation variables satisfying l.trunc<=x.trunc

x.trunc

vector of variables satisfying l.trunc<=x.trunc

GOF

if TRUE, a goodness-of-fit test statistics is computed

Details

Relevant paper is submitted for review

Value

n

sample size

alpha

alpha and its standard error

lambda_L

hazard of L and its standard error

lambda_X

hazard of X and its standard error

nu_L

shape parameter of L and its standard error

nu_X

shape parameter of X and its standard error

c

inclusion probability, defined by c=Pr(L<=X)

C

Cramer-von Mises goodness-of-fit test statistics

K

Kolmogorov-Smirnov goodness-of-fit test statistics

Author(s)

Takeshi Emura

References

Emura T, Pan CH (2016), Parametric maximum likelihood inference for copula models for dependently left-truncated data, submitted for publication.

Examples

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########### Brake pad data from Lawless (2003) ##############
l.trunc = c( 22.2 , 23.0 , 24.0 , 28.6 , 21.8 , 17.0 , 26.0 , 23.2 , 18.9 , 21.9 , 27.3 ,
       13.8 , 24.0 , 20.1 , 15.7 , 26.8 , 27.9 , 15.3 , 28.8 , 16.0 , 23.6 , 53.8 ,
       21.7 , 28.8 , 17.0 , 16.5 , 15.7 , 28.0 , 13.3 , 16.5 , 24.2 , 17.6 , 27.8 , 
       18.3 , 17.7 , 20.0 , 13.2 , 16.9 , 14.9 , 15.5 ,  7.0 , 15.8 , 15.0 , 38.3 , 
       11.2 , 38.2 , 26.7 , 17.1 , 29.0 , 18.3 , 18.4 , 18.2 , 15.9 , 16.4 , 23.6 , 
       19.2 , 23.3 , 20.4 , 20.9 , 28.5 , 23.2 , 17.9 , 46.1 , 39.3 , 11.8 , 17.7 , 
       30.9 , 22.4 , 45.0 , 18.2 , 30.2 , 21.8 , 18.2 , 23.0 , 27.2 , 10.9 , 25.5 , 
       12.4 , 39.9 , 17.7 , 26.3 , 14.1 , 21.0 , 11.2 , 10.8 , 25.7 , 32.4 , 13.6 , 
       19.1 , 16.1 , 53.3 , 57.3 , 36.5 , 19.7 , 20.8 , 30.8 , 20.0 , 39.6 )

x.trunc = c( 38.7 , 49.2 , 42.4 , 73.8 , 46.7 , 44.1 , 61.9 , 39.3 , 49.8 , 46.3 , 56.2 , 
       50.5 , 54.9 , 54.0 , 49.2 , 44.8 , 72.2 , 107.8 , 81.6 , 45.2 , 124.6 , 64.0 , 
       83.0 , 143.6 , 43.4 , 69.6 , 74.8 , 32.9 , 51.5 , 31.8 , 77.6 , 63.7 , 83.0 , 
       24.8 , 68.8 , 68.8 , 89.1 , 65.0 , 65.1 , 59.3 , 53.9 , 79.4 , 47.4 , 61.4 , 
       72.8 , 54.0 , 37.2 , 44.2 , 50.8 , 65.5 , 86.7 , 43.8 , 100.6 , 67.6 , 89.5 , 
       60.3 , 103.6 , 82.6 , 88.0 , 42.4 , 68.9 , 95.7 , 78.1 , 83.6 , 18.6 , 92.6 , 
       42.4 , 34.3 , 105.6 , 20.8 , 52.0 , 77.2 , 68.9 , 78.7 , 165.5 , 79.5 , 55.0 , 
       46.8 , 124.5 , 92.5 , 110.0 , 101.2 , 59.4 , 27.8 , 33.6 , 69.0 , 75.2 , 58.4 , 
       105.6 , 56.2 , 55.9 , 83.8 , 123.5 , 69.0 , 101.9 , 87.6 , 38.8 ,74.7 )

PMLE.Clayton.Weibull(l.trunc,x.trunc)


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