dgpTP | R Documentation |
Generates bivariate censored gap times from some known copula functions.
dgpTP(n, corr, dist, dist.par, model.cens, cens.par, state2.prob)
n |
Sample size. |
corr |
Correlation parameter. Possible values for the bivariate exponential distribution are between -1 and 1 (0 for independency). Any value between 0 (not included) and 1 (1 for independency) is accepted for the bivariate Weibull distribution. |
dist |
Distribution. Possible bivariate distributions are “exponential” and “weibull”. |
dist.par |
Vector of parameters for the allowed distributions. Two (scale) parameters for the bivariate exponential distribution and four (2 location parameters and 2 scale parameters) for the bivariate Weibull distribution. See details below. |
model.cens |
Model for censorship. Possible values are “uniform” and “exponential”. |
cens.par |
Parameter for the censorship distribution.
For censure model equal to “exponential” the argument |
state2.prob |
The proportion of individuals that enter state 2. |
The bivariate exponential distribution, also known as Farlie-Gumbel-Morgenstern distribution is given by
F(x,y)=F_1(x)F_2(y)[1+α(1-F_1(x))(1-F_2(y))]
for x≥0 and y≥0. Where the marginal distribution functions F_1 and F_2 are exponential with scale parameters θ_1 and θ_2 and correlation parameter α, -1 ≤ α ≤ 1.
The bivariate Weibull distribution with two-parameter marginal distributions. It's survival function is given by
S(x,y)=P(X>x,Y>y)=exp^(-[(x/θ_1)^(β_1/δ)+(y/θ_2)^(β_2/δ)]^δ)
Where 0 < δ ≤ 1 and each marginal distribution has shape parameter β_i and a scale parameter θ_i, i = 1, 2.
An object of class ‘survTP’.
Artur Araújo, Javier Roca-Pardiñas and Luís Meira-Machado
Araújo A, Meira-Machado L, Roca-Pardiñas J (2014). TPmsm: Estimation of the Transition Probabilities in 3-State Models. Journal of Statistical Software, 62(4), 1-29. doi: 10.18637/jss.v062.i04
Devroye L. (1986). Non-Uniform Random Variate Generation, New York: Springer-Verlag.
Johnson M. E. (1987). Multivariate Statistical Simulation, John Wiley and Sons.
Johnson N., Kotz S. (1972). Distributions in statistics: continuous multivariate distributions, John Wiley and Sons.
Lu J., Bhattacharya G. (1990). Some new constructions of bivariate weibull models. Annals of Institute of Statistical Mathematics, 42(3), 543-559. doi: 10.1007/BF00049307
Meira-Machado L., Faria S. (2014). A simulation study comparing modeling approaches in an illness-death multi-state model. Communications in Statistics - Simulation and Computation, 43(5), 929-946. doi: 10.1080/03610918.2012.718841
Meira-Machado, L., Sestelo M. (2019). Estimation in the progressive illness-death model: a nonexhaustive review. Biometrical Journal, 61(2), 245–263. doi: 10.1002/bimj.201700200
corrTP
.
# Set the number of threads nth <- setThreadsTP(2) # Example for the bivariate Exponential distribution dgpTP(n=100, corr=1, dist="exponential", dist.par=c(1, 1), model.cens="uniform", cens.par=3, state2.prob=0.5) # Example for the bivariate Weibull distribution dgpTP(n=100, corr=1, dist="weibull", dist.par=c(2, 7, 2, 7), model.cens="exponential", cens.par = 6, state2.prob=0.6) # Restore the number of threads setThreadsTP(nth)
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